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Topic Science & Mathematics

“Pure intellectual stimulation that can be popped into the [audio or video player] anytime.” —Harvard Magazine

An Introduction to Astronomy

“Passionate, erudite, living legend lecturers. Academia’s best lecturers are being captured on tape.” —The Los Angeles Times “A serious force in American education.” —The Wall Street Journal

Professor Alex Filippenko is currently the Richard and Rhoda Goldman Distinguished Professor in the Physical Sciences at the University of California, Berkeley. He is among the most highly cited astronomers in the world. His extensive career has brought him scores of awards and accolades, including election to the National Academy of Sciences, the highest honor given to an American scientist, and UC Berkeley’s Distinguished Teaching Award.

Cover Image: © NASA. Course No. 1810 © 2007 The Teaching Company.

PB1810A

Guidebook

THE GREAT COURSES ® Corporate Headquarters 4840 Westfields Boulevard, Suite 500 Chantilly, VA 20151-2299 USA Phone: 1-800-832-2412 www.thegreatcourses.com

Subtopic Astronomy

Understanding the Universe: An Introduction to Astronomy, 2nd Edition Course Guidebook Professor Alex Filippenko University of California, Berkeley

PUBLISHED BY: THE GREAT COURSES Corporate Headquarters 4840 Westfields Boulevard, Suite 500 Chantilly, Virginia 20151-2299 Phone: 1-800-832-2412 Fax: 703-378-3819 www.thegreatcourses.com

Copyright © The Teaching Company, 2007

Printed in the United States of America This book is in copyright. All rights reserved. Without limiting the rights under copyright reserved above, no part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any form, or by any means (electronic, mechanical, photocopying, recording, or otherwise), without the prior written permission of The Teaching Company.

Alex Filippenko, Ph.D. Professor of Astronomy University of California, Berkeley

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rofessor Alex Filippenko received his bachelor’s degree in physics (1979) from the University of California, Santa Barbara, and his doctorate in astronomy (1984) from the California Institute of Technology. He subsequently became a Miller Postdoctoral Fellow for Basic Research in Science at the University of California, Berkeley. In 1986, he joined the faculty at UC Berkeley, where he has remained through the present time. A member of the International Astronomical Union, Dr. Filippenko has served as president of the Astronomical Society of the Paci¿c and as councilor of the American Astronomical Society. An observational astronomer who makes frequent use of the Hubble Space Telescope and the Keck 10-meter telescopes, Dr. Filippenko’s primary areas of research are exploding stars (supernovae), active galaxies, black holes, gamma-ray bursts, and cosmology. He and his collaborators recognized a new class of exploding star, obtained some of the best evidence for the existence of small black holes in our Milky Way Galaxy, and found that other galaxies commonly show vigorous activity in their centers that suggests the presence of supermassive black holes. His robotic telescope at Lick Observatory in California is the world’s most successful search engine for relatively nearby supernovae, having discovered more than 800 of them since 1998. Dr. Filippenko also made major contributions to the discovery that the expansion rate of the universe is speeding up with time (the accelerating universe), driven by a mysterious form of dark energy—the top “Science Breakthrough of 1998,” according to the editors of Science magazine. Dr. Filippenko’s research ¿ndings are documented in more than 600 published papers, and he is one of the world’s most highly cited astronomers. He has been recognized with several major awards, including the Newton Lacy Pierce Prize of the American Astronomical Society (1992), the Robert M. Petrie Prize of the Canadian Astronomical Society (1997), and the Richtmyer i

Memorial Award of the American Association of Physics Teachers (2007). A Fellow of the California Academy of Sciences, and an elected member of the National Academy of Sciences. Dr. Filippenko has also been a Guggenheim Foundation Fellow (2001) and a Phi Beta Kappa Visiting Scholar (2002). He has held distinguished visiting positions at numerous colleges and universities, including the Marlar Lecturer at Rice University and both the Spitzer Lecturer and Farnum Lecturer at Princeton University. At the UC Berkeley campus, Dr. Filippenko has won the coveted Distinguished Teaching Award (1991) and the Donald S. Noyce Prize for Excellence in Undergraduate Teaching in the Physical Sciences (1991), each of which is generally given at most once per career. He was voted the “Best Professor” on campus seven times in student polls. Also, in 2002, he received the Distinguished Research Mentoring of Undergraduates Award, given by UC Berkeley. Dr. Filippenko has delivered hundreds of public lectures on astronomy and has played a prominent role in science newscasts and television documentaries, such as “Mysteries of Deep Space,” “Stephen Hawking’s Universe,” “Runaway Universe,” and more than 20 episodes of “The Universe” on The History Channel. With Jay M. Pasachoff, Dr. Filippenko coauthored an introductory astronomy textbook, The Cosmos: Astronomy in the New Millennium, now in its 3rd edition, which won the 2001 Texty Excellence Award of the Text and Academic Authors Association for the best new textbook in the physical sciences. This 2006 edition of Understanding the Universe combines and updates Dr. Filippenko’s previous introduction to astronomy courses, recorded for The Teaching Company in 1998 and 2003. He also recorded Black Holes Explained in 2009. Dr. Filippenko was the recipient of the 2004 Carl Sagan Prize for Science Popularization from the Trustees of Wonderfest, the San Francisco Bay Area Festival of Science. The Carnegie Foundation for the Advancement of Teaching and the Council for Advancement and Support of Education honored him as the “Outstanding Doctoral and Research Universities Professor of the Year” in 2006. In 2010, he won the Astronomical Society of the Paci¿c’s Richard H. Emmons award for undergraduate teaching.

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Table of Contents

INTRODUCTION Professor Biography ............................................................................i Course Scope .....................................................................................1 LECTURE GUIDES LECTURE 1 A Grand Tour of the Cosmos ..............................................................5 LECTURE 2 The Rainbow Connection .................................................................10 LECTURE 3 Sunrise, Sunset ................................................................................15 LECTURE 4 Bright Objects in the Night Sky .........................................................21 LECTURE 5 Fainter Phenomena in the Night Sky ................................................26 LECTURE 6 Our Sky through Binoculars and Telescopes....................................31 LECTURE 7 The Celestial Sphere ........................................................................36 LECTURE 8 The Reason for the Seasons ............................................................41 LECTURE 9 Lunar Phases and Eerie Lunar Eclipses ..........................................45 LECTURE 10 Glorious Total Solar Eclipses ............................................................50 iii

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LECTURE 11 More Eclipse Tales ...........................................................................56 LECTURE 12 Early Studies of the Solar System ....................................................60 LECTURE 13 The Geocentric Universe ..................................................................66 LECTURE 14 Galileo and the Copernican Revolution ............................................71 LECTURE 15 Re¿nements to the Heliocentric Model .............................................76 LECTURE 16 On the Shoulders of Giants ..............................................................81 LECTURE 17 Surveying Space and Time...............................................................86 LECTURE 18 Scale Models of the Universe ...........................................................91 LECTURE 19 Light—The Supreme Informant ........................................................96 LECTURE 20 The Wave-Particle Duality of Light .................................................101 LECTURE 21 The Colors of Stars.........................................................................107 LECTURE 22 The Fingerprints of Atoms .............................................................. 111 LECTURE 23 Modern Telescopes ........................................................................ 116 iv

Table of Contents

LECTURE 24 A Better Set of Eyes .......................................................................121 LECTURE 25 Our Sun, the Nearest Star ..............................................................127 LECTURE 26 The Earth, Third Rock from the Sun ...............................................132 LECTURE 27 Our Moon, Earth’s Nearest Neighbor .............................................137 LECTURE 28 Mercury and Venus.........................................................................142 LECTURE 29 Of Mars and Martians .....................................................................147 LECTURE 30 Jupiter and Its Amazing Moons ......................................................152 LECTURE 31 Magni¿cent Saturn..........................................................................157 LECTURE 32 Uranus and Neptune, the Small Giants ..........................................162 LECTURE 33 Pluto and Its Cousins......................................................................167 LECTURE 34 Asteroids and Dwarf Planets ..........................................................172 LECTURE 35 Comets—Gorgeous Primordial Snowballs .....................................177 LECTURE 36 Catastrophic Collisions ...................................................................181 v

Table of Contents

LECTURE 37 The Formation of Planetary Systems .............................................186 LECTURE 38 The Quest for Other Planetary Systems.........................................192 LECTURE 39 Extra-Solar Planets Galore! ............................................................197 LECTURE 40 Life Beyond the Earth .....................................................................202 LECTURE 41 The Search for Extraterrestrials......................................................207 LECTURE 42 Special Relativity and Interstellar Travel.........................................212 LECTURE 43 Stars—Distant Suns .......................................................................218 LECTURE 44 The Intrinsic Brightnesses of Stars .................................................223 LECTURE 45 The Diverse Sizes of Stars .............................................................228 LECTURE 46 Binary Stars and Stellar Masses ....................................................234 LECTURE 47 Star Clusters, Ages, and Remote Distances ..................................239 LECTURE 48 How Stars Shine—Nature’s Nuclear Reactors ...............................244 LECTURE 49 Solar Neutrinos—Probes of the Sun’s Core ...................................249 vi

Table of Contents

LECTURE 50 Brown Dwarfs and Free-Floating Planets .......................................254 LECTURE 51 Our Sun’s Brilliant Future ...............................................................259 LECTURE 52 White Dwarfs and Nova Eruptions..................................................263 LECTURE 53 Exploding Stars—Celestial Fireworks! ...........................................268 LECTURE 54 White Dwarf Supernovae—Stealing to Explode .............................272 LECTURE 55 Core-Collapse Supernovae—Gravity Wins ....................................277 LECTURE 56 The Brightest Supernova in Nearly 400 Years................................281 LECTURE 57 The Corpses of Massive Stars .......................................................286 LECTURE 58 Einstein’s General Theory of Relativity ...........................................291 LECTURE 59 Warping of Space and Time ...........................................................294 LECTURE 60 Black Holes—Abandon Hope, Ye Who Enter .................................299 LECTURE 61 The Quest for Black Holes..............................................................304 LECTURE 62 Imagining the Journey to a Black Hole ...........................................308 vii

Table of Contents

LECTURE 63 Wormholes—Gateways to Other Universes? .................................313 LECTURE 64 Quantum Physics and Black-Hole Evaporation ..............................318 LECTURE 65 Enigmatic Gamma-Ray Bursts .......................................................323 LECTURE 66 Birth Cries of Black Holes ...............................................................327 LECTURE 67 Our Home—The Milky Way Galaxy ................................................332 LECTURE 68 Structure of the Milky Way Galaxy .................................................336 LECTURE 69 Other Galaxies—“Island Universes” ...............................................342 LECTURE 70 The Dark Side of Matter .................................................................347 LECTURE 71 Cosmology—The Really Big Picture ..............................................352 LECTURE 72 Expansion of the Universe and the Big Bang .................................357 LECTURE 73 Searching for Distant Galaxies .......................................................363 LECTURE 74 The Evolution of Galaxies...............................................................368 LECTURE 75 Active Galaxies and Quasars .........................................................373 viii

Table of Contents

LECTURE 76 Cosmic Powerhouses of the Distant Past ......................................377 LECTURE 77 Supermassive Black Holes .............................................................383 LECTURE 78 Feeding the Monster.......................................................................388 LECTURE 79 The Paradox of the Dark Night Sky ................................................393 LECTURE 80 The Age of the Universe .................................................................398 LECTURE 81 When Geometry Is Destiny.............................................................404 LECTURE 82 The Mass Density of the Universe..................................................409 LECTURE 83 Einstein’s Biggest Blunder? ............................................................414 LECTURE 84 The Afterglow of the Big Bang ........................................................419 LECTURE 85 Ripples in the Cosmic Background Radiation ................................425 LECTURE 86 The Stuff of the Cosmos .................................................................431 LECTURE 87 Dark Energy—Quantum Fluctuations? ...........................................437 LECTURE 88 Dark Energy—Quintessence? ........................................................443 ix

Table of Contents

LECTURE 89 Grand Uni¿cation & Theories of Everything ...................................448 LECTURE 90 Searching for Hidden Dimensions ..................................................454 LECTURE 91 The Shape, Size, and Fate of the Universe....................................459 LECTURE 92 In the Beginning..............................................................................465 LECTURE 93 The InÀationary Universe................................................................470 LECTURE 94 The Ultimate Free Lunch? ..............................................................475 LECTURE 95 A Universe of Universes .................................................................480 LECTURE 96 ReÀections on Life and the Cosmos ...............................................486

SUPPLEMENTAL MATERIAL Useful Symbols...............................................................................491 Universe Timeline ...........................................................................492 Solar System Timeline ....................................................................494 Glossary .........................................................................................495 Biographical Notes .........................................................................517 Bibliography ....................................................................................522

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Understanding the Universe: An Introduction to Astronomy, 2nd Edition

Scope:

T

his visually rich course is designed to provide a nontechnical description of modern astronomy, including the structure and evolution of planets, stars, galaxies, and the Universe as a whole. It includes almost all of the material in my ¿rst two astronomy courses for The Teaching Company, produced in 1998 and 2003, but with a large number of new images, diagrams, and animations. The discoveries reported in the 2003 course are integrated throughout these new lectures, and more recent ¿ndings (through mid-2006) are included, as well. Much has happened in astronomy during the past few years; we will discuss the most exciting and important advances. Astronomical objects have been explored with breathtaking data obtained by the Hubble Space Telescope, the Chandra X-Ray Observatory, the Keck 10-meter telescopes, planetary probes, and other modern instruments. We will explore amazing phenomena, such as quasars, exploding stars, neutron stars, and black holes, and we will see how they increase our understanding of the physical principles of nature. We will also investigate recent newsworthy topics, such as the Cassini mission to Saturn, evidence for liquid water on ancient Mars, the discovery of many small bodies beyond Neptune in our Solar System, the detection of numerous planets around other stars, the nonzero mass of ghostly neutrinos, enormously powerful gamma-ray bursts, the conclusive evidence for a supermassive black hole in the center of our Milky Way Galaxy, the determination of the age of the Universe, the discovery of a long-range repulsive effect accelerating the expansion of the Universe, and progress in the uni¿cation of nature’s fundamental forces. Scienti¿cally reasonable speculations regarding the birth of the Universe, the possibility of multiple universes, and the probability of extraterrestrial life are also included.

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This course concentrates on the most exciting aspects of our fantastic Universe and on the methods astronomers have used to develop an understanding of it. The lectures present, in clear and simple terms, explanations of how the Universe “works,” as well as the interrelationships among its different components. Reliance on basic mathematics and physics is minimal but appropriate in some sections to deepen the interested viewer’s quantitative understanding of the material.

Scope

The course is divided into three major sections, each of which consists of several units. (These major sections are called “parts” during the lectures, but they are not to be confused with the eight 12-lecture “parts” used in packaging the lectures.) There are 24 lectures in section 1, entitled “Observing the Heavens.” The ¿rst unit, “Celestial Sights for Everyone,” describes simple daytime and nighttime observations that you can make to better appreciate the sky and what it contains. Various commonly observed phenomena, such as seasons, lunar phases, and eclipses, are also discussed. The second unit, “The Early History of Astronomy,” covers the study of astronomy from the ancient Greeks through Newton, including the transition from geocentric (Earth-centered) to heliocentric (Sun-centered) models of the Universe. In the third unit, “Basic Concepts and Tools,” we provide an overview of distance and time scales in the Universe to put our discussions in perspective. Because the study of light is of central importance to astronomy, we spend several lectures explaining its physical nature and utility. Modern telescopes, the main instruments used by astronomers, are also described. Section 2, “The Contents of the Universe,” consists of 46 lectures in 5 units. In the ¿rst unit, “Our Solar System,” we discuss the major constituents of our own planetary system, including the Sun, planets and their moons, comets, asteroids, and Kuiper-belt objects. The discovery of a distant body larger than Pluto and the subsequent, highly controversial demotion of Pluto from planetary status have recently made worldwide headlines. The formation of other stars and planetary systems, as well as the discovery of such extrasolar planets, is the subject of the second unit, “Other Planetary Systems.” During the past decade, about 200 planets have been found orbiting other stars, making this one of the most exciting areas of modern astronomy. The search for extraterrestrial life is also described.

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In the third unit of section 2, “Stars and Their Lives,” we learn about the properties of other stars and the various observations needed to deduce them. Nuclear reactions, the source of energy from the stars, are described, as well. We examine how stars eventually become red giants, subsequently shedding their outer layers to end up as dense white dwarfs, retired stars. The explosive fates of some rare types of stars are the subject of the fourth unit, “Stellar Explosions and Black Holes,” and we explain how the heavy elements necessary for life are created. Bizarre stellar remnants include neutron stars and black holes, the realm of Einstein’s general theory of relativity. We continue our exploration of black holes with such phenomena as black-hole evaporation and powerful gamma-ray bursts, as well as speculations that black holes are gateways to other universes. In the ¿fth unit, “The Milky Way and Other Galaxies,” we extend our explorations to the giant collections of stars called galaxies, along the way examining evidence for mysterious dark matter. Section 3, “Cosmology: The Universe as a Whole,” comprises the ¿nal 26 lectures of the course in 3 units. The ¿rst unit, “Cosmic Expansion and Distant Galaxies,” introduces the expansion of the Universe and shows how it is used to study the evolution of galaxies. We discuss active galaxies and quasars, in which matter is inferred to be falling into a central, supermassive black hole. In the second unit, “The Structure and Evolution of the Universe,” aspects of the Universe, such as its age, geometry, and possible fate, are considered. We examine evidence for the stunning conclusion that the expansion of the Universe is currently accelerating. We also describe the cosmic microwave background radiation—the generally uniform afterglow of the Big Bang—as well as the tiny irregularities that reveal the presence of early density variations from which all of the large-scale structure of the Universe subsequently formed. The nature of dark energy accelerating the Universe is explored in terms of modern attempts to unify forces, such as string theory. In the third and ¿nal unit, “The Birth of the Cosmos, and Other Frontiers,” we examine the very early history of the Universe, showing how the lightest elements formed during a phase of primordial nucleosynthesis. The recognition of several troubling problems with the standard Big Bang theory led to a magni¿cent re¿nement—an inÀationary epoch of expansion 3

that lasted only a tiny fraction of a second. The possible connection between inÀation and the currently accelerating expansion of space is also discussed. We then consider very speculative ideas regarding the birth of the Universe and the hypothesis of multiple universes. We end, in the last lecture, on a philosophical note, with some reÀections on intelligent life in the cosmos and of our place in the grand scheme of things. Ŷ

Overview of Course Organization

Scope

Major Section

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Lectures

Units

Observing the Heavens

2–24

x Celestial Sights for Everyone (2í11) x The Early History of Astronomy (12í16) x Basic Concepts and Tools (17í24)

The Contents of the Universe

25–70

x x x x

Cosmology: The Universe as a Whole

71í96

x Cosmic Expansion and Distant Galaxies (71í78) x The Structure and Evolution of the Universe (79í90) x The Birth of the Cosmos, and Other Frontiers (91í96)

Our Solar System (25í36) Other Planetary Systems (37í42) Stars and Their Lives (43í52) Stellar Explosions and Black Holes (53í66) x The Milky Way and Other Galaxies (67í70)

A Grand Tour of the Cosmos Lecture 1

“Get ready for a fantastic voyage through the Universe. We will explore just about all of the major topics in astronomy. I promise you a ride that you will never forget.”

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e are in a golden age of astronomy. Amazing discoveries are being made at a rapid pace with powerful instruments, such as the Hubble Space Telescope. Hardly a week goes by without an astronomical news story, and major headlines appear almost monthly. I have a number of major goals in this course. The ¿rst is simply to share with you the excitement and magni¿cence of the Universe: How does the Universe work? What are the most interesting new results? I’ll cover provocative, mind-boggling topics!

Astronomical News Stories of the Past Decade •

Spacecraft to various planets have revealed surprising new properties.



An object beyond the orbit of Pluto, and slightly larger than Pluto, has been found—the “10th planet,” according to some astronomers.



About 200 planets have been detected orbiting stars other than the Sun.



We understand the basic process by which stars are created from clouds of gas and dust.



The existence of black holes has been convincingly shown.



The birth and evolution of galaxies have been studied.



Tiny ripples in the distribution of material have been detected early in the history of the Universe; clusters of galaxies formed from these variations.



We have witnessed collisions between galaxies that induce giant bursts of star formation.



Colossal explosions have been seen billions of light years away.



The age of the Universe has been measured accurately.



The expansion rate of the Universe appears to be accelerating.



Most of the Universe consists of exotic dark matter and mysterious dark energy. 5

A second goal is to provide a survey of all of astronomy. This will give you a basic understanding of astronomy and, I hope, kindle your Socratic Àame. Socrates said, “Education is the kindling of a Àame, not the ¿lling of a vessel.” My third goal is to show you that astronomy is a quest for our origins, our place in the cosmos. How did we get here, and where are we going? Most of us have gazed with wonder at the stars and asked some of these questions. This is part of what makes astronomy such a personal and popular science. Another goal is to give you some idea of how science is done and to convey the thrill of scienti¿c discovery. Science is a dynamic process: New ideas are developed and tested and modi¿ed when necessary. Scientists want to ¿gure out how things work. Some of our views at the cutting edge of astronomy are changing yearly. What is said here reÀects the state of knowledge in mid-2006, and part of it may be out of date shortly. But there are certain foundations that are unlikely to change and upon which we can build. I will try to indicate which parts of the course are the most speculative and uncertain.

Course Contents

Lecture 1: A Grand Tour of the Cosmos

Part 1: “Observing the Heavens” (Lectures 1–24) • Unit 1: Celestial Sights for Everyone • Unit 2: The Early History of Astronomy • Unit 3: Basic Concepts and Tools Part 2: “The Contents of the Universe” (Lectures 25–70) • Unit 1: Our Solar System • Unit 2: Other Planetary Systems • Unit 3: Stars and Their Lives • Unit 4: Stellar Explosions and Black Holes • Unit 5: The Milky Way and Other Galaxies Part 3: “Cosmology: The Universe as a Whole” (Lectures 71–96) • Unit 1: Cosmic Expansion and Distant Galaxies • Unit 2: The Structure and Evolution of the Universe • Unit 3: The Birth of the Cosmos and Other Frontiers

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© iStockphoto/Thinkstock

Finally, I want to heighten your sense of awe and wonder about the cosmos and to increase your curiosity about the world around you.

A spiral galaxy consisting of more than 100 billion stars.

The course is mostly descriptive, non-technical, and non-mathematical. I will focus on concepts and qualitative explanations. Nevertheless, astronomy is a physical science, and many viewers do want a quantitative component. Hence, where appropriate, I will introduce simple mathematical and physical relationships, but their use will be minimal. Most of the quantitative parts will be easy to understand if you have a good knowledge of high-school algebra and geometry, as well as some high-school physics. However, if you don’t understand them, or are not in the mood for math and physics, you can largely ignore these interludes; you can get the main ideas without concentrating on the math. Some lectures are more technical than others, but at least a qualitative understanding should be accessible to most viewers. The primary textbook recommended as a supplement to these lectures is The Cosmos: Astronomy in the New Millennium (3rd edition, 2007; Thomson/ Brooks-Cole, available on amazon.com), by Jay M. Pasachoff and Alex Filippenko. It spans most, but not all, of the topics covered in this course, in roughly (but not exactly) the same order. It also includes many of the photographs and diagrams shown in the video lectures. “Cosmos” means “the Universe,”—but more speci¿cally, the Universe regarded as an orderly, harmonious whole. Pasachoff and I hope to have presented an orderly, harmonious overview of astronomy to the general reader. In the video 7

lectures, I show an assortment of photographs and movies, covering some of the topics to be included in the course. You might want to leaf through the recommended textbook and look at many of the stunning photographs. Ŷ

Important Terms black hole: A region of space-time in which the gravitational ¿eld is so strong that nothing, not even light, can escape. Predicted by Einstein’s general theory of relativity. dark energy: Energy with negative pressure, causing the expansion of the Universe to accelerate. dark matter: Invisible matter that dominates the mass of the Universe. galaxy: A large (typically 5000 to 200,000 light years in diameter), gravitationally bound system of hundreds of millions (and up to a trillion) stars.

Lecture 1: A Grand Tour of the Cosmos

light year: The distance light travels in one year—about 10 trillion kilometers, or 6 trillion miles. planet: A body that primarily orbits a star (so that moons don’t count), is large enough to be roughly spherical (typically, larger than about 600 km in diameter), gravitationally dominates its region of space (that is, has largely cleared away other debris), and has never undergone nuclear fusion. planetary system: A collection of planets and smaller bodies orbiting a star. quasar: A star-like, extremely luminous (powerful) object billions of light years away. star: A self-luminous, gravitationally bound ball of gas that shines (or used to shine) because of nuclear reactions in its core. The Sun is a typical star. Universe: “All that there is.” (Actually, there could be other, physically disjoint universes with which we have no direct interactions!) 8

Suggested Reading The standard textbooks recommended to accompany these video lectures are as follows: Pasachoff and Filippenko. The Cosmos: Astronomy in the New Millennium, 3rd ed. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. (This is a longer but somewhat outdated version of The Cosmos, listed above.) Several monthly nontechnical magazines on astronomy should also be consulted; they have a wealth of useful information about new discoveries, current events in the sky, and so on. Among the best 3 are Sky and Telescope (www.skyandtelescope.com), Astronomy (www.astronomy.com), and Mercury (www.astrosociety.org). Viewers who want to explore much more mathematics and physics should consult the following textbooks: Carroll and Ostlie. An Introduction to Modern Astrophysics. Shu, The Physical Universe. The Astronomical Society of the Paci¿c (ASP) serves as a link among professional astronomers, amateur astronomers, teachers, and the general public. The society provides a wide variety of services, and I encourage you to join the ASP. See its Web site at www.astrosociety.org.

Questions to Consider 1. What do you hope to get out of this course? 2. In what ways do you think the study of astronomy is an investigation of our origins?

3. How is the pace of discovery in astronomy a sign of the ¿eld’s health and intellectual vitality?

4. What are some of the most exciting astronomical discoveries of which you have heard during the past year or two? 9

The Rainbow Connection Lecture 2

“There are plenty of beautiful things to see in the daytime sky—full of color, full of wonderful geometry, all produced by the complex interaction of light waves with water in its liquid state and in the solid form of ice crystals.”

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Lecture 2: The Rainbow Connection

hough the night sky is full of light and color, the daytime sky also contains some intriguing natural sights. One such phenomenon is the rainbow. When sunlight enters a spherical raindrop, the light is refracted, or bent, by varying degrees, depending on its color. Violet light is bent the most, and red, the least. The light is then reÀected, or bounced, off the back side of the raindrop and exits at the front at an angle relative to the incoming light ray. This reÀected light forms the primary rainbow. Each color is reÀected at a slightly different angle as measured from the center of the rainbow—the point opposite the Sun—to where the rays enter your eye. The radius of a primary rainbow is about 42°—more speci¿cally, 42° for red light and 40° for violet light. Depending on the angle of reÀection, each raindrop produces a certain color. These colors will change depending on the angle at which you look at the rainbow. The rays you perceive as red come from a different set of drops than the rays you perceive as blue. Every drop along a light ray of a given color bends that same color to your eye. The very drop that reÀects blue to your eyes can reÀect another color to an observer elsewhere. Similarly, the angle of the Sun affects how much of a rainbow’s arc is visible. If the Sun is close to the horizon, you will see nearly a full semicircle. If the Sun is high, you will see a smaller arc closer to the ground. Full-circle rainbows are visible from an airplane. From the ground, you can see nearly a full circle when a rainbow appears over a canyon; part of the arc extends below the true horizon into the canyon. Why don’t the different colors of a rainbow mix together and become blurred? Light is reÀected off a raindrop at different angles, depending on

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the angle at which the light entered the water droplet. However, there is an area where light enters the drop and exits at nearly the same angle. Because this exit angle changes minimally as a function of the entrance point, the rays bunch up at a certain angle, thus reÀecting a speci¿c color. If sunlight is blocked, “You need raindrops in only a partial rainbow is visible. Rainbows appear to move as you move. If you change a particular direction of locations, the rainbow will be formed from the sky, and you need a different set of raindrops. them to be illuminated by sunlight. If there In strong sunlight, a secondary bow is aren’t raindrops … you sometimes visible at a radius of 51° from the point opposite the Sun. A secondary won’t see a rainbow.” bow occurs when light enters the bottom of a raindrop and bounces twice within the raindrop to exit at a completely different angle compared with the light forming the primary bow. The colors of the secondary rainbow form opposite to the primary one. In a primary bow, blue appears on the inside, and red, on the outside. In a secondary bow, red is on the inside, and blue is on the outside. Next to the blue light of the primary rainbow, you can sometimes see faint bands, called supernumerary bows, produced by light waves interfering with each other. When two light waves are in phase, the result is constructive interference; when out of phase, destructive interference. Two rays can enter a raindrop at two different points yet have the same exit angle. But the two rays travel different paths inside the raindrop. Constructive interference creates a bright supernumerary bow; destructive interference creates a faint one. Solar halos are similar to rainbows in that they are created by refracted light, but in ice crystals, not raindrops. With a radius of 22°, solar halos—rings around the Sun—are created when light enters long and skinny hexagonal ice crystals. The ice crystals usually occur in high-altitude cirrus clouds, where the temperatures are very cold, regardless of Earth’s surface temperature. Sundogs, or mock suns, are phenomena related to solar halos and usually appear as a particularly bright part of the halo’s outer edge. They are produced by hexagonal ice crystals, just as halos are, but the crystals are Àat

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© iStockphoto/Thinkstock

and plate-like. Sundogs can be so bright that you can often see them without seeing the rest of the halo. You can also see lunar halos, which are fainter than solar halos but easier to see because the Moon’s glare is far dimmer than that of the Sun.

Lecture 2: The Rainbow Connection

Light refracted by ice crystals creates a solar halo.

Additional and similar phenomena can occur in the atmosphere during the day, as well. Under exceptional conditions, a secondary halo—with a radius of 46°—appears around the Sun. Also, tangential arcs occur under very clear and cold conditions. Coronas are multicolored halo-like rings around the Sun or Moon, but they have much smaller angular radii than regular halos. Though called coronas, they have nothing to do with the outer atmosphere of the Sun, which is also called the corona. Coronas are formed by diffraction, when light is bent as it passes around a droplet of water, together with the wave interference of light, as in the supernumerary bows. You can see such a corona by looking

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at a bright headlight through fog; it is caused by this bending of light around droplets and the constructive and destructive interference of that light with itself. Another phenomenon, known as “the glory,” is still not fully understood. A ring of light appears around the shadow of an object cast on a cloud far from it. Here, light bends around and within water droplets and is reÀected. Surface waves are also present, traveling through the raindrop. Sun pillars form a column of light above the Sun and are most easily visible just after sunset. Light reÀects off Àat, hexagonal ice crystals in a way similar to sunlight reÀecting off rippling water on the surface of a pond or lake. Ŷ

Important Terms corona: The very hot, tenuous, outermost region of the Sun, seen during a total solar eclipse. diffraction: A phenomenon affecting light as it passes any obstacle, spreading it out. glory, the: A thin halo of light around the shadow of an object projected on a cloud; caused by the bending of light around and within water droplets. halo (solar or lunar): A circle of light around the Sun or Moon, having a radius of about 22 degrees, formed by light passing through hexagonal ice crystals. horizon: The great circle de¿ned by the intersection of the celestial sphere with the plane tangent to the Earth at the observer’s location; it is 90 degrees away from the zenith. interference: The property of radiation, explainable by the wave theory, in which waves in phase can add (constructive interference) and waves out of phase can subtract (destructive interference).

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sundog: A pair of bright spots on the outer edge of the solar halo at roughly the Sun’s altitude above the horizon. sun pillar: A faint pillar of light above the Sun in the sky, best visible after sunset.

Suggested Reading Lynch and Livingston, Color and Light in Nature. Minnaert, Light and Color in the Outdoors. Parviainen, www.polarimage.¿ (solar halos and other atmospheric phenomena). Light and Optics, ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/opt/home.rxml (rainbows, solar halos, sundogs, and other atmospheric phenomena).

Questions to Consider 1. How could you determine the approximate location of raindrops that produce a rainbow? (Think about viewing the rainbow against a backdrop of objects that are at different distances from you.)

Lecture 2: The Rainbow Connection

2. Under what conditions might you see a full 360-degree circle of a rainbow?

3. If you move toward the end of a rainbow, in search of the proverbial pot of gold, what will happen to the position of the rainbow? Will you ever reach the rainbow’s end?

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Sunrise, Sunset Lecture 3

“The Earth is shadowing part of the atmosphere. … As the sun dips farther below the horizon, the shadow grows more and more and looms above you; twilight starts when the whole shadow envelops you. At that point, the planets and stars begin to come out, and it’s time to start observing the night sky.”

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hy is the sky blue? Blue light rays from the Sun are selectively scattered (reÀected) by air molecules, producing the blue daytime sky away from the Sun’s direction. Violet light, having an even shorter wavelength than blue light, is scattered even more ef¿ciently than blue light, but there is not as much violet sunlight, and human eyes are not as sensitive to it. Green light, having a longer wavelength than blue light, is not scattered as ef¿ciently as blue light, so blue is the predominant color of the daytime sky. As the Sun sets, its color progresses through a range, from white to yellow, to orange, and ¿nally, sometimes, to red. As the Sun rises in the sky in the morning, the color scheme is reversed. Closer to the horizon, sunlight travels through a longer atmospheric path, which causes more scattering of light out of your line of sight. Because yellow, orange, and red light Several atmospheric are scattered out of your line of sight less than conditions contribute violet, blue, or green light, the yellow, orange, to the vivid colors or red light is more likely to reach your eyes, that characterize making the Sun appear that color. both sunrises and Particulate matter, such as dust or smoke, in sunsets, turning the the atmosphere also affects the color of the Sun’s white light and setting and rising Sun. Violet and blue light the normal daytime are absorbed most easily by dust and smoke in blue sky into an the air, as is green light to a lesser extent. The more dust, smog, or other pollution in the air, artist’s palette. the more absorption of violet, blue, and green 15

light there will be, producing a more orange or red sunset. Clouds also reÀect the setting Sun’s rays, adding color to the sky. Light that reaches clouds and is reÀected from them tends to be yellow, orange, or red, because the violet, blue, and green light has been scattered away by air or absorbed by particulate matter. The Moon can appear in different shades of yellow, orange, or red when it is rising or setting, for exactly the same reasons the Sun does.

Lecture 3: Sunrise, Sunset

© iStockphoto/Thinkstock

When the Moon and the Sun appear a little bit above the horizon upon setting or rising, they are actually just below the horizon. On entering the atmosphere, light is refracted, or bent, but our eyes don’t perceive this bending. They see only the direction from which the light was coming, which makes the Sun or the Moon appear to be higher than its true position. The magnitude of this effect is about one full Sun or Moon diameter. In other words, when the Moon or the Sun is just kissing the horizon, it is actually one whole diameter below the horizon.

Sunrise in Kruger Park, South Africa.

The green Àash is a hard-to-see yet fascinating phenomenon that occurs just before the Sun fully sets or just as it begins to rise. To see the green Àash, the skies must be clear and free of dust. You must have a clear view of the horizon, unobstructed by mountains or buildings. Lasting only a second or two, the Àash is actually a green button-like spot of light visible at the top of the Sun just before it sets or rises. The Àash is created, in part, because the Sun’s true position on the horizon is actually lower than it appears as a result of the bending of light. Violet and blue light rays, having short wavelengths, 16

are bent more than the longer-wavelength yellow, orange, and red light rays. Green rays are intermediate in wavelength and are bent at an intermediate angle. Thus, you see the green sunrays between red and blue, though in reality, these colors overlap quite a bit. Projected back onto the sky, the setting Sun seems to consist of several mostly overlapping disks of different colors; violet is highest and red is lowest, with green in the middle. Violet and blue light are scattered in the atmosphere and absorbed by dust; therefore, the violet and blue are not visible, which leaves green as the next shortest wavelength visible to our eyes. The red disk sets ¿rst, followed by the orange, then the yellow. The green disk sets last, but because it overlaps the other disks, only the very top sliver is visible just before it sets, creating the green Àash. An orange or red Sun indicates dust in the atmosphere, which lessens the chances of seeing the green Àash. A more yellowish-white setting Sun offers a better chance. Mirages, which make the Sun appear as if a piece has been broken off, actually cause the green Àash to be visible for a few seconds. A mirage occurs when the Sun’s rays are highly distorted, bending at different angles due to different layers in the atmosphere that have different temperatures and densities. Mirages come in two main types: An inferior mirage occurs when cool, dense air is above hot, less dense air. This typically occurs over a hot asphalt road or sand, when the shimmering heat waves appear just above the surface and look like water. The “water” actually consists of light rays from the blue sky. A superior mirage occurs when cold, dense air is below hot, less dense air. This typically occurs over a cold body of water, such as the ocean. Under inferior-mirage conditions, incoming light rays bend toward the denser, cooler air above, reaching the eye from a more horizontal angle and creating the “lake in the desert” effect. Under superior-mirage conditions, incoming light bends downward, reaching the eye at a steeper angle and making objects appear higher above the surface than they really are. The superior-mirage effect is strongest from the lowest points, which appear higher than other points that are actually physically higher on or above Earth’s surface. These mirages can also produce inverted images of objects. Ships sailing on the ocean, for example, can appear inverted. 17

© iStockphoto/Thinkstock

Just before sunset over the ocean.

Lecture 3: Sunrise, Sunset

Applying the properties of mirages to the setting Sun, we see how they enhance the green Àash. The Sun becomes distorted when it nears the horizon, causing a part of it to appear as if it’s hovering above the horizon as a result of the mirage effect. When the top piece of the Sun “breaks off,” the green button portion separates from the rest of the Sun, hovering above the horizon for an extra few seconds, allowing you to see the green Àash. When looking at the Sun, even low on the horizon, avoid staring at it directly for more than a few seconds so as not to burn your eyes. Once desensitized from staring at the Sun, your eyes won’t perceive the green Àash as easily. Other phenomena are visible as the Sun rises and sets. Buddha’s rays, or crepuscular rays, occur when sunlight ¿lters through gaps in the clouds, forming rays of light with dark bands in between. Buddha’s rays appear to diverge, or fan out, from the Sun but are actually almost parallel. This perspective effect makes intrinsically parallel edges appear to converge as distance increases. For example, a railroad track appears to converge at its farthest visible point, the vanishing point, though the tracks are actually parallel. Although the rays are brightest in the general direction of the Sun, Buddha’s rays can sometimes appear directly opposite from where the Sun 18

is setting. These are called anti-solar crepuscular rays, or sometimes, anticrepuscular rays. Another phenomenon that appears shortly before sunrise or after sunset is a dark blue band just above the horizon—Earth’s shadow. The setting Sun is still visible from the perspective of the higher, more brightly lit atmosphere; however, the Sun as seen from lower parts of the atmosphere has already set. As the Sun gets lower below the horizon, the dark part of the atmosphere climbs progressively higher, until essentially all of the visible atmosphere is in Earth’s shadow and there is no longer a clear demarcation. Ŷ

Important Terms crepuscular rays: Beams of light shining through gaps in clouds, usually best seen near sunset or sunrise. green Àash: A subtle green glow sometimes visible in very clear skies just as the last part of the Sun is setting (or the ¿rst part is rising). mirage: An image of an object, often inverted, formed by light passing through layers of air having different temperatures. wavelength: The distance over which a wave goes through a complete oscillation; the distance between two consecutive crests or two consecutive troughs.

Suggested Reading Lynch and Livingston, Color and Light in Nature. Minnaert, Light and Color in the Outdoors. Parviainen, www.polarimage.¿ (green Àash, mirages, and so on). Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Young, mintaka.sdsu.edu/GF (green Àash, mirages, and so on).

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Questions to Consider 1. Suppose air molecules were to preferentially scatter red light instead of blue light. What would be the approximate color of the daytime sky, away from the Sun’s direction?

2. If you were to ignore the effects of Earth’s atmosphere on sunlight, and you calculated the total amount of time between sunrise and sunset, why would your answer be shorter than the actual time interval?

3. Why does the color of a sunset change with time, and why do different

Lecture 3: Sunrise, Sunset

clouds sometimes have different colors at a given time?

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Bright Objects in the Night Sky Lecture 4

“Now that the Sun has set, let’s start looking at the stars. There are 88 constellations in the sky, mostly of ancient Greek, Egyptian, and Chinese origin. These are familiar-looking patterns. Some are a bit hard to distinguish; others are quite easy.”

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e have learned about some of the sky’s amazing natural shows during the day. Now we focus on the nighttime skies, beginning with a brief review of Earth’s rotation and an introduction to some of the more familiar constellations of the Northern Hemisphere. Earth rotates on its axis on a 24-hour cycle. As the axis spins from west to east, stars rise in the east and set in the west. As your perspective—your location on Earth—changes, what you see in the sky also changes. Earth orbits the Sun, which accounts for the change in seasons, as well as changes in what you see in the night sky. Constellations are groups or patterns of stars that are easily visible in the sky. The ancient Greeks, Egyptians, and Chinese named constellations after familiar-looking animals or people or in honor of them. Today, we have additional modern constellations, such as Telescopium, in honor of telescopes. Knowing some of the more prominent “A lot of people stars in the sky can help identify the constellations think that Polaris, and vice versa. the North Star, is the brightest Well-known constellations include Leo (the Lion) star in the sky— and Ursa Major (the Great Bear). Generally, these and other constellations are named in honor of far from true. something, not because they explicitly resemble It’s actually that object or entity. The Great Bear contains a more relatively faint.” familiar asterism, a group of stars that is not itself a full constellation but, rather, part of one. This particular asterism is the Big Dipper, which forms part of the Great Bear. The two end stars of the bowl of the Big Dipper are known as the pointer stars because they roughly point toward the north celestial pole, very close to 21

which is Polaris, the North Star. Polaris appears at the end of the tail of Ursa Minor, the Small Bear, which also has an asterism within it, the Little Dipper. Though a naked-eye star, Polaris is relatively faint. Like most other stars, it is actually a multiple-star system, not a single star. The two main components of Polaris are easily separated into Polaris A and Polaris B. Polaris A has a close companion that requires very sharp optics, such as Orion and Scorpius those of the Hubble Space Telescope, to discern. rion is the brightest constellation in the sky and one of the most Betelgeuse, in the left shoulder recognizable. Scorpius (the Scorpion) of Orion, is an enormous star, a is another, but it is not quite as easy supergiant. It is much bigger to ¿nd because of its generally fainter than the diameter of Earth’s stars. In Greek mythology, Orion is the orbit, which is 186 million great hunter, whose arrogance annoyed miles—Jupiter is about 5 his friends. Scorpius, too, became times farther from the Sun annoyed with Orion, and the two than Earth, and Betelgeuse is battled until Scorpius stung Orion to about the size of Jupiter’s orbit death. Zeus took pity on Orion and put around our Sun. Betelgeuse him up in the sky, but he put Scorpius will explode as a supernova on the opposite side of the sky so that later in its life. the two would never again bother each other. As the Scorpion is rising, Orion To the southeast of Orion’s is setting, and vice versa. belt is Sirius, the Dog Star, and the brightest in our sky. Sirius has a small, faint companion, known as a white dwarf, or a dead star that is roughly the same mass as the Sun and compressed into a volume about the size of Earth. A teaspoonful-size portion of a white dwarf would weigh several tons.

Lecture 4: Bright Objects in the Night Sky

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Easily visible in the sky is Vega in the constellation Lyra the Harp, seen during summer in the Northern Hemisphere. A young star, Vega has a dusty disk of gas circling it. Deneb in Cygnus the Swan—often called the Northern Cross—is another bright star. Together with Altair in Aquila (the Eagle) and Vega, Deneb forms an easily recognizable star pattern called the Summer Triangle. 22

Some of the stars you see in the sky are actually planets. How do we distinguish between a planet and a star? Unlike stars, planets change positions from night to night relative to the other stars. Although constellations rotate across the sky throughout the seasons, their stars don’t change position relative to one another. In general, planets twinkle less than stars. However, if it’s close to the horizon, a planet can twinkle just as much as a star straight overhead because of the greater amount of atmosphere through which one looks near the horizon. What causes twinkling, and how does the atmosphere affect it? The atmosphere is turbulent, with many layers of air at different temperatures and densities. As the light from a star passes through the atmosphere, it bends (refracts). Because the atmosphere changes constantly, the refraction of light also changes. The constant change in the refraction of light makes a star or planet appear to twinkle. The effect is similar to sunlight reaching the bottom of a swimming pool. Both bright and dark regions continually shift as the water concentrates the light rays in some areas and not in others. Apparent twinkling is also affected by your vantage point; when you look at a celestial object near the horizon, more layers of atmosphere cause more bending of light and, therefore, enhanced twinkling. Stars high in the sky twinkle less because there are fewer layers of atmosphere between you and the star. If you compare two star-like objects at the same altitude above the horizon and one is twinkling and the other is not, the latter is likely to be a planet. Why? Even through a telescope, stars look like points of light. Planets are physically much smaller than stars but a lot closer to Earth. Thus, through a telescope, you can see that a planet is more like a disk, with many points of light on its surface. Even though every point on the planet is twinkling, some points twinkle more brightly than others at any given moment. Many points across the planet’s disk, all twinkling at different light levels, will average out in brightness, merging in such a way that the source of light appears nearly constant in brightness. When Sirius, a very bright star, is close to the horizon, it sometimes twinkles in color, which changes rapidly. Like the Sun, a star near the horizon is actually lower than it appears because of the refraction of light. The different colors in the light are bent at different angles, making the colors 23

appear at different points in the sky. The star’s colors are displaced upward, each one Àashing—twinkling—independently, sometimes faintly and sometimes brightly, so that at any given moment, one color is more visible than another. Other celestial objects and phenomena are easily visible in the night sky, including phases of the Moon and meteors. You can also see man-made satellites. Satellites, such as the International Space Station, occasionally move across the sky. The Iridium satellites consist of about 70 objects once used for communications. Their bright reÀective panels sometimes reÀect the Sun in Àashes that last for a few seconds. Iridium Àares are sometimes mistaken for bright meteors. Bright Àashes seen near sunrise or sunset could be satellite reÀections. However, if you see one during the middle of the night, at least a few hours after sunset or a few hours before sunrise, it is more likely to be a meteor. Ŷ

Important Terms

Lecture 4: Bright Objects in the Night Sky

asterism: A grouping of stars that is not itself a full constellation but is part of a constellation. The Big Dipper is one example. constellation: One of 88 regions into which the celestial sphere is divided. The pattern of bright stars within a constellation is often named in honor of a god, person, or animal. meteor: The streak of light in the sky produced when an interplanetary rock enters Earth’s atmosphere and burns up as a result of friction. If the rock reaches Earth’s surface, it is called a meteorite. refraction: The bending of light as it passes from one medium to another having different properties. supergiant: The evolutionary phase following the main sequence of a massive star; the star becomes more luminous and larger. If its size increases by a very large factor, it becomes cool (red).

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supernova: The violent explosion of a star at the end of its life. Hydrogen is present or absent in the spectra of Type II or Type I supernovae, respectively. white dwarf: The evolutionary endpoint of stars that have initial mass less than about 8 solar masses. All that remains is the degenerate core of He or C–O (in some cases, ONeMg).

Suggested Reading Dickinson, Nightwatch. Pasachoff, A Field Guide to Stars and Planets. ———, Peterson First Guide to Astronomy. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. Why are arti¿cial satellites in low-Earth orbit visible only in twilight, shortly after sunset and before sunrise, whereas satellites far from Earth are also visible much later during the night?

2. Do you think the brightest stars in the sky are necessarily the intrinsically most powerful stars? Is some other variable also important?

3. If the stars seem to twinkle very little one night, but much more the next night, compare the properties of the atmosphere on the two nights.

4. If stars are physically much, much larger than planets but appear only as points of light even when viewed through a telescope, what can one say about the relative distances of stars and planets?

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Fainter Phenomena in the Night Sky Lecture 5

“Faint stars are being washed out by the glow of the city. The bright stars are still visible, but the faint ones are not. … Bright city lights really hurt; so does bright moonlight. You don’t want to look for the Milky Way when there’s a really huge, full Moon out, illuminating the whole sky. It just washes these faint things out.”

Lecture 5: Fainter Phenomena in the Night Sky

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hough the sky is full of phenomena that are easily visible, even from within a bright city, many spectacular sights require dark skies to see clearly. Such sights include the Milky Way, auroras, and the zodiacal lights. The band of light we call the Milky Way is formed by billions of stars in a galaxy shaped like a disc, about 100,000 light years across and 1000 light years thick. The Milky Way Galaxy (often simply called “the Galaxy”) bulges in the middle, with its nucleus in the very center. Our Sun is about two-thirds of the way out from the center to the edge, although there’s no well-de¿ned edge of the Galaxy. If you look along the plane of the Galaxy, a multitude of stars is visible in any direction. If you look perpendicular to the plane, you see relatively few stars because the whole plane is only about 1000 light years thick, much thinner than the extent of the disk in other directions. Because stars in the plane of the Galaxy surround the Sun, the Galaxy’s band of light forms a full circle around us. However, at most, half of the band is visible at any given time because the other half is below the horizon. The Milky Way has relatively dense clouds of gas and dust mixed with stars, which in some places are thick enough to actually block our view of more distant stars. The center of the Galaxy contains a supermassive black hole, nearly 4 million times the mass of the Sun. From the Southern Hemisphere, you can see the brightest part of the Milky Way nearly straight overhead. Also clearly visible from this vantage point is the Southern Cross constellation and the Magellanic Clouds—two satellite galaxies gravitationally bound to our Galaxy and orbiting it. The Large Magellanic Cloud is about 170,000 light years away and contains the Tarantula Nebula, a glowing cloud of gas with recently formed and

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newly forming stars. The Small Magellanic Cloud is about 210,000 light years away. Other phenomena are more easily viewed from the Southern Hemisphere, though some are also visible in the Northern Hemisphere. The nearest star to our Sun is Alpha Centauri, actually a double star system whose closest star to Earth is Proxima Centauri. Both stars are about 4.2 light years away. To the west of the Southern Cross is the diffuse Eta Carina Nebula, a glowing cloud of gas and dust. Eta Carina is a massive, erupting star in the nebula, perhaps 150 times the mass of our Sun, and incredibly unstable. This star will likely explode within the next few hundred thousand years. Sometimes, planets can affect the apparent shapes of constellations; for example, Jupiter can appear inside the constellation of Scorpius, making it look different than expected. From the Southern Hemisphere, Scorpius and Sagittarius, a constellation to the east of Scorpius, are relatively high in the sky, compared to their visibility from the Northern Hemisphere. The central part of our Galaxy is in the direction of the constellation Sagittarius. The zodiacal light is a conical, diffuse band of light sometimes visible when the sky is very dark but not too long after sunset or too long before sunrise. Its glow begins at the western horizon (after evening twilight has ended) or at the eastern horizon (before morning twilight begins), stretching upward in the sky. It consists of sunlight scattered by dust and gas in the plane of the Solar System. The scattering is most ef¿cient in the forward direction; thus, the zodiacal light is brightest in directions closest to the Sun. Because the plane of the Solar System forms its steepest angle relative to the horizon during February and March in the evening and during October and November in the morning, these are generally the best months for viewing the zodiacal light. Two other spectacular sights you can see with the naked eye at night are bright comets and auroras. Comets are concentrations of ice, dust, and rock from distant parts of the Solar System. As they approach the Sun, comets evaporate, freeing gases and dust particles that reÀect sunlight to form the long, diffuse tail. Sunlight and charged particles from the Sun push the tail of the comet back, so the tail generally points away from the Sun. 27

Lecture 5: Fainter Phenomena in the Night Sky

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Charged particles emanating from the Sun cause another beautiful phenomenon: the auroras, or the northern and southern lights. The auroras are bands of shimmering light in multiple colors of red, green, and sometimes, blue. They are created when charged particles, primarily electrons, from the Sun interact with atoms (and some molecules) in the atmosphere. The charged particles from the Sun interact with Earth’s magnetic ¿eld, which we’ll discuss in another lecture. Charged particles have a hard time crossing magnetic ¿eld lines, but can move along ¿eld lines. The charged particles are trapped preferentially in certain bands where the magnetic Active Aurora Borealis, also called the ¿eld is particularly strong; these “Northern Lights.” are called the Van Allen belts. The trapped particles move along the magnetic ¿eld lines toward Earth. Close to the poles, where the magnetic ¿eld lines intersect Earth’s thin atmosphere (about 100 km thick), the trapped particles, especially electrons, interact with the atmospheric atoms (and some molecules). Electrons hitting the atoms and molecules kick the bound electrons to higher energy levels. Then, the electrons cascade down to lower levels, in the process emitting colorful light. The different colors are caused by emission of light from “Auroras can also be seen different kinds of atoms and molecules from space. Space shuttle in Earth’s atmosphere, such as nitrogen astronauts often see and oxygen, excited to different auroras looking down at the electronic energy levels. The colors and light patterns of the auroras change atmosphere of the Earth.” quickly over time because the number

of electrons and the amount of interaction with the atmosphere changes.

Did You Know?

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f Earth’s magnetic ¿eld were stronger, the auroras would be con¿ned to even more northerly or more southerly latitudes because a stronger magnetic ¿eld is more able to con¿ne the charged particles. If Earth’s magnetic ¿eld were very weak, these charged particles would hit Earth in quite a few places and cause more mutations of cells. So, the risk of cancer would be greater if the Earth’s magnetic ¿eld were considerably weaker.

Typically, the auroras that are most visible are nearer to Earth’s poles. Occasionally, however, the magnetic ¿elds allow charged particles to reach Earth’s surface relatively close to the equator. Auroras are especially prominent after major eruptions on the Sun’s surface, when unusually large numbers of energetic particles are ejected and subsequently reach Earth. By watching the Sun, astronomers can roughly predict when the next great auroral display will be visible. Auroras are visible from space and have been seen on other planets. Ŷ

Important Terms aurora: The northern or southern lights, caused by energetic particles from the Sun interacting with atoms and molecules in Earth’s upper atmosphere, making them glow. comet: An interplanetary chunk of ice and rock, often in a very eccentric (elongated) orbit, that produces a diffuse patch of light in the sky when relatively near the Sun as a result of evaporation of the ice. electron: Low-mass, negatively charged fundamental particle that normally “orbits” an atomic nucleus. Large Magellanic Cloud: A dwarf companion galaxy of our Milky Way Galaxy, about 170,000 light years away; best seen from Earth’s southern hemisphere. 29

Milky Way: The band of light across the sky coming from the stars and gas in the plane of the Milky Way Galaxy (our Galaxy). nebula: A region containing an above-average density of interstellar gas and dust. zodiac: The band of constellations through which the Sun moves during the course of a year. zodiacal light: A faint glow in the night sky around the ecliptic, stretching up from the horizon shortly after evening twilight and shortly before morning twilight, from sunlight reÀected by interplanetary dust.

Suggested Reading Dickinson, Nightwatch. Parviainen, www.polarimage.¿ (auroras, comets, and so on). Pasachoff, A Field Guide to Stars and Planets. Lecture 5: Fainter Phenomena in the Night Sky

———, Peterson First Guide to Astronomy. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. Suppose the average number of stars per unit area of the sky were essentially independent of direction in the sky. What might one conclude about the shape of our Galaxy or our location within it?

2. Why would you expect planets to occasionally appear in the same direction in the sky as the band of zodiacal light?

3. Why are auroras most easily visible from far northern or far southern latitudes on Earth?

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Our Sky through Binoculars and Telescopes Lecture 6

“Binoculars and telescopes collect more light, making objects brighter and allowing you to see fainter stars in the sky. They also magnify objects, making them look bigger or closer.”

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elescopes and binoculars allow you to better view fainter and more distant celestial objects in the night sky. Let’s look at how they work and discuss the two main types of telescopes. Telescopes collect light, making objects appear brighter than your eye alone could detect. Telescopes also magnify objects, making them look bigger. In a previous lecture, we discussed how the rays of the Sun are nearly parallel when they reach Earth because of the Sun’s great distance from Earth. Because stars and most planets are even farther from Earth, their light is parallel to a very high degree of accuracy. Refracting telescopes use a primary lens to bring the incoming parallel light to a focus. In this type of telescope, light is collected and refracted (bent) by the lens. Rays at different distances from the center of the lens are bent at different angles, bringing them to the same focus. Rays that approach the lens from different directions (for example, from the Astronomy in History top and bottom edges of a planet) are focused to efracting telescopes were invented different parts of the focal in Holland around the year 1600, plane of the lens. and Galileo built his own soon thereafter, becoming the ¿rst to systematically make From the focal plane in a and interpret astronomical observations using a telescope. refracting telescope, light travels to the eyepiece lens, which magni¿es the image of an object and allows your eye to see it. The focal length of a lens is the distance between the lens and the focal plane. The magni¿cation of the apparent size of an object can be determined by dividing the focal length of the primary lens by the focal length of the eyepiece lens. Because a bigger

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primary lens captures more rays of light, objects look brighter when viewed with a lens that has a larger diameter.

Lecture 6: Our Sky through Binoculars and Telescopes

Refracting telescopes have a problem called chromatic aberration: Different colors of light are bent at different angles and, therefore, they do not have the same focal length. Specially designed refracting telescopes consisting of two primary lenses eliminate part of this problem, but such telescopes can be expensive. ReÀecting telescopes, on the other hand, use mirrors to collect light and bring it to a common focus. All of the light rays, regardless of color, are brought to the same focus without chromatic aberration. ReÀecting telescopes, invented by Isaac Newton around 1670, come in several styles. One style (known as the Cassegrain telescope) has a hole in the primary mirror. Incoming light rays bounce off the primary mirror, reÀect back to a secondary mirror, bounce off that, then go through the hole in the primary mirror before arriving at the eyepiece lens. Instead of having a hole in the mirror, another style (the Newtonian telescope) uses a tilted secondary mirror to direct incoming light to the eyepiece, which is off to the side of the tube. This was the kind of telescope used by Newton. Each part of the primary mirror forms a complete image of the object. The larger the primary mirror, the brighter the object will appear. Binoculars are essentially two refracting telescopes joined together. What celestial objects can be easily seen with binoculars? With the naked eye, you can see the Summer Triangle, which consists of the stars Vega, Deneb, and Altair. Going from Vega and Deneb, look toward the constellation Andromeda to ¿nd Messier 31 (M31), another galaxy, known as the Andromeda Galaxy; the nearest large collection to our own Galaxy, it is about 2.5 million light years away. You can also look for a pair of clusters known as the double cluster in Perseus. The Orion Nebula, in the constellation Orion (speci¿cally, in the sword of the great hunter), is a giant glowing cloud of gas and dust within which new stars are currently forming. The group of stars called the Pleiades, or the Seven Sisters, is visible with binoculars. You can also scan the Milky Way with binoculars to ¿nd an array of nebulae (clouds of gas) and star clusters, particularly near the tail of Scorpius, visible in the Northern Hemisphere during summer.

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© iStockphoto/Thinkstock

Binoculars can be used to ¿nd star clusters and nebulae.

The Moon is also a fascinating object to view with the aid of binoculars, which accentuate its irregular surface of craters and lava plains. Known as the maria, these plains were once thought to be dried-up seas, but we now know that they are frozen, dead lava plains. Telescopes offer an even better view of celestial objects because, mounted on a tripod, they reduce the shakiness that comes with handheld binoculars. Telescopes also collect more light, magnify the images more, and create greater clarity. The Moon’s craters are most easily seen near the place where darkness begins on its surface—that is, where either sunrise or sunset is occurring and where the light comes in at a glancing angle to make long shadows. Through a telescope, concentrate your attention on this region, the terminator—the termination of the area where light shines on the Moon. This enhances the view of its ridges, mountain chains, valleys, and craters. Sometimes, you can see the Moon occulting, or covering up, one of the planets.

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Back at the Summer Triangle, locate Cygnus the Swan—the Northern Cross—and go down to the bottom of the cross to view a double star, Albireo (ȕ Cygni). Near Vega is the constellation Hercules, within which is a cluster consisting of hundreds of thousands of stars, or perhaps a million, gravitationally bound together in a very tight group. Within Lyra the Harp, you can see the Ring Nebula, a cloud of gas ejected by a dying star. Near the end of the Big Dipper’s handle, you can view the Whirlpool Galaxy, M51. Although you won’t see much detail through a small telescope, it is a stunning spiral galaxy. Local amateur astronomy clubs, which often hold “star parties” (viewing sessions), provide opportunities for the public to view the night sky through a variety of telescopes, some quite powerful. Ŷ

Lecture 6: Our Sky through Binoculars and Telescopes

Name to Know Newton, Isaac (16421727): English mathematician and physicist; developed three laws of motion and the law of universal gravitation, all published in The Principia (1687). Invented the reÀecting telescope, determined that white light consists of all colors of the rainbow, and invented calculus. At age 27, became Lucasian Professor of Mathematics at Cambridge University. Became Warden of the Mint in 1696; knighted in 1705.

Important Terms eyepiece: A small tube containing a lens (or combination of lenses) at the eye end of a telescope, used to examine the image. reÀecting telescope: Telescope that uses a mirror instead of a lens to collect light; unlike the refracting telescope, it brings all colors into focus together. refracting telescope: Telescope that uses a lens to collect light and bring it to a focus. spiral galaxy: One of the two major classes of galaxies de¿ned by Edwin Hubble; made up of a roughly spherical central “bulge” containing older stars, surrounded by a thin disk in which spiral arms are present.

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star cluster: A gravitationally bound group of stars that formed from the same nebula. terminator: The line between night and day on a moon or planet; the edge of the part that is lighted by the Sun.

Suggested Reading Dickinson, Nightwatch. Kitchen and Forrest, Seeing Stars. Pasachoff, A Field Guide to Stars and Planets. ———, Peterson First Guide to Astronomy. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. Does the hole in the center of the primary mirror in a Cassegrain telescope produce a hole in the object that is being viewed? What about the secondary mirror of a Newtonian telescope?

2. Telescopes are often advertised according to the amount by which they magnify the apparent size of an image. Do you think this magni¿cation is very relevant when looking at stars instead of planets?

3. Besides not suffering from chromatic aberration, can you think of some other advantages of reÀecting telescopes over refracting telescopes?

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The Celestial Sphere Lecture 7

“Go out, lie down in a sleeping bag, look at the sky, and watch over the course of hours the stately progression of the stars across the sky. ... Also, watch as the constellations that you can see change from season to season.”

Lecture 7: The Celestial Sphere

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stronomers have de¿ned 88 constellations in the heavens, all of which are seen against a backdrop called the celestial sphere. Each star is a member of one—and only one—constellation, though their boundaries are arbitrary. In most cases, these constellations consist of stars that are not physically bound to one another by gravity or any other force. Stars in any particular constellation weren’t formed in the same place; they just happen to be in approximately the same direction in space. An example is Cassiopeia, the Vain Queen, which looks like a W. Cassiopeia’s 5 main stars vary in distance from Earth, from 54 light years away (ȕ Cassiopeia) to 613 light years away (Ȗ “The stars of the Cassiopeia). A light year is the distance that light travels in 1 year, approximately 6 trillion miles, constellations have but fainter stars are not necessarily farther away nothing to do with than brighter stars. one another. They happen to be at From our perspective on Earth, we can see only about half of the celestial sphere at any given approximately the moment. When you stand at a given location, same line of sight your zenith is the point straight overhead. The in the sky, but they horizon is 90 degrees away in all directions were not physical along lines tangent to Earth or a smooth surface groupings of stars.” in the absence of geographic features. To visualize your horizon, extend a plane tangent to the surface so that it intersects the celestial sphere. You can’t see objects that fall below that horizon. If the celestial sphere were close in, only stars along a limited arc would be visible. If the celestial sphere were farther away, you’d see a larger arc. Because the

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celestial sphere is almost in¿nitely far away compared with Earth’s diameter, about half of the celestial sphere is above your horizon at any given time. Your position on Earth determines what part of the celestial sphere you can see. What’s visible from San Francisco, California (latitude roughly 40° north), largely differs from that seen in Quito, Ecuador (latitude roughly 0°), for example, but there is some overlap. At the poles (latitude 90° north or south), the observed part of the celestial sphere differs even more. In addition to the zenith and the horizon, we can de¿ne a few other interesting parts of the celestial sphere. The celestial equator is the projection of Earth’s equator onto the celestial sphere. It is a great circle—that is, a circle formed by the intersection of a sphere and a plane that passes through the center of the sphere. The meridian is another great circle, passing through the celestial poles and the zenith, as seen from a given location on Earth. A star crosses the meridian when it reaches its highest elevation above the horizon. Imagine extending the North and South Poles outward, along the axis of Earth’s rotation. The north celestial pole is the intersection of the North “Fainter stars are Pole’s extension with the celestial sphere, and not necessarily the south celestial pole is the intersection of the farther away than the South Pole’s extension with the celestial sphere. brighter stars. You The apparent rotation of the celestial sphere is could have a faint the result of Earth’s rotation on its own axis. star that’s nearby, Earth rotates in one direction, and the stars but it’s intrinsically move across the sky in the opposite direction. not as powerful as As your position on Earth changes, so does the appearance of the celestial sphere. From the another star that’s equator, Polaris—the north celestial pole star— farther away—so it appears on the horizon. At 20° north latitude, looks fainter.” Polaris is 20 degrees above the horizon; at 40° north latitude, it’s 40 degrees up toward the zenith, and so on, until you reach the North Pole, where Polaris is right overhead at 90 degrees. As your position changes relative to the equator, for example, certain stars become visible, while others disappear below the horizon line. As Earth rotates, stars appear to move across the sky. The closer 37

you look to the celestial poles, the less the stars appear to move. Similarly, stars farther from the celestial poles appear to move in great arcs across the sky throughout the night.

Lecture 7: The Celestial Sphere

Circumpolar stars are stars that never rise or set, as seen from a given location on Earth. They circle the pole, but don’t dip below the horizon. As seen from Earth’s North or South Pole, all of the visible stars are circumpolar. Each star circles around the sky at a constant elevation above the horizon. From the equator, stars appear to rise and set perpendicular to the horizon, arcing across the sky. There are no circumpolar stars. At intermediate latitudes, some stars (those close to the visible celestial pole) would be seen as circumpolar, while others would rise and set at an angle, slanted relative to the horizon. Because of Earth’s orbit around the Sun, the sky also changes over the course of the year. This orbiting accounts for the different positions and the appearance and reappearance of some constellations on an annual cycle. As seen from the equator in December, the constellation Orion begins to rise at sunset. By midnight, Orion is overhead, and at sunrise, Orion sets again. As seen from the equator, Orion is overhead at sunset in March and overhead at midnight in December. Sunset is roughly 6 hours earlier than midnight; thus, over the course of 3 months, Orion has risen 6 hours earlier. A constellation’s rising and setting changes at a rate of 4 minutes per day. Except for near the poles, the stars rise 4 minutes per day earlier with each successive night. (Near the poles, stars don’t rise or set at all; they just circle the poles, being circumpolar stars.) If Earth weren’t orbiting the Sun, then in one 24-hour day/night cycle, both the Sun and other stars would become aligned every 24 hours as a result of Earth’s own rotation. The changing perspective causes the solar day (the time interval been two consecutive meridian crossings of the Sun—or noon to noon) to be about 4 minutes longer than the sidereal day (the time interval between two consecutive meridian crossings of a given star). The Sun’s path in the sky is called the ecliptic. The constellations through which the Sun passes during its yearly journey across the sky are the zodiacal constellations. In September, if the Sun weren’t bright, you would see it projected against the stars of Virgo. In March, if you could see the stars during the day, you would see the Sun projected against Pisces. Planets 38

also wander slowly among the zodiacal constellations. However, this planet wandering among the stars is not the same thing as the daily east-to-west rotation of the celestial sphere caused by Earth’s rotation. Given that constellations move around from season to season, how do you know where to look for them? Special star charts show constellation positions at different times of the year. Planispheres are another useful tool and have rotating circles you align appropriately, depending on the time of year and time of night. In addition, every star has a speci¿c set of coordinates, similar to longitude and latitude lines on Earth. A star’s latitude is called declination, which is a coordinate that de¿nes the number of degrees a star is above the celestial equator, up to 90°. A star’s longitude is called right ascension, which is a coordinate that de¿nes the number of hours a star is along the celestial equator, up to 24 hours. By knowing the declination and right ascension of a star, as well as the time of night, you can point a telescope to the proper location of the celestial sphere to see it. An equatorially mounted telescope is ¿xed so that its axis is parallel to the axis of Earth’s rotation. Its other axis swings perpendicularly to this. The telescope can be rotated around the axis parallel to Earth’s axis of rotation to counter the rotational effect of Earth. If this weren’t possible, the position of the star would constantly move out of the telescope’s ¿eld of view as Earth rotated. Some commercially available telescopes allow you to input the name of a star or planet, and the telescope’s computer points the telescope directly to that object. Ŷ

Important Terms celestial equator: Projection of Earth’s equator onto the celestial sphere. celestial sphere: The enormous sphere, centered on the Earth, to which the stars appear to be ¿xed. ecliptic: The path followed by the Sun across the celestial sphere in the course of a year.

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gravity: The weakest of nature’s fundamental forces but the dominant force over large distances because it is cumulative; all matter and energy contribute, regardless of charge. great circle: The intersection of a sphere with a plane passing through the center of the sphere. The meridian and the celestial equator are both great circles. meridian: A great circle passing through the celestial poles and the zenith; the highest point in the sky reached by a star during each day-night cycle. pole star: A star approximately at a celestial pole (Polaris, in the north). zenith: The point on the celestial sphere that is directly above the observer.

Suggested Reading Dickinson, Nightwatch. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Tirion, The Cambridge Star Atlas.

Lecture 7: The Celestial Sphere

Questions to Consider 1. As viewed from a given location on Earth, some stars never set (that is, they are circumpolar stars). Is it also the case that some stars never rise, if viewing them from the same location?

2. Given that the sky revolves once per day/night cycle, how many degrees does it appear to revolve in one hour?

3. As viewed from Earth’s equator over the course of a year, is the entire celestial sphere visible at some time during the night? In other words, can all stars in the celestial sphere be viewed from Earth’s equator? What if you are viewing from Earth’s North Pole or from Earth’s South Pole? 40

The Reason for the Seasons Lecture 8

“The seasons are not caused by changes in the distance between Earth and the Sun over the course of a year. If this were so, the seasons wouldn’t be opposite each other in the Northern and Southern Hemispheres.”

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he celestial sphere and the relationship between the celestial equator and the ecliptic—the path of the Sun—play an important role in explaining the seasons. The most signi¿cant differences between seasons are the day’s length: how long the Sun remains above the horizon and how high it reaches before setting again.

Earth rotates on its axis at a tilt of 23.5° relative to the axis of its orbit around the Sun. The orientation of Earth’s axis is ¿xed—relative to the distant stars—as it orbits the Sun and spins. As a spinning object, Earth doesn’t change the absolute direction of its axis of spin, but its orientation relative to the Sun does change. In the Northern Hemisphere, June 22 (solstice) is the ¿rst day of summer, when the hemisphere is most tilted toward the Sun. In the Southern Hemisphere, it is the ¿rst day of winter, when that hemisphere is most tilted away from the Sun. The opposite occurs in each hemisphere on December 22 (solstice). During the Southern Hemisphere spring and summer, the South Pole experiences perpetual daytime for about 6 months. Much of the Northern Hemisphere has daytime skies, too, but the North Pole experiences perpetual nighttime for about 6 months. During winter in the Northern Hemisphere and summer in the Southern Hemisphere, mid-northern latitudes spend part of their time bathed in sunshine but a greater fraction of their time in darkness. Six months later, the situation is reversed. The equinox describes that time when Earth’s equator is most pointed toward the Sun. On approximately September 22 and March 22, the equator of Earth is pointed toward the Sun, and both poles experience an equal amount of light. During the equinox, equal days and nights occur everywhere on Earth, 12 hours each of day and night. The locations of sunrise and sunset change throughout the year, as does the Sun’s highest position in the sky as seen from any given location on Earth. As 41

autumn commences, the Sun begins to rise to the south of due east. In winter, it rises south of east. In the summer, the Sun rises north of east. During the equinoxes, the Sun rises due east (and sets due west). When the Sun is high, as in the summer months, a cylindrical beam of light strikes a relatively small area on Earth, causing it to heat up more and creating hotter temperatures. When the Sun is low, as in the winter months, the light is spread out over a larger area, heating each unit of area less and causing cooler temperatures.

Lecture 8: The Reason for the Seasons

Near the solstices, Earth’s tilt causes one hemisphere to be closer to the Sun during the day than the other hemisphere, but this effect is negligible because Earth’s radius is so small relative to its distance from the Sun. Instead, the Sun’s height above the horizon accounts for how much heat Earth receives at any given location. Earth’s orbit is elliptical, meaning that during certain points in its orbit around the Sun, it comes closer to the Sun but only by 3%. This small ¿gure does not have much effect on temperatures. Earth is closest to the Sun during the Northern Hemisphere winter, in early January, creating some extra heat and slightly mitigating winter’s cold. Earth’s relative closeness to the Sun in January does not make Southern Hemisphere summers much hotter because most of the Southern Hemisphere has vast oceans, which take much more time to heat than land. The position of Earth in relation to the Sun throughout the year causes other interesting phenomena. As discussed in a previous lecture, the refraction—or bending—of the Sun’s rays as the Sun approaches the horizon makes the Sun appear higher above the horizon than it really is. Therefore, during the Northern Hemisphere summer, for example, the Sun appears above the horizon for a little longer than 6 continuous months as seen from the North Pole. At the Tropic of Cancer—23.5° north latitude—the Sun appears overhead on June 22. At the Tropic of Capricorn—23.5° south latitude—the Sun appears overhead on December 22. The analemma is a phenomenon that describes the position of the Sun at a given time of day over the course of the year. Taking photographs of the Sun’s position from a ¿xed point at the same time every day over time will illustrate the Sun’s ¿gure-8 pattern of changing position. The analemma is caused by Earth’s elliptical orbit around the Sun; Earth doesn’t travel at the same speed at all times. Another reason for the analemma is that the celestial equator and 42

the ecliptic are tilted relative to each other. The analemma accounts for the fact that at noon, the Sun is not crossing the meridian (its highest point in the sky), as expected. Instead, depending on the season, the Sun is a bit to the east or to the west of the meridian. The difference between where the Sun should be, according to clock time, and where it actually is can be as much as about 15 minutes. This time varies by season and throws off sundials. Some natural phenomena occur oppositely in Earth’s two hemispheres. Because of Earth’s rotation, hurricanes rotate counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere. This is a consequence of the coriolis force, which affects the movement of air over great distances. The coriolis force does not, however, cause water to drain clockwise or counterclockwise depending on the hemisphere. This force affects only large-scale distances and has no bearing on such small-scale physical matters as draining water. Stars rise in the east and set in the west, which is clockwise around the south celestial pole as seen from the Southern Hemisphere and counterclockwise around the north celestial pole as seen from the Northern Hemisphere. The constellation Orion also looks different in the two hemispheres. In the north, it’s right side up; in the south, it’s upside down. Because of the gravitational inÀuence of the Moon and the Sun, Earth’s axis of rotation slowly changes orientation over the course of about 26,000 years. Earth behaves in a manner similar to that of a spinning gyroscope, which undergoes a conical motion called precession instead of being toppled by gravity. Earth’s axis precesses because its axis of rotation resists being changed by the gravitational forces of the Sun and the Moon. Gradually, over the course of about 13,000 years, precession will cause the seasons to reverse in their respective hemispheres, so that in the north, summer will begin on what we now call December 22. Ŷ

Important Terms analemma: The apparent ¿gure-8 path made by the Sun in the sky when photographs of the Sun’s position taken at a given time of day throughout the year are superimposed on each other. 43

equinox: One of two points of intersection between the ecliptic and the celestial equator, or the time of the year when the Sun is at this position. precession: A conical motion undergone by spinning objects pulled by an external force not directed along the axis. The Earth’s precession causes the direction of the north celestial pole to shift gradually with time. solstice: The northernmost or southernmost point on the celestial sphere that the Sun reaches, or the time of the year when the Sun reaches this point.

Suggested Reading Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. ———, A Field Guide to Stars and Planets. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Tirion, The Cambridge Star Atlas.

Questions to Consider

Lecture 8: The Reason for the Seasons

1. What would the seasons be like if: (a) Earth’s axis of rotation were parallel to the axis of Earth’s orbital plane, and (b) the axis of rotation were in the orbital plane?

2. Explain why, for an observer at the North Pole, the Sun changes its elevation (altitude) in the sky over the course of a year but the stars do not.

3. If someone were to tell you that Earth’s changing distance from the Sun causes the seasons, what arguments might you give to convince them otherwise?

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Lunar Phases and Eerie Lunar Eclipses Lecture 9

The Moon goes through a series of phases due to a changing geometrical relationship between the position of the Sun, the Earth, and the Moon. Also, the Moon can sometimes be eclipsed by the Earth’s shadow.

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he Moon is perhaps the most commonly observed celestial object in the sky, characterized by its changing appearance—the lunar phases. The Moon has eight well-de¿ned phases over the course of its orbit, beginning with the new moon—which is dark—and proceeding through waxing crescent, ¿rst quarter (or half moon), waxing gibbous, full moon, waning gibbous, third quarter (or half moon), waning crescent, and back to new moon again. The cycle from new moon to new moon, or full moon to full moon, takes about 1 month (roughly 29.5 days). It takes about 2 weeks for the Moon to go from new to full or full to new. Lunar phases are caused by the changing spatial relationship among the Sun, Earth, and the Moon. In other words, as the Moon orbits Earth, we see its lit face from a different perspective each night. At all times, the Sun illuminates the side of the Moon that faces the Sun, but as the Moon orbits Earth, varying portions of its lit side become visible from Earth. At new moon, the Moon is roughly between Earth and the Sun, so that the lit side of the Moon faces away from Earth; at full moon, Earth is roughly between the Sun and Moon, so that the lit side of the Moon faces Earth. The terminology describing phases of the Moon can be confusing. What we call the ¿rst-quarter moon we actually see as half the Moon lit up. Though it is half lit, it’s only one-quarter of the way around Earth in its orbit, hence the name. In the same vein, the full moon is only halfway around its orbit, but we still call it a full moon. Not just a nighttime sight, the Moon is visible during the day. The times of day it is visible depend on its phase. The Moon rises and sets at different times depending on its phase. Though you can’t see the Moon during its new phase, it is aligned with the Sun; it rises at sunrise and sets at sunset. The full moon is in the opposite direction 45

of the Sun, rising as the Sun sets and setting as the Sun rises. Lunar phases correspond to times at which they are visible. At 6:00 p.m., the ¿rst-quarter moon is on or near the meridian. At 9:00 p.m., the ¿rst-quarter moon is closer to the western horizon. At midnight, the ¿rst-quarter moon is on the western horizon, setting. At 3:00 a.m., the ¿rst-quarter moon has set and is not visible. (Occasionally, astronomers are asked to serve as expert witnesses in criminal trials to verify the position and phase of the Moon on the night a crime was committed.)

Lecture 9: Lunar Phases and Eerie Lunar Eclipses

Other interesting phenomena are associated with the Moon, including earthshine and optical illusions. Sometimes, the dark side of the Moon is faintly lit—from the Moon, Earth appears nearly fully lit. Earthshine is created when light is reÀected from Earth to the Moon, then reÀected back to Earth. It is less pronounced as the crescent moon grows, in part because the bright waxing crescent begins to outshine the faint light on the dark side of the Moon. A waxing crescent moon from Earth’s perspective corresponds to a waning gibbous Earth from the Moon’s perspective. The rising Moon near the horizon appears very large, but this is an optical illusion. When we see a rising Moon, especially a full or gibbous moon, it appears large to our eyes because we are comparing its size to that of much smaller objects in the foreground, such as buildings, trees, or people. Even when viewed over a clear horizon, such as an ocean—with nothing to compare with the Moon’s size—the Moon looks larger because our brains fool us into thinking so. Because the Moon’s orbit of Earth is elliptical, it actually is closer to Earth at certain times during its orbit. Yet this still doesn’t make it look bigger near the horizon on a given night because an elliptical orbit takes a full month and the Moon appears large near the horizon on most nights. Oddly, the true angular size of the rising Moon is actually smaller than the angular size of the Moon later that same night when it’s high up in the sky. Why? At midnight, the Moon is closer to Earth than it is when rising or setting; roughly one Earth radius closer, or about 1/60 of the distance (or roughly 2%) to the Moon. What happens during a lunar eclipse? If the Moon is between the Sun and Earth during a new moon and Earth is between the Moon and the Sun during a full moon, why don’t solar and lunar eclipses occur at every new and 46

full moon, respectively? The plane of the Moon’s orbit around Earth is not exactly coincident with the plane of Earth’s orbit around the Sun. Because of the tilt between Earth’s orbital plane and that of the Moon, the Moon is either above or below Earth’s shadow most of the time when the Moon is full. Similarly, the Moon’s shadow usually misses Earth during a new moon.

“The rising Moon looks gargantuan compared to how it looks when it’s higher up in the sky. … It’s only its apparent size that looks large compared to familiar objects. The true angular size of the Moon when it’s rising is actually smaller than later that same night when it’s high up in the sky.”

When the Moon does fall in Earth’s shadow, a lunar eclipse occurs. During the partial phases of a total lunar eclipse— when only part of the Moon falls in Earth’s shadow—it takes about an hour for the Moon to enter the shadow and another hour to exit the shadow. During a total lunar eclipse, the Moon remains in Earth’s shadow for about an hour, in addition to the 2 hours it takes to enter and exit Earth’s shadow. Earth’s shadow, cast into space, intersects the Moon only if the alignment is just right, which can occur during two so-called eclipse seasons per year. A total eclipse of the Moon is not completely dark. It appears more like a coppery red or orange, though colors vary. Some light from the Sun goes through Earth’s atmosphere, refracting (bending) toward the Moon and illuminating the Moon’s dark face. That light then reÀects off the Moon back to Earth. During some eclipses, one part of the Moon can be illuminated more than another, creating a 3-dimensional effect. Yellow, orange, and red light are the predominant colors that illuminate the Moon. Violet, blue, and green colors are both scattered (reÀected) by molecules of air and dust and absorbed by dust and smoke, diminishing these colors. A lot of dust in Earth’s atmosphere causes dark eclipses. Less dust makes for brighter eclipses because more light can reach the Moon. The part of the Moon that is closest to the edge of Earth’s shadow looks brighter because more light can ¿lter into Earth’s shadow by bending through Earth’s atmosphere. 47

A total lunar eclipse is visible from the entire dark side of Earth. In other words, everywhere in this hemisphere, as long as you have good weather and the Moon isn’t blocked by objects, you will see the dark or partially illuminated Moon. Total lunar eclipses, although intrinsically rare, occur once every year or two and are visible from roughly half of Earth’s surface. Ŷ

Important Terms earthshine: Sunlight illuminating the Moon after having been reÀected from the Earth. eclipse: The passage of one celestial body into the shadow of another or the obscuration of one celestial body by another body passing in front of it.

Suggested Reading

Lecture 9: Lunar Phases and Eerie Lunar Eclipses

Harris and Talcott, Chasing the Shadow. Long, The Moon Book. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. In Lecture 8, we talked about the reversal of seasons between Earth’s two hemispheres, set to happen over the course of about 13,000 years. Given that this reversal is in part related to the Moon’s gravitational pull, will the Moon’s phases, as viewed from Earth, also be affected?

2. If tonight you see a ¿rst-quarter moon, then 2 weeks from now, will you be able to see the Moon during the ¿rst few hours of the night?

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3. Describe the phases of Earth you would see over the course of a month if you were on the Moon. (Assume you are always on the side of the Moon facing Earth.)

4. In what way is the orange/red color of the fully eclipsed Moon related to the orange/red color of the setting Sun as seen from Earth?

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Glorious Total Solar Eclipses Lecture 10

“Any given location on Earth experiences a total solar eclipse roughly only once every 360 years, on average.”

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Lecture 10: Glorious Total Solar Eclipses

ike the Moon, the Sun also has interesting features that can be viewed with the right equipment. The Sun is basically a featureless disk with a gaseous surface. The surface is called the photosphere and has a distinct boundary. On the photosphere are features called sunspots, which are dark and cooler areas near the Sun’s surface. Sunspots change quickly over time, so that if you photographed them each day, you would see changes in their size, shape, and location over time. Galileo was the ¿rst to notice sunspots moving across the disk of the Sun and, therefore, inferred that the Sun rotated. While sunspots are interesting features to view, you should never look directly at the Sun with the naked eye, unless it is totally eclipsed by the Moon. Otherwise, you could cause serious damage to your eyes. To view sunspots, you “[Galileo] also inferred need to use a proper ¿lter. The best kind that the Sun is not is shade 14 welder’s glass, which is thick enough to block out the damaging rays. You blemish-free. ... It isn’t can also see a magni¿ed view of the Sun the perfect celestial with a telescope that is properly out¿tted sphere that people in with ¿lters. The telescope should be ¿tted the Roman Catholic with a ¿lter at the top end so that the sunlight Church wanted it to is blocked before it enters the telescope. Again, never view the Sun directly through be. That’s part of what put Galileo in trouble.” a telescope or binoculars without the proper ¿lters. Without a ¿lter, the large amount of light collected by the telescope or binoculars could crack the eyepiece and seriously damage your eyes. You can also look at sunspots with a device called a SunspotterTM or by projecting an image of the Sun through a telescope onto a sheet of paper.

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The Sun experiences both partial and total eclipses during certain times when the Moon is new, or dark. During the new moon phase, the Moon moves between the Sun and Earth. But in order for an eclipse to occur, the alignment has to be just right. How can such a small object as the Moon block the Sun as seen from Earth? The Sun is about 390 times physically larger than the Moon, and entirely by coincidence, the Sun is also farther away than the Moon by a factor of 390. Because of the Moon’s and Sun’s relative sizes and distances from Earth, they subtend, or cover, about the same angle in the sky—half a degree. Thus, when aligned just right, the Moon can block the Sun’s photosphere as viewed from Earth.

© iStockphoto/Thinkstock

Normally, the Moon does not obstruct the Sun’s photosphere, but when it does—if it blocks the entire photosphere—you see the faint, tenuous corona of the Sun. The Sun’s corona changes shape from one eclipse to another because it is structured by the shape of the magnetic ¿elds emanating from the Sun, and these change with time.

Inner corona of the Sun and the “diamond ring” effect.

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Why don’t solar eclipses occur with each new moon? For the same reason lunar eclipses don’t occur during each new and full moon: The Moon’s orbit around Earth is not in the same plane as Earth’s orbit around the Sun—their orbits are tilted relative to each other by about 5°. Eclipses can occur only at certain times of the year. Most of the time, the shadow of the Moon does not hit Earth. Usually, a total eclipse occurs over a range of locations on Earth, but other spots don’t see the eclipse or, at least, not a total eclipse. The farther away you are from the path of totality (the point at which the Sun is completely covered), the less of the Sun is eclipsed from your perspective.

Lecture 10: Glorious Total Solar Eclipses

Let’s explore how you can safely view a solar eclipse and what you might see. With a pinhole camera, you can examine the partial phases of an eclipse. You can make a pinhole camera using simple objects at home. Such a device is just an opaque screen with a hole in it through which the image is projected onto an opposing viewing screen. Simply puncture a hole through a piece of cardboard; shadow a viewing screen—a white piece of paper will do—with the cardboard to create a small image of the Sun on the screen. When the Sun is eclipsed, you will see a crescent shape or whatever the Sun’s shape happens to be at the time. Holes through leaves in trees also serve as pinhole cameras and produce a series of images on the ground surface below. You can also project the image of the Sun through a telescope to get a magni¿ed view or use a monocular or refracting telescope to project the Sun onto someone’s shadow. A pair of binoculars creates two images of the Sun. Just before totality, only a little bit of the Sun’s photosphere shows, creating a diamond-ring-like appearance where a small portion of the Sun’s light sparkles in one section along the edge of the Moon. If the sunlight passes through valleys on the Moon’s surface, you can sometimes see a series of sparkling, diamond-like lights called Baily’s beads. You can brieÀy (for a few seconds) view the diamond ring and Baily’s beads with the naked eye, but do not use binoculars or a telescope. During totality, many phenomena come into view. You can see a thin layer right above the photosphere called the chromosphere. It is somewhat hotter than the photosphere. You can also see the much more extensive, much hotter corona. You might also see protrusions from the Sun—called prominences— which are hot plumes of gas running along magnetic ¿elds away from 52

the Sun’s outer edges. The chromosphere, corona, and prominences are completely safe to view with the naked eye, through binoculars, or through a telescope. They are much fainter than the photosphere. As the Moon moves across the Sun and out of totality, another diamond-ring-like effect occurs and, perhaps, more of Baily’s beads. The totality portion of a solar eclipse typically lasts just 1 or 2 minutes. The maximum duration is only about 7.3 minutes, which is extremely rare. During totality, twilight sky colors appear all around the horizon. A small amount of light hitting the atmosphere is reÀected toward you. Blues and greens are absorbed and scattered out of your line of sight, while the reds and oranges remain visible. Shadow bands can appear just before and just after totality. Shadow bands are a rippling effect of light on the ground caused by different layers of the atmosphere bending the sunlight in different ways as it hits the atmosphere and continues to Earth. Similar to the shimmering bands of light you see reÀected in a swimming pool, shadow bands are created when the tiny bit of uneclipsed Sun twinkles alternately brighter and dimmer. Another phenomenon is the racing shadow of the Moon. You can sometimes see it approaching just before totality and racing away after totality. More easily viewed from above, the Moon’s shadow runs across the ground because the Moon is orbiting Earth during an eclipse. The shadow is projected to a progressively different location from west to east along the face of Earth. The projection of the shadow intersects Earth at different locations to produce a curved path on our spherical planet. Ŷ

Name to Know Galileo Galilei (15641542): Italian mathematician, astronomer, and physicist; was the ¿rst to systematically study the heavens with a telescope. Discovered the phases of Venus and the four bright moons of Jupiter, providing strong evidence against the geocentric model for the Solar System. After being sentenced by the Inquisition to perpetual house arrest, he published his earlier studies of the motions of falling bodies, laying the experimental groundwork for Newton’s laws of motion. 53

Important Terms Baily’s Beads: During a solar eclipse, the effect of sparkling lights created by sunlight passing through valleys on the Moon’s surface. chromosphere: Hot, thin layer of gas just below the Sun’s corona and above the photosphere. pinhole camera: A hole in an opaque sheet used to project an image of the Sun. prominences: Hot plumes of gas streaming from the Sun’s photosphere along the lines of the Sun’s magnetic ¿elds. sunspots: Cooler regions on the Sun’s photosphere that appear as dark blotches.

Suggested Reading Espenak, Fifty Year Canon of Solar Eclipses.

Lecture 10: Glorious Total Solar Eclipses

Harris and Talcott, Chasing the Shadow. Littmann, Willcox, and Espenak, Totality. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. The image produced by a pinhole camera is inverted. Similarly, the lens of your eye produces an inverted image on the retina. Why, then, do you think we see people and other objects right side up?

2. During a total lunar eclipse, what would someone on the Moon see when looking toward the Sun?

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3. Why can’t we observe the solar corona every day from Earth’s surface? 4. Why is a total solar eclipse visible from only a small fraction of Earth’s surface, whereas a total lunar eclipse is visible from about half of Earth’s surface?

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More Eclipse Tales Lecture 11

“In a few hundred million years, most eclipses will be annular. … The reason for this is that the Moon is gradually receding away from the Earth … at a rate of about four centimeters per year. So, although right now the Moon is often big enough to cover the Sun’s photosphere, in a few hundred million years, usually it will be too small; and in half a billion years, it’ll always be too small to cover the Sun’s disk.”

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Lecture 11: More Eclipse Tales

hough scientists now know what causes solar eclipses, their occurrences throughout history have given rise to various interpretations. Ancient peoples interpreted solar eclipses in many interesting ways. Some cultures believed that a dragon was trying to devour the Sun; some believed that the Sun was ¿ghting with its lover, the Moon, or that the two were making love discreetly in darkness; some thought that the Sun simply grew angry, sad, or ill, disappearing to recuperate. An annular eclipse occurs when the Moon is not quite at the right distance from Earth to completely cover the Sun’s photosphere. Annular refers to the annulus (ring) of the Sun that remains visible. The annulus is part of the bright photosphere; thus, you should always use eye protection when viewing an annular eclipse. Because the Moon’s orbit is elliptical, sometimes it’s farther from Earth than average and, at times, closer to Earth. When the Moon is farther than average from Earth, it is too small in angular size to cover the Sun, and an annulus of the Sun appears during what would otherwise be a total solar eclipse. Similarly, Earth’s orbit about the Sun is elliptical. Thus, when the Sun looks bigger than average, the Moon might not be large enough to cover the photosphere, causing an annular eclipse. During a hybrid solar eclipse, both an annular and a total eclipse occur but at different places on Earth; some places experience a total eclipse while others experience an annular eclipse. How? At those positions on Earth that are closest to the Moon, near the center of the eclipse path, the Moon’s angular size is just big enough to cover the Sun, creating a total solar eclipse. At those positions on Earth that are farther from the Moon, near the beginning 56

and end of the eclipse path, the apparent size of the Moon is too small to cover the Sun, creating an annular eclipse. In a few hundred million years, the vast majority of eclipses will be annular because the Moon is gradually moving away from Earth. Conversely, more than a few hundred million years ago, the Moon was considerably closer to Earth, which made it completely cover the Sun’s photosphere during a total solar eclipse. Coronas, prominences, and the chromosphere weren’t as easily visible because the Moon fully or partially covered these phenomena. No other planet has moons of the right size and at the right distance to produce a total solar eclipse as dramatic as we experience on Earth. On the other hand, Jupiter occasionally experiences double eclipses. Astronomers can correctly predict when and where eclipses will occur. A number of eclipses have changed history. For example, in 585 B.C., an eclipse took place in what is now central Turkey, where the Medes and the Lydians were engaged in a 5-year battle. When the eclipse occurred, the armies took it as a sign to end their war. Scienti¿cally, the most famous eclipse was the one that provided the ¿rst observational con¿rmation of a prediction “The ¿rst written from the general theory of relativity, which record of a total solar was conceived by Albert Einstein. eclipse was in the The theory, published in 1916, postulates that year 2134 B.C. in mass warps space and time, producing the China. The two royal phenomenon of gravity. Particles follow their natural paths through curved space-time; astrologers, Hsi and indeed, this is why planets orbit the Sun. The Ho, had apparently theory predicts that light should also follow a neglected to predict curved path and, therefore, that light coming this event and were from a star—as viewed from Earth—actually beheaded as a result.” does not come from the same direction as the star’s true location because of this bending. Einstein calculated how much the bending should be. This effect seems impossible to measure because stars are invisible during the day. During a total solar eclipse, however, bright stars are visible, and their apparent positions can be measured. These apparent positions can be compared with 57

the “true” positions, as measured in a photograph taken during a time of year when those stars are visible at night, with no Sun along the line of sight. During a total solar eclipse in 1919, Arthur Eddington, a British astrophysicist, made measurements of the stars and found that, in accordance with Einstein’s predictions, their apparent positions were displaced outward from the Sun compared with their positions as measured in photographs taken at night. This displacement is greatest for stars whose light rays come closest to the edge of the Sun, smaller for stars that don’t quite graze the edge of the Sun, and smaller still for those stars whose light rays don’t come close to the Sun’s edge. In all cases, it is a very slight effect—so slight that, in retrospect, Eddington’s measurements were not compelling. Measurements during subsequent eclipses were used to con¿rm the predicted bending. News of the apparent con¿rmation made Einstein an instant celebrity among the lay public worldwide, and the New York Times ran a headline story about it. Ŷ

Names to Know

Lecture 11: More Eclipse Tales

Eddington, Sir Arthur (1882–1944): British astrophysicist who studied the physical structure of stars and was an expert on Einstein’s general theory of relativity. Through his observations of a total solar eclipse in 1919, he helped to con¿rm this theory. Einstein, Albert (18791955): German-American physicist, the most important since Newton. Developed the special and general theories of relativity, proposed that light consists of photons, and worked out the theory of Brownian motion (the irregular, zigzag motion of particles suspended in a Àuid is due to collisions with molecules). Responsible for E = mc2, the world’s most famous equation.

Important Terms general theory of relativity: Einstein’s comprehensive theory of mass (energy), space, and time; it states that mass and energy produce a curvature of space-time that we associate with the force of gravity.

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space-time: The four-dimensional fabric of the Universe whose points are events having speci¿c locations in space (three dimensions) and time (one dimension).

Suggested Reading Harris and Talcott, Chasing the Shadow: An Observer’s Guide to Solar Eclipses. Littmann, Willcox, and Espenak, Totality: Eclipses of the Sun. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Will, Was Einstein Right? Putting General Relativity to the Test.

Questions to Consider 1. If the Moon were placed at twice its current distance from Earth, physically how large would it have to be so that total solar eclipses could still occur?

2. Describe the conditions under which the thickest (widest) annulus is seen during an annular solar eclipse. Where should the Moon and Earth be in their respective elliptical orbits?

3. Is the bending of starlight by the Sun’s gravitational ¿eld the same physical phenomenon as the bending of sunlight around Earth during a total lunar eclipse?

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Early Studies of the Solar System Lecture 12

“The Sun, Moon, and planets were associated with gods, and people believed that human traits and lives were inÀuenced by the planets’ positions. Thus, astrology provided much of astronomy’s roots. As human consciousness evolved, celestial objects became the subject of wonder; the human relationship with the cosmos became a focus of study.”

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Some cultures left behind extensive documents, from which we’ve gained much knowledge. By studying ancient ruins, we can learn what people knew about the heavens. This link between archaeology and astronomy is called

Corel Stock Photo Library

Lecture 12: Early Studies of the Solar System

eaving behind our observations of familiar celestial sights, we focus on the early history of astronomy, beginning with a brief look at the perspectives of the ancients. Astronomy had its roots in such ancient civilizations as Mesopotamia, Babylon, India, Egypt, and China. Early people looked at the heavens for practical purposes: They needed to know when to plant crops, when rivers might Àood, and when other natural events might occur. Stars also helped them navigate.

Stonehenge. 60

archaeoastronomy, the study of ancient structures and their astronomically signi¿cant alignments. Stonehenge in England is a famous example, with its giant standing stones forming a circle 100 feet wide. Stonehenge had signi¿cant social, political, and religious implications for the ancients, but archeoastronomers have also found astronomical alignments, indicating that the builders knew something of the stars. The most prominent alignment is with the Heel Stone, which is outside of the main circle. Astronomy in History As viewed from the center of Stonehenge, the Sun rises along ome people have suggested the Heel Stone at the moment that Stonehenge was suf¿ciently of the summer solstice. complex and elaborate to even allow the prediction of eclipses: lunar and The Egyptian pyramids also solar eclipses. That hypothesis has exhibit signi¿cant alignments, been discredited. There’s no real such as pointing toward evidence that Stonehenge could do certain stars. However, as with something as complicated as the Stonehenge, some alignments prediction of solar eclipses. may be purely coincidental, and scientists run the risk of mistaking coincidence for signi¿cance. About 1000 years ago, the Mayans had an advanced understanding of astronomy, as evidenced in numerous structures. From the Mayan-built Caracol in Chichen Itza, you can see the position of sunrise or sunset at the solstices and the equinoxes. The Mayans’ elaborate calendar involved Venus, the Moon, the Sun, and other celestial objects.

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Ancient Greek astronomy led to the greatest inÀuence on modern Western thought. Aristotle’s theories are particularly important. The ancient Greeks knew that Earth is roughly spherical, and Aristotle clearly articulated arguments to prove this. By observing Earth’s shadow, which always projected an arc on the Moon during a lunar eclipse, Aristotle deduced that Earth must be spherical. If Earth were a Àat, circular disk, then sometimes it would cast a circular shadow, and other times, an elliptical shadow. Also, phases of the Moon show that it is spherical, suggesting that Earth is, too.

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Further, Aristotle used the different positions of the stars to argue that Earth is a sphere. Different stars are visible in the sky at different latitudes on Earth but at the same longitude and at the same time. From 20° north latitude, Polaris appears lower in the sky than at 40°. In addition, other stars shift their positions, which Aristotle argued could only indicate a round Earth. Later, more evidence surfaced: Ships approaching from far away come over a horizon. On a Àat, in¿nite Earth, they would grow dimmer and smaller as they sailed away, instead of sinking below the horizon.

Lecture 12: Early Studies of the Solar System

Aristarchus of Samos was another great astronomer. Although he underestimated the true distance of the Sun, Aristarchus correctly deduced that it was very large and distant. His calculations were based on the Moon’s phases. To see a precisely quarter moon—half of the visible face of the Moon, whether its ¿rst or third quarter—the angle between Earth, Moon, and Sun must be precisely a right angle. Though Aristarchus made some incorrect assumptions, he measured this angle to roughly determine the relative distance of the Sun and how many times larger it was than the distance between Earth and the Moon. In practice, this measurement is dif¿cult to make because the Sun is so far away from us. The angle Aristarchus tried to measure is nearly 90°, regardless of how far away the Sun is. Indeed, Aristarchus measured this angle to be 87°. It’s also dif¿cult to measure the precise moment of the ¿rst or third quarter moon. In performing his calculations, Aristarchus had to assume a circular and uniform orbit of Earth and Moon. (We now know that these orbits are elliptical and that the orbital speeds change.) Despite Aristarchus’s errors, his idea was correct and ingenious. From measurements, Aristarchus erroneously calculated that the Sun is 19 times more distant than the Moon—the true value is 390 times—but he correctly reasoned that the Sun was much larger than the Moon. Aristarchus argued that because the shadow of Earth was not much bigger than the Moon, Earth must be 2 to 3 times the size of the Moon. (Earth is actually 3.7 times bigger.) Thus, according to Aristarchus, if the Sun is 19 times bigger than the Moon, and Earth is 2 to 3 times the size of the Moon, 62

then the Sun must be about 7 times bigger than Earth. In reality, the Sun is 109 times physically larger than Earth; again, Aristarchus was wrong, but his idea was correct. Finally, because the Sun is considerably larger than Earth and very distant, Aristarchus also reasoned that the Sun, not Earth, is the dominant object in the Universe. Eratosthenes determined Earth’s circumference. Eratosthenes noticed that a rod sticking up from the ground casts a shadow, even at noon, at many locations. But at some locations, Syene to be exact, at noon during the summer solstice, there was no shadow. On the same day in Alexandria, north of Syene but at the same longitude, the rod cast a short shadow. By knowing the length of the shadow and the length of the stick, the angle that the Sun makes relative to the stick can be calculated. Through a series of geometric calculations, Eratosthenes determined Earth’s circumference to within an error of about 1%. The next great astronomer to come along was Hipparchus, perhaps the greatest astronomer of pre-Christian antiquity. His studies were done c. 160–127 B.C. Hipparchus made the ¿rst accurate catalog of about 850 stars, including their positions and their apparent brightness. He also re¿ned the method of Aristarchus of Samos and found that the Moon’s distance is about 59 Earth radii. The correct number is 60 Earth radii, meaning that the distance of the Moon from Earth is 60 times Earth’s radius. Hipparchus determined the length of the year to within 6 minutes. He also noticed that the direction of the north celestial pole changed slightly with time. It had changed over the 150 years or so during which accurate records had been kept. As mentioned in a previous lecture, because of the gravitational forces of the Moon and Sun on Earth, Earth’s tilted axis of rotation slowly undergoes a conical motion called precession. In about 13,000 years, summer and winter will be reversed in the two hemispheres from what they are now. Hipparchus noticed and measured the precessing motion of Earth. Ŷ

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Names to Know Aristarchus of Samos (roughly 310230 B.C.): Greek astronomer; measured the Sun-Earth distance relative to the Earth-Moon distance. Realized that the Sun is much larger than the Earth and reasoned that the Sun (rather than the Earth) is at the center of the Universe, predating Copernicus by 1800 years. Aristotle (384í322 B.C.): The most inÀuential early Greek philosopher. He lectured on a vast range of subjects; however, many or most of his beliefs in physics and astronomy turned out to be wrong. Developed a widely adopted geocentric (Earth-centered) model of the Universe consisting of 55 spheres. Correctly concluded that the Earth is spherical. Eratosthenes (276194 B.C.): Greek geographer who estimated the circumference of the Earth to within 1% accuracy through measurements of the length of a stick’s shadow at different locations on Earth.

Lecture 12: Early Studies of the Solar System

Hipparchus (c. 160–c. 127 B.C.): Greek astronomer who made the ¿rst accurate star catalogue. Re¿ned the methods of Aristarchus of Samos. Determined the length of the year to within six minutes and noticed that the direction of the north celestial pole changes with time.

Important Terms apparent brightness: The amount of energy received from an object per second, per square centimeter of collecting area. It is related to luminosity and distance through the equation b = L/(4Sd2), the inverse-square law of light. archaeoastronomy: The study of the astronomical signi¿cance of ancient buildings and other structures.

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Suggested Reading Fraknoi, Morrrison, and Wolff, Voyages through the Universe, 3rd ed. Hoskin, ed., The Cambridge Concise History of Astronomy. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pedersen, Early Physics and Astronomy: A Historical Introduction.

Questions to Consider 1. Had you been alive 2000 years ago, do you think you would have believed in a geocentric (Earth-centered) model of the Universe or a heliocentric (Sun-centered) model, as did Aristarchus?

2. Discuss the importance of assuming that the Sun is very distant if the method of Eratosthenes is used to determine the circumference of Earth.

3. How compelling do you ¿nd Aristotle’s arguments for a spherical Earth?

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The Geocentric Universe Lecture 13

“It’s reasonable to think that the Earth isn’t moving. If I jump up in the air, or if you do, the Earth doesn’t go sailing out from under me, right? So, if it were moving quickly around the Sun, the Earth should go sailing out from under us. We now know that it shouldn’t because of inertia.”

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arly Greek astronomers had observed the movement of the planets from night to night slowly among the stars. This movement is unrelated to the general rising of stars in the east and setting in the west as a result of Earth’s axial rotation. The Greeks also noticed that, at times, the planets appeared to move backward among the stars. Normally, the planets move among the stars in a forward, or prograde, motion from west to east. But for a little while every year, each of the planets moves east to west in a retrograde, or backward, motion. The prograde-to-retrograde-to-prograde movement can form an S-shaped ¿gure, or it can be a loop. It is not a straight line because the planes of the planets orbiting the Sun are slightly tilted relative to one another. Many hypotheses about the origin of the Star of Bethlehem have been proposed over the centuries. Some believe it was a comet; others, a nova or supernova. For various reasons, however, these ideas all fail.

Lecture 13: The Geocentric Universe

Astronomy in History

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hypothesis proposed by Michael Molnar states that the Magi actually practiced an obscure form of astrology and interpreted a particular planetary alignment to foretell the birth of Christ. Other astrologers might not have seen such an alignment as being particularly signi¿cant. The Star of Bethlehem may have been Jupiter moving through the constellation Aries the Ram near the time of its retrograde motion, along with other astrologically signi¿cant conditions, such as the presence of the Sun in Aries. Saturn was near this alignment as well, but Mars and Mercury (generally bad omens) were far away. Moreover, Jupiter and Aries were rising in the east, just ahead of the Sun, at this time. Molnar’s hypothesis is supported by a number of factors, including what we now know were these special planetary alignments 2000 years ago. 66

The apparent motion of planets among the stars, including their retrograde motion, was important to Aristotle and Ptolemy in developing the Earthcentered model of the Universe. Most ancient Greek astronomers believed that the Earth was the center of the Universe and that it was stationary. The Earth couldn’t possibly rotate or orbit the Sun; if it did, people would Ày off. To the ancient Greeks, the stars appeared to be embedded in a celestial sphere that rotated around the Earth. The planets, Sun, and Moon were also embedded in their own spheres, which rotated around the Earth between Earth and the stars. Thus, Earth was the center of these spheres. Aristotle proposed such a geocentric, or Earth-centered, model, the key to which is a stationary Earth. If Earth were orbiting the Sun and if the celestial sphere were nearby, then at one position of the Earth’s orbit, Polaris would be along the line to the north celestial pole. But six months later, Polaris would be nowhere near the apparent extension of our Earth’s north pole. Of course, Polaris is more or less ¿xed in the sky at any given latitude, which is what the Greeks observed. Moreover, constellations and asterisms would appear to change shape as viewed from Earth over the course of a year, but they don’t. Today, we know that the celestial sphere is much farther away than the Greeks thought, which was the Àaw in their reasoning. The Earth is moving, but they assumed that the celestial sphere was nearby and concluded that the Earth is not moving because of the apparent absence of changes in shape of the constellations. To account for the retrograde motion of planets, Aristotle proposed that the planetary spheres had to be rotating in a complex manner. In his system, there were 55 nested spheres inÀuencing one another’s motion. Ptolemy (2nd century A.D.), a great astrologer, produced a better system than Aristotle’s for predicting planetary positions as a function of time. Ptolemy suggested that Earth was slightly offset from the center of a deferent, or planetary sphere. Another point, called the equant, was the center, around which the deferent rotated at a uniform angular rate. To explain retrograde motion, Ptolemy theorized that planets moved along paths called epicycles that were centered on the deferent, the planetary sphere. Epicycles were essentially their own self-contained spheres, along which the planets moved. As a planet moved along its epicycle in the same direction as the deferent, it would be moving in a prograde fashion. If a planet moved in the opposite 67

Lecture 13: The Geocentric Universe

direction in its epicycle around the deferent, that opposite motion could make the planet appear to move backward among the stars, or go retrograde. Ptolemy’s system was complicated, but it gave accurate results and was accepted for nearly 1500 years. Nonetheless, people still believed in a “perfect reality” represented by Aristotle’s nested spheres. The Polish astronomer Nicolaus Copernicus also focused on the retrograde motions of the planets to develop his heliocentric, or Sun-centered, theory of the Universe. Independently reviving the ancient hypothesis of Aristarchus, Copernicus developed a model of the Sun as the center of the Universe, with Earth and the other planets orbiting the Sun. This concept naturally explained how planets went into retrograde motion. Because each planet is a different distance from the Sun, each orbits the Sun at a different rate. Mars, for example, takes longer to orbit the Sun than Earth does. For a time, Mars appears to move backward because Earth actually passes by Mars in its own orbit of the Sun. Similarly, planets closer to the Sun than Earth is (Mercury, Venus) go through retrograde motion as they pass Earth in their orbits around the Sun. Copernicus did not place the Sun in the actual center of the Universe. The Sun had to be slightly off center for his theory to work because he assumed that planets had perfectly circular orbits. Circular orbits would not have allowed for the changing angular speed of a planet across the sky during different times of the year. Copernicus’s off-center circular “Copernicus came along, and orbits worked well because they he presented an alternate mimicked an ellipse—especially a nearly circular ellipse—with the Sun hypothesis: the hypothesis at one focus. of a Sun-centered Universe. He did not let this theory be However, Copernicus still needed published until the day of his epicycles to account for the small difference in an observed position of death. He just was afraid of a planet from its predicted position. what might happen to him if Copernicus’s epicycles weren’t he published such a heretical needed to explain the retrograde theory before he was already motion, but they were used to dead of natural causes.” ¿ne-tune his theory for agreement between observed planetary positions 68

and predicted positions. By using detailed observations and geometry, Copernicus was also able to determine the relative distances of planets from the Sun with remarkable accuracy. Ŷ

Names to Know Copernicus, Nicolaus (14731543). Polish astronomer; proposed the heliocentric (Sun-centered) model of the planetary system. He showed how the retrograde motion of planets could be explained with this hypothesis. His book De Revolutionibus was published the year of his death. Ptolemy, Claudius (85165). Greek astronomer who developed an elaborate model for planetary motions, based on Aristotle’s geocentric Universe, that endured for more than 1400 years. Compiled the Almagest, a set of 13 volumes that provides most of our knowledge of early Greek astronomy.

Important Terms ellipse: A set of points (curve) such that the sum of the distances to two given points (foci) is constant. nova: A star that suddenly brightens, then fades back to its original intensity; caused by the accretion of stellar matter from a companion star. supernova: The violent explosion of a star at the end of its life. Hydrogen is present or absent in the spectra of Type II or Type I supernovae, respectively. prograde motion: The apparent motion of the planets when they appear to gradually move from west to east among the stars; retrograde motion is the opposite direction. retrograde motion: The apparent backward (east-to-west) motion among the stars that planets undergo for a short time each year.

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Suggested Reading Gingerich, The Eye of Heaven: Ptolemy, Copernicus, Kepler. Gingerich and MacLachlan, Nicolaus Copernicus: Making the Earth a Planet. Kuhn, The Copernican Revolution: Planetary Astronomy in the Development of Western Thought. Molnar, The Star of Bethlehem: The Legacy of the Magi. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Pedersen, Early Physics and Astronomy: A Historical Introduction.

Questions to Consider 1. Describe how you can tell when observing the sky whether a planet is in prograde or retrograde motion.

2. Describe the astronomical conditions that may explain the appearance of the Star of Bethlehem.

3. How did the heliocentric model of Copernicus explain the apparent Lecture 13: The Geocentric Universe

retrograde motion of the planets? Consider planets both closer to the Sun and farther from the Sun than Earth is.

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Galileo and the Copernican Revolution Lecture 14

“How was the Copernican system proven to be correct? That task came to Galileo, whose telescopic observations in 1610, and in the years thereafter, con¿rmed that the heliocentric hypothesis was the correct one.”

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n the 16th century, there were two competing hypotheses for the nature of the Universe. In Aristotle’s geocentric system, all celestial bodies rotated on spheres around a stationary, non-rotating Earth. Claudius Ptolemy had a detailed version of the geocentric model in which planets moved along epicycles, whose centers moved along a deferent around the Earth. The Ptolemaic system was particularly adept at accurately predicting the positions of planets. In particular, retrograde motion would occur when a planet was moving along its epicycle in a direction opposite to the motion of the deferent.

In Nicolaus Copernicus’s heliocentric system, ¿rst published upon his death in 1543, Earth and other planets orbit the Sun, which is at the center of the Universe. The planets more distant from the Sun have slower orbital speeds than the planets less distant from the Sun. Retrograde motion is a natural consequence of the changing perspective when Earth passes an outer planet in its orbit or when an inner planet passes Earth. A good analogy is found by considering a traf¿c circle with several different lanes and outer cars moving more slowly than inner cars. When an inner car is passing an outer car, the outer car appears to move backward (retrograde), whereas the rest of the time, it appears to move forward. Although no epicycles were needed to explain retrograde motion in Copernicus’s Sun-centered system, some epicycles were required to get better agreement between the observed and predicted positions of planets. Copernicus’s heliocentric model of the Universe was initially not widely accepted. One reason was that his system was no better at predicting the movements of planets than Ptolemy’s geocentric model. Further, to believe that the Sun—not Earth—was the center of the Universe was heretical. 71

Galileo’s telescopic observations, beginning in 1610, con¿rmed that the planets orbit the Sun. Galileo Galilei found the Copernican system more philosophically attractive than Ptolemy’s model and set out to see whether it was true by conducting observations. He believed that observations should be used to determine the truth or falsity of hypotheses. He was also a faithful Catholic, but he questioned some of the teachings of the Church. Galileo improved on the design of early Dutch toy telescopes, allowing him to see considerable detail in the heavens. One of Galileo’s followers, Benedetto Castelli, encouraged Galileo to observe Venus, believing that if the Copernican system were correct, Venus should go through a complete set of phases, as the Moon does. After looking at Venus over the course of many months, Galileo indeed observed the planet go through a set of phases, Astronomy in History from new to crescent, ow exactly do Galileo’s observations quarter, gibbous, full, and of Venus strike a blow to the Ptolemaic back through the phases to system? In the Ptolemaic model, Venus new again. is between Earth and the Sun, and its epicycle does not cross the Sun’s orbit; therefore, Venus could exhibit only the new—or dark—and crescent phases. In the Copernican system, in which both Venus and Earth orbit the Sun, sometimes Venus is between the Earth and the Sun, in which case it appears new; at other times, it is on the other side of the Sun as viewed from Earth, allowing for a full phase.

Galileo made a number of other important observations. He observed that Jupiter itself rotates. From this, he hypothesized that perhaps the Earth rotates, as well. He found that Jupiter has moons orbiting it. They proved that objects can orbit other bodies, not just the Earth. The observations demonstrated that as Jupiter moves through the sky—with its moons following—the moons aren’t left behind. Thus, the Earth could orbit the Sun, and objects associated with Earth are not left behind. Galileo also found that our own Moon has craters, mountains, and valleys, like Earth, and realized that perhaps Earth isn’t unique. Galileo observed changing sunspots, noting that the Sun isn’t perfect, and found that the Sun rotates, as well. He saw that Saturn has what he described as “handles”; his telescope wasn’t good enough to show 72

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Lecture 14: Galileo and the Copernican Revolution

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that these “handles” were actually Saturn’s rings. Finally, he found that the Milky Way consists of an almost countless number of stars, and he wondered whether there might be other planets—other worlds—orbiting them. However, Galileo suppressed at least one set of observations that did not directly support the heliocentric hypothesis. He noticed that some stars in the sky appeared double, but he didn’t know that they were physically bound together by gravity. He simply believed the fainter star to be more distant. If the fainter star was indeed more distant, then under the heliocentric hypothesis, the stars should appear in slightly different positions, depending on where the Earth is in its orbit. Yet when Galileo observed these double stars, “To avoid being locked he found no shift over the course of six months. He may have suppressed this up in a dungeon or observation because he realized that his killed, as Bruno was, crucial assumption—the fainter star being [Galileo] recanted his more distant than the bright one—might belief in the Copernican be wrong. theory. Though the Galileo published his ¿ndings in two famous legend goes that, as works, which were not well received by he knelt before the the Roman Catholic Church. Galileo’s Inquisition, he said Sidereus Nuncius (Starry Messenger) was under his breath, ‘And published in 1610. His Dialogue on the Two Great World Systems was published yet it moves’ (referring in 1629, which he intentionally wrote in to the Earth).” popular, witty Italian so as to be accessible to everyone. The Catholic Church didn’t object to Galileo’s models explaining his observations, but they did object to the belief that these models represented truth. The Church and the Inquisition believed that his book was written to convince the public that the Copernican system was correct, which was an attack on the Bible. To avoid being imprisoned or killed, Galileo recanted his belief in the Copernican theory but spent the rest of his life under house arrest. He used that time to organize and publish his earlier observations and experiments, and perhaps, he redid a few of his experiments.

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The most famous of his ¿ndings was that a light object and a heavy object, both of the same size, hit the ground at the same time when dropped from a height, neglecting air resistance. With air resistance, objects of different sizes fall at different speeds. Galileo also found that an object accelerates as it falls. Thus, if an object travels 1 unit of distance in 1 second, after a total of 2 seconds, it travels 4 units of distance; after 3 seconds, 9 units; and after 4 seconds, a total of 16 units. This observation and Galileo’s other results were the basis for Newton’s subsequent development of the laws of motion. In 1992, Pope John Paul II of¿cially pardoned Galileo, stating that the Church had been overly harsh when it condemned Galileo in 1633. Ŷ

Suggested Reading Drake, Galileo: A Very Short Introduction. Gingerich, The Eye of Heaven: Ptolemy, Copernicus, Kepler.

Lecture 14: Galileo and the Copernican Revolution

Gingerich and MacLachlan, Nicolaus Copernicus: Making the Earth a Planet. Kuhn, The Copernican Revolution: Planetary Astronomy in the Development of Western Thought. MacLachlan, Galileo Galilei: First Physicist. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Sobel, Galileo’s Daughter: A Historical Memoir of Science, Faith, and Love.

Questions to Consider 1. By including many additional smaller epicycles on the larger epicycles in the Ptolemaic model, do you think that the accuracy of the predicted planetary positions can be continually improved?

2. How did Galileo’s observations of Venus serve to disprove the Ptolemaic model of the Universe?

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3. Examining each of Galileo’s telescopic discoveries separately, do you think they tended to support, oppose, or be irrelevant to the heliocentric hypothesis?

4. If an apple and the Moon are the same distance from Earth, compare the acceleration of the apple toward the Earth with the acceleration of the Moon toward the Earth based on what you know from Galileo’s experiments on falling bodies.

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Re¿nements to the Heliocentric Model Lecture 15

“The ¿rst law that [Kepler] ¿gured out in the year 1604 is that the planetary orbits are ellipses, not circles. The Sun is not at the center of the ellipse, but rather is at one focus of the ellipse.”

Lecture 15: Re¿nements to the Heliocentric Model

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oughly 70 years after the publication of Copernicus’s book Concerning the Revolutions, Galileo’s observations proved Ptolemy’s system wrong and the Copernican system as probably the correct description of physical reality. However, even before Galileo’s groundbreaking observations, other scientists had made some re¿nements to the Copernican model. One idea combined the features of both the heliocentric and the geocentric system, suggested by the Danish nobleman Tycho Brahe. Basically, Tycho thought that everything except the Moon orbits the Sun, and the Sun, along with its orbiting planets, orbits the Earth. At that time, no one really knew that the Earth was moving; that idea was just conjecture by Copernicus. However, neither the geocentric camp nor the heliocentric camp was particularly pleased with this combination of motions. At a young age, Tycho saw a partial solar eclipse and was impressed that astronomers had been able to predict it. He then dedicated his life to making ever more accurate observations of the Moon, Sun, and planets in order to enhance the predictive power of physics and these models. Tycho discovered a supernova, an exploding star, in 1572. He didn’t know the physical nature of the star—that it was a star at the cataclysmic end of its life, visible with the naked eye. Until then, people had thought that the heavens were immutable, and Tycho’s observation went a long way toward dispelling that belief. Tycho set up an observatory, where he made accurate observations of the planets. He had no telescope, but he had other instruments that measured the altitude of a planet above the horizon and its angular distance from stars. Before Tycho’s early death in 1601, he had hired a superb mathematician, Johannes Kepler, to analyze his data. Kepler re¿ned the Copernican model with three important empirical laws. Kepler’s laws were empirical because he had no physical explanation for them. He simply found that, quantitatively, they appeared to be true. Later, Newton demonstrated why.

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Kepler’s ¿rst law states that planetary orbits are ellipses, not circles. The Sun is not at the center but at one focus of the ellipse, while nothing is at the other focus. An ellipse is de¿ned as a shape in which the sum of the distances from any two foci (¿xed points), a + b, is a constant. In an ellipse, the long axis is called the major axis; the short axis is the minor axis. Half these lengths are the semimajor and semiminor axes, respectively. The semimajor axis is close to the average distance between a planet and the Sun. The eccentricity of an ellipse is the distance between the foci divided by its major axis. As the foci move farther apart, the ellipse becomes more highly eccentric, or more elongated. For nearly circular orbits, the semimajor axis is simply the orbital radius. Kepler’s second law states that a line between the Sun and a planet sweeps out in a pie shape in equal areas as long as the time intervals are equal. When a planet is close to the Sun, it moves faster than when it is far from the Sun. An extreme example of this is the highly eccentric orbits of many comets, which spend very little time near the Sun. Kepler’s third law states that the square of a planet’s orbital period is proportional to the cube of its semimajor axis, or average distance from the Sun. In mathematical form, this law is P2 = kR3, in which P is the orbital period, R is the semimajor axis, and k is a constant (the same for all planets). The more distant a planet is from the Sun, the longer it takes to complete an orbit. Kepler called this third law the “harmonic law,” suggesting an almost musical relationship between orbital periods and sizes.

Did You Know?

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hen discussing planets in our Solar System, it is sometimes convenient to use units based on Earth’s orbit. We write Pp2 = 3 kRp , in which the subscript p refers to a given planet. Similarly, we write PE2 = kRE3, in which the subscript E refers to Earth. Dividing one equation by the other, the constant k cancels out: (Pp / PE)2 = (Rp / RE)3. If we adopt units of years for Pp and AU (astronomical units) for RE , we have Pp2 = Rp3 because PE = 1 year and RE = 1 AU. If we know that the orbital period of Mars is 1.88 years (Pp = 1.88), then 1.882 = 3.53 = Rp3; thus, the semimajor axis of Mars’s orbit is the cube root of 3.53, or 1.52 (Rp = 1.52 AU). 77

Lecture 15: Re¿nements to the Heliocentric Model

Kepler’s third law also applies to objects orbiting the Earth—in particular, satellites. A satellite just above the Earth’s surface travels about 230 degrees in 1 hour—about two-thirds of a full circle—whereas the Earth itself rotates about 15 degrees per hour. A satellite orbit at 3.25 Earth radii from Earth’s center traverses It turns out that most 42 degrees in 1 hour. But if the satellite is of the planets have at 6.5 Earth radii from Earth’s center, then orbits that are nearly it traverses 15 degrees in 1 hour; that is, it traverses the same angular distance as the circular; the ellipses Earth’s rotating surface. That means that have only a very small this satellite will appear stationary above a eccentricity. This particular point on the Earth’s surface. This is is the reason that the idea behind geostationary orbits. Copernicus’s system Isaac Newton now enters the scene, a with circular orbits brilliant but eccentric English physicist who worked quite well. made many magni¿cent contributions to physics and astronomy. Newton developed calculus, a form of mathematics, as well as the laws of motion and the law of universal gravitation; he also invented a form of telescope, the Newtonian reÀecting telescope. Newton’s ¿rst law of motion states that a body continues to be at rest or in motion in a straight line with constant speed unless a force acts on it. We rarely see this in operation because frictional forces are almost always present, slowing a body down until it stops. This was a revolutionary idea; the medieval view held that a continuous force was needed to keep a body moving. In particular, a planet doesn’t need any force to keep it going. The second law is expressed algebraically as a = F/m (or, more commonly, F = ma), in which F is force, m is the mass of the particle on which the force is applied, and a is the particle’s acceleration. The term velocity refers to both speed and direction, and acceleration is the rate at which velocity changes speed or direction or both. Pulling on a planet from the side changes the direction of motion but not the speed. This is how the gravitational force of the Sun keeps a planet curving in its orbit. A large mass is accelerated less than a small mass for a given force. 78

The third law states that for every action, there is an equal and opposite reaction. In other words, forces always come in pairs and act in opposite directions. When you jump off a chair and the Earth’s force of gravity brings you down again, you exert just as strong a force on the Earth as it does on you. It’s the mass dependence in the second law that makes the difference: That force accelerates the enormously massive Earth far less than it accelerates you. An orbital example would be the Earth and Moon exerting equal forces on each other, but the Moon gets much more acceleration because it is only 1/80th as massive as Earth. The Earth is accelerated, though, and it follows a little monthly orbit 1/80th as large as that of the Moon. Rocket propulsion also provides a familiar example. The force pushing gas out of a rocket is balanced by an oppositely directed force on the rocket, propelling it forward. Ŷ

Names to Know Brahe, Tycho (15461601). Danish astronomer; measured the positions of planets with unprecedented accuracy, laying the foundations for Kepler’s work. Discovered and studied a bright supernova in 1572; thus, the “sphere of ¿xed stars” is not immutable, in contradiction to Aristotelian and Christian dogma. Kepler, Johannes (15711630). German mathematician and astronomer; was Tycho Brahe’s assistant and gained access to Brahe’s data after his death. Developed three empirical laws of planetary motion that represent a signi¿cant revision of the Copernican model. Studied a very bright supernova in 1604.

Important Terms astronomical unit (AU): The average distance between the Sun and the Earth (1.5 u 108 km). eccentric: Deviating from a circle. Eccentricity is a measure of this.

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Kepler’s third law: If one object orbits another, the square of its period of revolution is proportional to the cube of the semimajor axis (half of the long axis) of the elliptical orbit.

Suggested Reading Christianson, Isaac Newton and the Scienti¿c Revolution. Ferguson, The Nobleman and His Housedog: Tycho and Kepler: The Unlikely Partnership That Forever Changed Our Understanding of the Heavens. Gingerich, The Eye of Heaven: Ptolemy, Copernicus, Kepler. Gleick, Isaac Newton. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Thoren, The Lord of Uraniborg: A Biography of Tycho Brahe.

Lecture 15: Re¿nements to the Heliocentric Model

Questions to Consider 1. If planetary orbits can be reasonably approximated as circles centered on the Sun, can you use Kepler’s third law to derive an equation relating the orbital speeds and distances of planets?

2. Why does a satellite speed up as it spirals toward the Earth due to friction with the outer atmosphere? Naively, it seems that the friction should cause it to slow down.

3. What is the semimajor axis of a comet that orbits the Sun with an orbital period of 100 years? Compare this with the semimajor axis of Uranus, about 20 AU.

4. How might you demonstrate that Earth is orbiting the Sun, thus disproving Tycho Brahe’s model of the Universe?

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On the Shoulders of Giants Lecture 16

“The generalization of Kepler’s ¿rst law, where Kepler said that the orbits are ellipses with the Sun at one focus—Newton was able to prove that, but he generalized it, and he said that really, the trajectories of particles are conic sections. That includes circles, ellipses, parabolas, and hyperbolas.”

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saac Newton proposed the law of universal gravitation, a force acting between objects and tending to pull them together. Supposedly, an apple fell on or near Newton, and he guessed that qualitatively, the same force acts upon the Moon, making it fall toward the Earth. This is the Earth’s gravitational force. It was sensible to suppose that all bits of matter within an object contribute to the gravitational force exerted by the object. Thus, the Earth’s gravitational force is proportional to the total mass of Earth, and an apple’s pull toward Earth is proportional to the apple’s total mass. Given that Newton’s third law states that forces are equal and opposite—the force exerted by the apple is equal in magnitude to the force exerted by the Earth—the two forces must be proportional to the product of their masses. A gravitational force proportional to the product of the two masses, together with Newton’s second law (F = ma), is consistent with Galileo’s ¿nding that two bodies of equal physical size but differing mass fall at the same rate. Newton theorized that gravity spreads out over a sphere, diminishing with distance—speci¿cally, the inverse square of distance. Newton’s formula describes the law of gravitation: F

Gm1m2 d2

, in which F is the magnitude

of the gravitational force between two objects, G is Newton’s gravitational constant, m1 is the mass of the ¿rst object, m2 is the mass of the second object, and d is the distance between the two objects. The form of mathematics Newton invented to perform his calculations, called the calculus, showed that the gravitational force of the Earth acts as though all of the Earth’s mass were concentrated in its center.

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© Photos.com/Thinkstock

The relevant distance between an apple and Earth is the distance between the center of the apple and the center of Earth. The relevant distance for the Moon is the distance between the center of the Moon and the center of Earth. Earth’s radius is roughly 6400 kilometers, the relevant distance for the case of the apple and the Earth attracting each other. The relevant distance for the Moon is about 384,000 kilometers from Earth, roughly 60 times Earth’s radius. If Newton is correct, the acceleration felt by the Moon 2

Lecture 16: On the Shoulders of Giants

§ 1 · should be ¨ ¸ of that felt by the © 60 ¹ 2 1 § 1 · apple, and ¨ ¸ is . 3600 © 60 ¹

Newton is depicted contemplating gravity under the infamous apple tree.

At the Earth’s surface, the measured acceleration due to gravity is 980 centimeters per second, per second—980 cm/s2—which is equal to 32 feet per second, per second. Thus,

1 of that measurement is 0.27 centimeters 3600

per second, per second—the known acceleration of the Moon and that which it must maintain in order to orbit the Earth. Newton believed that the law of gravitation was universal and that Jupiter attracts its moons in the same way that Earth attracts its Moon. How does gravity produce an orbit and prevent the Moon from hitting Earth? According to Newton’s ¿rst law, in zero gravity, an object launched perpendicular to the direction of Earth results in motion along a straight line at constant speed. According to Newton’s second law, releasing that object from rest with gravity causes it to accelerate toward Earth because of 82

gravity’s force. Combining these two motions, we can examine them along small time steps. The Moon falls toward Earth during each moment it takes to travel a short distance perpendicular to Earth, but its new distance from the center of the Earth remains unchanged. During the next moment, the same thing happens, but now, the tangential motion (perpendicular to the direction of Earth) is in a slightly different direction because of the acceleration during the preceding moment. Again, the new distance remains unchanged. Thus, along numerous tiny steps of time, a smooth curved orbit is formed. In other words, the Moon really does fall toward Earth, but it never hits because the tangential motion keeps it away. It keeps missing the Earth, in a sense. If Earth’s gravity were eliminated, the Moon would continue to move with constant speed and direction along the tangent to the orbit at the instant gravity disappeared. Newton illustrated his point by demonstrating that as the speed at which an object is thrown or projected increases, the object travels a farther distance before falling to Earth because of gravity. For example, a cannonball ¿red at great speed will eventually fall to the ground, but the distance will be greater than expected because the surface of the Earth partially curves away from the ball’s trajectory. Similarly, if an object were ¿red suf¿ciently fast, it would follow a trajectory that matched the Earth’s curvature, never hitting the ground but, rather, orbiting the Earth. If an object travels fast enough, it can escape the Earth’s gravitational pull. This speed is known as the escape velocity. At Earth’s surface, the escape velocity is 11.1 kilometers per second. Newton could generalize Kepler’s laws and apply them to situations in which objects attracted each other by gravity. Newton proved Kepler’s ¿rst law: that orbits are ellipses with the Sun at one focus. Furthering this, Newton stated that an object’s trajectory is really a section of a cone—a circle, ellipse, parabola, or hyperbola. If an object is gravitationally bound to another object, the orbit is generally an ellipse—the curve formed when a plane intersects a cone at an angle less steep than the cone’s side. Only if conditions are special does one get a perfectly circular orbit. If an object is unbound (that is, traveling at a speed greater than its escape velocity), the orbit is generally a hyperbola—the curve formed when a plane intersects a cone at an angle steeper than the side of the cone. If an object is just barely unbound (that is, traveling at its escape velocity), its orbit is a parabola— 83

the curve formed when a plane intersects a cone at an angle parallel to the cone’s side. Newton derived the constant of proportionality from Kepler’s third law: ­° ½° 4S2 3 3 P2 ® ¾ R = kR , in which m1 and m2 are the masses of two ª º  G m m ° 1 2 ¼¿ ¯° ¬ bodies and G is Newton’s gravitational constant. For planetary orbits, let m1 be the Sun’s mass and m2 be the planet’s mass. The constant k in Kepler’s version depends on m2 ; thus, it’s really not a constant. However, because the mass of each planet is much smaller than the Sun’s mass, the combination 4S2 is nearly constant for all planets. [G (m1  m2 )]

If the mass m2 is negligible relative to m1, we can ignore m2. Therefore, ª 4S2 º 3 « » R , in which ¬« (Gm1 ) ¼» m1 is the mass of the dominant object, that is, the Sun. If P and R of the small object are measured, we can solve for m1 , which allows us to determine the Sun’s mass. Assuming that Earth’s mass is negligible and using the known values of P (1 year) and R (1 AU) for Earth, we ¿nd that the mass of the Sun is m1 = 2 u 1033 grams. This is indeed far larger than the mass of the Earth (m2 = 6 u 1027 grams), thereby proving that m2 is negligible in comparison.

Lecture 16: On the Shoulders of Giants

Newton’s version of Kepler’s third law becomes P 2

We can also use Newton’s version of Kepler’s third law to determine the orbital speeds of different planets. For any planet, ª 4S2 º 3 « » R . Call this equation (1). If the planet’s orbit is roughly ¬« (Gm1 ) ¼» circular, then the circumference of the orbit (2SR) must equal the planet’s speed multiplied by the time period of the orbit: 2SR = vP. This is an application of distance = speed u time, which is true for constant speed. Thus, P2

P

m1 84

2SR . Substituting this v 2 v R . Equivalently, v G

into equation (1) and rearranging, we ¿nd that § Gm1 · ¨ R ¸ © ¹

1

2

§1· , so we see that v v ¨ ¸ ©R¹

1

2

.

Therefore, the speed of a planet is inversely proportional to the square root of its semimajor axis. In other words, distant planets move more slowly than those near the Sun. Ŷ

Important Term escape velocity: The minimum speed an object must have to escape the gravitational pull of another object.

Suggested Reading Christianson, Isaac Newton and the Scienti¿c Revolution. Cohen, The Newtonian Revolution. Gleick, Isaac Newton. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. What is the speed of a planet orbiting 3 AU from a star that is three times as massive as the Sun?

2. If a hypothetical planet is four times farther from the Sun than Earth is, what is its orbital speed (not period) relative to Earth’s?

3. Which is greater: the Earth’s gravitational force on the Sun or the Sun’s gravitational force on the Earth? Explain.

4. Why was it important to verify Newton’s prediction that the “constant” in Kepler’s third law actually depends on the mass of the planet under consideration?

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Surveying Space and Time Lecture 17

“The nearest big galaxy to our own, the Andromeda Galaxy, is 2.4 million light years away. … You can see it, and yet the light has been traveling to you for 2.4 million years—right around when early hominids were wandering around on Earth.”

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e now come to the third unit in the ¿rst major section of this course. In this unit, we will discuss some of the basic concepts and tools used by astronomers. We begin by getting some idea of the absolute size of the Solar System and of the rest of the Universe. Determining the absolute physical scale of the Solar System was a big problem in In this lecture series, we often use the metric system. science up until the 18th century. A key to getting the distance • The unit of length is the meter (m). scale was a transit of Venus • One meter is 39.37 inches, a bit across the face of the Sun, when larger than a yard. Venus travels between Earth • One kilometer (km) = 1000 m, or and the Sun, a rare event. Venus about 0.62 mile. transited the Sun in 1761 and 1769, enabling astronomers to • One centimeter (cm) = 1/100 m, or determine the physical length about 0.39 inch. of the astronomical unit (AU), • The unit of mass is the gram (g). which is de¿ned as the average • There are 453.6 grams in 1 pound. distance of the Sun from the Earth. Depending on the • One kilogram (kg) = 1000 g, or location on Earth from which about 2.2 pounds. you look, the exact position of • The unit of time is the second (s). Venus on the disk of the Sun will shift a bit. This is known as a parallax. By measuring the angle of the shift and knowing the length of the baseline over which the shift occurred, you can determine the size and shape of the unique triangle that de¿nes that parallax.

Lecture 17: Surveying Space and Time

Please Note

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The Hubble Heritage Team (AURA/STScI/NASA)

Astronomers used this image of spiral galaxy NGC 4414 to calculate its distance from Earth (60 million light years).

The problem is that the shift for two observers separated by an Earth radius is only about one-third of the diameter of Venus—very small—and dif¿cult to determine for people in the mid-18th century. Instead of measuring the actual parallax shift, you can measure the time Venus takes to transit (go across) the face of the Sun. The transit as seen from point P on Earth takes some total time, T. And the transit as seen from point P c (read “P prime”) on Earth takes some total time, T c . The difference between those transit times is correlated with the angular parallax shift, D (alpha). These measurements were made by a number of observers who developed a value for the AU, which is about 150 million kilometers—or 93 million miles—the average distance to the Sun from Earth. 150 million kilometers = 93 million miles = 1 AU. To avoid writing out many zeros, 150 million kilometers can be written as 1.5 u108 kilometers (or 9.3 u107 miles), the preferred scienti¿c notation. (Note that 1 mile § 1.6 km.) 87

When dealing with stars or galaxies that are so far away, the AU is an inadequate unit. Instead, we talk about distances in terms of the time it takes light to travel in space from one place to another. The speed of light in a vacuum, 3 u 105 km/s (or 186,000 miles per second), is constant. It is the greatest possible speed with which information can travel through space. If speed is constant, then distance equals speed multiplied by time ( d vt ). Thus, solving for time, we get t = d/v, and for light, this becomes t = d/c. Light traveling from the Moon, 3.84 u 105 km away, takes t = (3.84 u 105 km)/(3 u 105 km/s) § 1.3 seconds (s) to reach us. We say that the Moon is about 1.3 light seconds away. This led to the noticeable delay in the responses of lunar astronauts to questions from people on Earth, which were transmitted via radio signals traveling at the speed of light.

Lecture 17: Surveying Space and Time

Given that t = d/c = (1/c)d, the light travel time is proportional to distance, and (1/c) is the constant of proportionality. The Sun is 390 times farther from Earth than the Moon is. Hence, light from the Sun takes (1.3 s)(390) § 500 seconds to reach us. This is about 8.3 minutes (1 minute = 60 seconds). We say that the Sun is 8.3 light minutes away. If the Sun were to abruptly stop shining, we wouldn’t know it for 8.3 minutes because the light just prior to that event is already on its way and will take 8.3 minutes to reach us. A light year is the distance light travels in 1 year: d = (3 u 105 km/s)(1 year). Converting 1 year into seconds: (1 year)(365.25 days/year)(24 hours/day) (60 minutes/hour)(60 seconds/minute) = 3.15 u 107 seconds; one can easily remember this as being roughly ʌ u 107 s, in which ʌ is the irrational number 3.14159… Thus, d = 9.6 u 1012 km, about 10 trillion kilometers. The nearest star, Proxima Centauri (a companion of Alpha Centauri), is 4.2 light years away. Other stars visible in the night sky can be hundreds or thousands of light years away. Thus, different stars are seen at different times in the past. The nearest large collection of stars, the Andromeda Galaxy, is 2.4 million light years away. Galaxies are typically millions of light years apart. The faint light just now reaching us from distant galaxies many billions of light years away allows us to see them as they were billions of years ago. Hence, the ¿nite speed of light gives us a kind of “fossil record” of the Universe’s history. If we assume that distant parts of the Universe are

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fundamentally similar to nearby parts, we can gain insights into how our own cosmic environment may have evolved. Distance scales naturally bring us to time scales. Many events happened in the history of the Universe that were critical to the eventual emergence of human intelligence. Here, we highlight seven of them. The Universe was born about 13.7 billion years ago, give or take half a billion years; this is the measured time since the Big Bang. All the galaxies are moving away from each other. If we extrapolate backward in time, we ¿nd that these galaxies (or at least the material of which they now consist) were all in the same place 13.7 billion years ago, at the birth of the Universe. Many A Second Glance galaxies, such as our own o place astronomical time Milky Way Galaxy, formed scales into perspective, let’s about 13 billion years ago, compress the 14-billion-year history within the ¿rst billion years of the Universe into one day, or after the Big Bang. We know 86,400 seconds. Thus, the Big Bang this by measuring the ages of occurred at t = 0 and now is at 24 the oldest stars, such as those hours. Our Galaxy formed just a in globular star clusters. few hours after the Big Bang. Our Solar System formed at about 16 The third major event was the hours; in other words, two-thirds formation of the Solar System of the day had passed before the about 4.6 billion years ago. We Solar System formed. Homo sapiens determine this by radioactive appeared about 1 second ago, and a dating of meteorites and Moon long human lifetime of 100 years is rocks. Next, unicellular life 0.0006 seconds—less than 1/1000 emerged at least 3.5 billion of a second. Our lives are a blink of years ago, as evidenced in an eye in the history of the Universe, the fossil records (seen in the illustrating that astronomical time form of stromatolites—giant scales are very, very long. colonies of cyanobacteria). There is indirect evidence for life 3.8 billion years ago. Then, around 550 million years ago, what’s referred to as the Cambrian explosion took place, a giant diversi¿cation of complex, hard-bodied animals, such as trilobites. Dinosaurs ruled for more than 150 million years, suddenly becoming extinct roughly 65 million years

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ago—the great Cretaceous/Tertiary extinction. Mammals then emerged, culminating with early hominids—about 4.5 million years ago—and, ¿nally, Homo sapiens developed about 150,000 or 160,000 years ago. Ŷ

Important Terms Big Bang: The birth of the Universe in a very hot, dense state 13.7 billion years ago, followed by the expansion of space. parallax: Apparent movement of an object due to a change in the position of the observer. The parallax of a star is de¿ned as the angular distance subtended by 1 AU, the distance between the Earth and the Sun, as seen from the star.

Suggested Reading Horwitz, Blue Latitudes: Boldly Going Where Captain Cook Has Gone Before. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Lecture 17: Surveying Space and Time

Sagan, Cosmos.

Questions to Consider 1. How would our view of the Universe differ if the speed of light were in¿nite?

2. Why is it useful to talk about distance in terms of light years? 3. Geologists study different strata to determine conditions on Earth long in the past. How is it that astronomers are able to see parts of the Universe appearing as they were in the past?

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Scale Models of the Universe Lecture 18

“It’s interesting to ask yourself, what is emptier in the universe? Are atoms emptier than planetary systems? Are they emptier than galaxies? Is the universe as a whole the emptiest thing?”

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he Universe has been in existence for about 14 billion years; thus, astronomical time scales are very long. Distance scales in the Universe are also hard to fathom, but scale models can help put these distances into perspective. Suppose that the Sun (1.4 u 106 km in diameter—109 times the diameter of the Earth) were only the size of the period at the end of this sentence (about 0.5 mm). The nearest star, 4.2 light years away, would be about 14 kilometers away on this scale. The Milky Way Galaxy, about 105 light years in diameter, would be 320,000 kilometers in size—not quite the distance to the Moon (384,000 km away). Astronomers must also consider objects on tiny scales, such as atoms and subatomic particles. Suppose one atom were the size of an apple, about 8 centimeters in diameter. On this scale, a human (20 billion times larger) would be 1.6 million kilometers high—more than four times the distance to the Moon. Nevertheless, the nucleus of the atom (a single proton, in the case of hydrogen) would be only 1.6 millionths of a meter (1.6 Pm) in diameter. Thus, hydrogen is 99.999999999999% empty! Other objects, though opaque, also consist almost entirely of empty space—99.99999999% empty. Electrons are in a cloud surrounding the nucleus of an atom and make up a much bigger volume (but the electrons themselves have essentially zero volume). The reason that atoms are so big lies in the study of quantum physics and can be explained by a combination of the Heisenberg uncertainty principle (which we’ll discuss in a subsequent lecture) and the Pauli exclusion principle, which prevents electrons from accumulating in the same regions of an atom. Even if we add more electrons, making bigger and bigger atoms, the electrons have to stay comfortably spaced from each other.

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Lecture 18: Scale Models of the Universe

Which structure is emptiest, an atom, the Solar System, our Galaxy, or the whole Universe? To gain a deeper perspective of size scales in the Universe, we compare how empty these different structures are. The ratio of the radius of the electron cloud to the radius of a proton in a hydrogen atom is about 5 × 104, or 50,000. An example of a comparable ratio in our Galaxy is the distance to the nearest star, 4.2 light years, divided by the radius of the Sun. But 4.2 light years divided by 700,000 kilometers (the radius of the Sun) is a ratio of about 60 million, 6 × 107—much bigger than the ratio of 50,000 (5 × 104) that we found for an atom. Thus, our Galaxy is much emptier than an atom. The analogous ratio in our Solar System might be the distance of the Earth The universe is much to the Sun divided by the Sun’s radius: 1 less empty than an AU y 700,000 kilometers § 200, which is atom. Despite the vast far less than the ratio for an atom (50,000). By this calculation, an atom is far emptier distances between than our Solar System. galaxies, the ratio of the distances between galaxies to the radii of galaxies is smaller than the ratio of the radius of the electron cloud to the radius of a proton.

Considering the Universe as a whole, we take the ratio of the distance of a relatively nearby galaxy, such as the Andromeda Galaxy, to our own Milky Way Galaxy’s radius. Andromeda is about 2.5 million light years away, and our Galaxy’s radius is about 50,000 light years. That ratio, then, is about 48. But 48 is much less than 50,000. Thus, using the distance between galaxies relative to the radii of the individual galaxies as a measure of the emptiness of the Universe, an atom is much emptier. The Universe as a whole isn’t all that empty; much less empty than atoms or than stars within a galaxy. To appreciate these size scales, the distances between objects, and the fact that certain regions of the Universe are relatively empty while others are ¿lled with activity, we view the Universe on progressively larger or smaller scales, each a factor of 10 larger or smaller than the preceding one. We start with a familiar scale, looking at the Very Large Array (a set of radio telescopes in New Mexico) as viewed from a height of 100 meters. If we steadily decrease the scale by a factor of 10, we get closer by a factor of 10, going from 100 92

meters to 10 meters, to 1 meter, to 1/10 meter, and so on. Our journey takes us to a kangaroo rat, and we peer into the nucleus of one of its kidney cells on a scale of 10–6 meter (1 micrometer), ¿nally revealing the structure of DNA on a scale of 10–9 meter (1 nanometer). The outer shell of electrons in a carbon atom has a diameter of about 10–10 One popular analogy is meter (0.1 nanometer, equivalent to to compare the number 1 angstrom unit). The nucleus of the of stars in the Milky Way atom is much smaller, and we begin to Galaxy to that of the see it clearly from a distance of 10–14 grains of sand on a beach. meter (10 femtometers). Between the electron shell and the nucleus is largely Depending on numerous empty space. The quarks that make up factors, there may or may protons and neutrons are visible on a not be as many grains of scale of 10–16 meters. sand on a beach as stars in Going back to the familiar scale of the our Galaxy. Either way, the Very Large Array, we next increase our numbers are fantastically view by a factor of 10 with each step, large, and it is helpful to going from 100 meters to 1000 meters think of analogies to put (1 kilometer), to 10,000 meters, and some intuitive scale to the so on. We see the entire state of New 6 Mexico from a distance of 10 meters size of things. (1000 km). Going out another factor of 10, to a distance of 107 meters, much of North America comes into view. As we increase the scale, we see the entire Earth, then the inner part of the Solar System, and ¿nally, the entire Solar System from a distance of 1013 meters (roughly 100 AU from the Earth). Moving out several factors of 10 in distance, we reach a scale of 1017 meters, or about 10 light years. The Sun appears very small from this distance, and we ¿nally see a few other stars. From a distance of 1020 meters, about 10,000 light years from the Sun, we see a plethora of stars, including part of a spiral arm. Moving out to 1022 meters, a million light years from the Sun, the entire Milky Way Galaxy and its two main satellite galaxies, the Magellanic Clouds, can be seen. From a distance of 1024 meters, or 100 million light years, we see that our Galaxy is just one of tens of thousands of galaxies in a supercluster. Going to even larger scales, 1026 meters or 10 billion light 93

years, where distances up to 13.7 billion light years are visible, we are actually looking back in time 13.7 billion years. We see the small variations in density from which the large-scale structure of the Universe formed. Through 43 orders of magnitude—that is, powers of 10—starting from about 10 billion light years from the Milky Way Galaxy and ending on a scale of 10–16 meters, we have gone from the largest scales in the observable Universe to the inner world of atomic nuclei. We can use everyday analogies to illustrate powers of 10 to gain a more intuitive feeling for numbers spanning a vast range. For example, if $1.00 equals 1 meter, then 1 centimeter equals 1¢—1/100 of $1.00 is 1¢; 1/100 of a meter is 1 centimeter. The radius of an atom is 1 angstrom—a unit equivalent to 10–8 centimeters, or 1/100,000,000 of a cent. But no one talks about 1/100,000,000 of a cent; already, then, the money analogy isn’t working on a scale the size of an atom. On a large scale, one light year is 1013 kilometers, or 1016 meters (10 quadrillion meters)—$10 million billion. Again, the scale doesn’t work because our Galaxy is 100,000 times bigger than that, and the Universe is another factor of 100,000 larger. Ŷ

Lecture 18: Scale Models of the Universe

Important Terms angstrom (Å): A unit of length commonly used for visible wavelengths of light; 1 Å = 108 cm. large-scale structure: The network of clusters, voids, and other shapes seen on the largest scales of the Universe. neutron: Massive, uncharged particle that is normally part of an atomic nucleus. Pauli exclusion principle: Wolfgang Pauli’s explanation for the arrangement of electrons in an atom. The quantum mechanical principle states that no two electrons can be in the same “quantum state” (same con¿guration) in an atom at the same time.

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proton: Massive, positively charged particle that is normally part of an atomic nucleus. The number of protons in the nucleus determines the chemical element. quark: A fundamental particle with fractional charge; protons and neutrons consist of quarks.

Suggested Reading Davidson, Secret Worlds: The Universe Within, micro.magnet.fsu.edu/ primer/ java/scienceopticsu/powersof10/. Eames Of¿ce, Powers of 10, www.powersof10.com/. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Sagan, Cosmos.

Questions to Consider 1. Construct a scale model of our Solar System by choosing a speci¿c object to represent the Sun or the Earth. Consult a standard textbook for a data table of sizes and distances.

2. Suppose the distance from the Sun to Pluto, 40 AU § 6 u 109 km, were compressed to the size of a pen (15 cm). On this scale, what would be the distance from the Sun to Aldebaran, a bright star (the eye of Taurus the Bull) whose true distance is roughly 60 light years?

3. Estimate the number of atoms in a human, assuming an atom has a radius of 1 angstrom (108 cm), and compare this with the approximate number of stars in the Milky Way Galaxy (about 1011).

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Light—The Supreme Informant Lecture 19

“What is light? It seems like a simple question, but in fact it’s very complex, and it occupied physicists for hundreds of years.”

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Lecture 19: Light—The Supreme Informant

s we discussed, galaxies and stars are so far away that we measure their distance in light years—that is, the time it takes light to travel across space from point A to point B. With a few exceptions, most astronomical objects are studied through the light they emit. But what is light? This seems like a simple question, but in fact, de¿ning light is complex and has preoccupied physicists for hundreds of years. We can grasp the idea of light’s properties by passing what we call white light, sunlight, through a prism to produce a spectrum, or a rainbow. Isaac Newton was the ¿rst to systematically decompose white light into its spectrum of colors with the use of a prism. He noticed that if any one color were isolated and sent through a prism, it remained the same color. This experiment suggests that glass somehow takes white light and spreads it out into its intrinsic component colors. Thus, Newton realized that white light is this spectrum of colors. He veri¿ed this idea by passing the light through two prisms with a lens in between. The lens bent the light beams back to parallel and sent the rainbow of colors through the second prism to get white light back out again. We can measure the amount of light at each color—red through violet—and plot the amount of light, its brightness or intensity, along a vertical axis; along the horizontal axis, we can plot each color band. This brightness versus color is what we call a spectrum, which in turn, offers quantitative information about the physical nature of the objects that we are studying. One way to remember the order of the light color spectrum is with the mnemonic device Roy G. Biv, or red, orange, yellow, green, blue, indigo, violet. Visible light is one form of electromagnetic radiation, produced as waves with different lengths and frequencies. A static electric ¿eld exists around a stationary charge, such as an electron. A static magnetic ¿eld exists around

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a stationary magnet. If a proton (positively charged ion) is placed next to another proton at rest, the ¿rst proton will move away from the stationary one along radial lines. If an electron (negatively charged ion) is placed next to the stationary proton, the electron will be attracted along these radial lines, or lines of force. A magnet also has lines of force, but they run from a north pole to a south pole only; they do not radiate in all directions. If you break a magnet in half, each piece still has a north pole and a south pole. There is a deep connection between electric and magnetic ¿elds. A current— which consists of electrons in motion through a wire—produces a magnetic ¿eld, as in an electromagnet. Conversely, passing a loop of wire through a magnetic ¿eld produces a current in the wire. As a magnetic ¿eld moves, it changes in strength and direction, going from strong to weak and then back again (in the opposite direction) in a wave-like motion. This oscillation (sinusoidal change) of the magnetic ¿eld produces an electric ¿eld. The electric ¿eld also oscillates in a wave-like motion, perpendicular to its associated “Different kinds of magnetic ¿eld, changing in strength and electromagnetic direction as it moves, just as the magnetic ¿eld does. The two waves consist of selfradiation are propagating, oscillating electric and magnetic fundamentally the ¿elds perpendicular to each other and same thing, but perpendicular to their direction of motion. they have different An oscillating electric ¿eld produces an wavelengths, different oscillating magnetic ¿eld and vice versa. These propagate as electromagnetic waves. frequencies. They’re seen in different James Clerk Maxwell modi¿ed and ways using different combined four equations of electromagnetism detectors, but they’re that were known during his time to produce an equation that described this propagation all fundamentally the of electric and magnetic ¿elds: oscillating same thing.” (vibrating), propagating, and self-generating. Maxwell calculated the speed of these waves, which turned out to be none other than the known speed of light. Thus, light is a vibration of electric and magnetic ¿elds, an electromagnetic wave traveling at 300,000 kilometers per second. 97

Let’s look at this wave and some of its properties. The wavelength, denoted by the Greek letter O (lambda), is the distance from one wave crest to the next. This has units of length, such as centimeters. The frequency, denoted by the Greek letter Q (nu), is the number of times per second that a crest passes a ¿xed point Q; the units are 1/seconds, or hertz (Hz). Hence, the period of the wave, P (in seconds), is simply 1/Q. In general, the length per wave (O) multiplied by the number of waves per second (Q) gives the length per second traversed by the wave. This is its speed, v: OQ = v. In our case, v = c, the speed of light. Different colors of visible light correspond to electromagnetic waves having different wavelengths. The typical unit of wavelength of visible light is measured in angstroms (Å), which is 10–10 meters, or 0.1 nanometer (0.1 nm). Violet, blue, green, yellow, orange, and red light correspond to wavelengths of about 4000 Å, 4500 Å, 5000 Å, 5500 Å, 6000 Å, and 6500 Å, respectively. The spectrum of visible light extends beyond what we can see, including infrared, or beyond red, and ultraviolet, or beyond violet.

Electromagnetic Radiation Spectrum

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he main types of electromagnetic radiation and their approximate numerical dividing lines are as follows:

Lecture 19: Light—The Supreme Informant

• Gamma rays have wavelengths shorter than about 0.1 Å. • X-rays have wavelengths roughly in the range 0.1 to 100 Å. • Ultraviolet (UV) light spans wavelengths of 100 to 4000 Å. • Visible (optical) light is in the range 4000 to 7000 Å. • Infrared (IR) radiation goes from 7000 Å to about 1 mm. • Radio waves are longer than 1 mm and often up to 10 km or more. Gamma rays 0.1 Å

UV rays IR rays X-rays Radio waves 100 Å

1 mm

Optical light violet 4000 Å

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green 5000 Å

red 6000 Å

7000 Å

There are no qualitative differences between the types of electromagnetic waves, but the instruments and techniques used to detect them are often very different. The human eye is sensitive to visible light (4000 to 7000 Å), only a minuscule fraction of the entire electromagnetic spectrum. All electromagnetic waves in a vacuum travel with the same speed, c, regardless of O. The measured speed of light is independent of the relative speeds of the observer and the light source. This is admittedly counterintuitive, but it has been completely veri¿ed; indeed, it is one of the foundations of Einstein’s theory of relativity. Ŷ

Name to Know Maxwell, James (18311879). Scottish physicist; showed that visible light is only one form of electromagnetic radiation, whose speed can be derived from a set of four equations that describe all of electricity and magnetism. Also investigated heat and the kinetic theory of gases.

Important Terms electromagnetic radiation: Self-propagating, oscillating electric and magnetic ¿elds. From shortest to longest wavelengths: gamma rays, X-rays, ultraviolet, optical (visible), infrared, and radio. spectrum: A plot of the brightness of electromagnetic radiation from an object as a function of wavelength or frequency.

Suggested Reading Bova, The Beauty of Light. Kirkpatrick and Wheeler, Physics: A World View, 4th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Sobel, Light. Verschuur, Hidden Attraction: The History and Mystery of Magnetism.

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Questions to Consider 1. Why is electromagnetic radiation so important to astronomers? Why might it be useful to study objects over a broad range of wavelengths?

2. What are some examples in which you know that magnetic or electric ¿elds play a prominent role? Is there evidence that one type of ¿eld induces or interacts with the other?

3. Announcers at a certain radio station say that they are at “95 FM on

Lecture 19: Light—The Supreme Informant

your dial,” meaning that they transmit at a frequency of 95 MHz (95 megahertz, or 95 million cycles per second). What is the wavelength of the radio waves from this station?

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The Wave-Particle Duality of Light Lecture 20

“The energy of a photon is Planck’s constant, h, multiplied by its frequency. It does not have a corresponding mass. A photon is a massless particle. If you stopped it, you would destroy it; it would no longer exist. It only has energy as it’s traveling. It has no mass if you stop it; it ceases to exist.”

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n the previous lecture, we learned that light is a wave of electromagnetic radiation, changing electric and magnetic ¿elds that reinforce, support, and create one another as they move and propagate through space. How do we know light is a wave? There’s abundant evidence in nature to demonstrate that light is a wave, including the phenomena of supernumerary bows on the inner part of rainbows and the corona-like light effect that sometimes occurs around the Sun and Moon when viewed through clouds or fog. To understand these phenomena, we have to look at how waves interfere with one another, both constructively and destructively. Where the crests of the two waves meet, they reinforce each other constructively. Where a crest and a trough meet, they combine destructively, effectively canceling each other out. Two light waves that are in phase—constructive interference— whose crests and troughs are lined up, add together to make bigger crests and troughs. This creates a higher amplitude for the wave, or brighter light. If the waves are out of phase—destructive interference—where a crest is lined up with another wave’s trough, no light is produced. Light waves bending around water droplets go through holes or spaces between these water droplets, like light streaming through fog. But they also bend around the individual droplets to create semicircular wavelets of light having different paths. The wavelets of light can both constructively and destructively interfere, depending on the difference in paths. This type of interference is what creates the corona effect of light around the Moon or the Sun, the soft glow of rings of light close to the Sun or Moon that you sometimes see through fog.

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Lecture 20: The Wave-Particle Duality of Light

The patterns of light waves, whether constructively or destructively interfering, shift for different angles, different wavelengths, and different thicknesses of the objects they penetrate. For a good example of how light waves interact with each other to produce different light or colors, look at how light glints off a soap bubble and the patterns of colors it produces. In a supernumerary bow, two paths of two different rays penetrate a water droplet and emerge, having traversed slightly different path lengths. If they emerge out of phase, destructive interference occurs and creates a dark region in the bow. If they emerge in phase, constructive interference occurs and creates a brighter part of the bow. Light can also be a particle, forming little packets of energy called photons. A photon might be viewed as a package of energy with electromagnetic waves inside, each with a different color—that is, different wavelength and different frequency. White light consists of many photons with a range of wavelengths and frequencies; collectively, we say these photons produce white light. Experiments can distinguish the particle nature of light or the wave nature of light but never both simultaneously, which is explained in further detail below. A photon has no rest mass, but its energy, E, is given by the product of Planck’s constant, h, and its frequency Q: E = hQ. Planck’s constant is very small (6.627 u 10–27 erg seconds, in which an erg is a unit of energy); thus, the energy of any given photon is usually very small. Because a photon is a massless particle, if you stopped it, it would no longer exist. It has energy only as it travels. High-energy photons have higher frequencies but short wavelengths. Lowfrequency photons have lower frequencies but longer wavelengths. Thus, red-light photons have longer wavelengths, and violet-light photons have shorter ones. The energy of a photon is directly proportional to its frequency or inversely proportional to its wavelength: E = hQ, which can also be written as E = hc/O, because OQ = c. What prompted physicists to think that light could be quantized—that is, subdivided into small, measurable increments? Max Planck was the ¿rst to deduce the relationship between energy and the frequency of radiation. Planck considered the energy in a hot oven, which according to the classical theory of waves, should have progressively more and more waves of shorter 102

and shorter wavelength. This overabundance of short-wavelength waves, the energy in an oven, should technically be in¿nite—what’s called the ultraviolet catastrophe. However, an in¿nite amount of energy has not been spent heating up an oven, which would occur according to the wave theory. With the formula E = hQ, Planck quantized, or subdivided, the energy of light, thereby making the ultraviolet catastrophe problem disappear. Albert Einstein also quantized light and initially introduced the idea of photons when he considered a phenomenon called the photoelectric effect. Einstein noticed that when long-wavelength light, such as red light, is shone on a piece of metal, no electrons are ejected from the metal. Blue or violet light shone on the metal, however, produces electrons that pop off the metal’s surface. This “I’ve just given you indicates that light with longer wavelengths evidence that light is not able to store enough energy to pop off an electron, but shorter-wavelength light is. is a particle. Yet … I Thus, Einstein proposed that photons hit the said that it’s a wave, metal one at a time, and the blue and violet emphatically a wave. photons individually have enough energy to It shows all these kick off an electron, but the green and red photons individually do not have enough interference effects. energy to do so. So, which is it? Is it a particle or a wave? It’s Another indication of photons comes from the both. It’s really both Compton effect. If you shine electromagnetic at the same time, and radiation at a stationary electron, the wave that bounces off the electron is longer than this is the essence of the wave that hits it. For example, a blue quantum physics.” wave shone on the electron bounces off as a red wave, and the electron moves away in some diagonal direction. According to the wave theory, the electromagnetic wave interacting with the electron should cause it to oscillate (vibrate) at exactly the same frequency as the incoming wave; thus, the electron should emit a wave of exactly the same frequency—but it doesn’t. When a photon hits an electron, causing that electron to move, the photon loses energy, further evidence that light is also composed of photons, each with a certain amount of energy equal to Planck’s constant times the frequency. 103

Given the evidence, we can demonstrate that light is both a particle and a wave—a duality that is the essence of quantum physics. Collectively, many photons having the same energy produce an electromagnetic wave with the corresponding wavelength O. Sunlight and the light from most light bulbs consists of photons having a broad range of energies or wavelengths. Individual photons also have wave-like properties. Constructive and destructive interference effects, such as those seen in waves Àowing through gaps in a breakwater, are produced even when photons are sent one at a time through holes in a screen. Thus, a photon must interfere with itself, and it can do this only by passing through all of the holes, behaving like a wave. If we determine which hole the photon went through, the interference (wave-like) effects disappear; the photon acts like a particle because the measurement “disturbs” the photon, destroying the wave. This is a consequence of the Heisenberg uncertainty principle, set Did You Know? forth by Werner Heisenberg. Therefore, hat Einstein proposed either the wave-like or particle-like was that light comes with properties of light can be measured in these energy packages that he a given experiment, but both cannot be called photons. The photons hit measured simultaneously. the metal one at a time. The blue and violet photons individually This wave-particle duality of light have enough energy to kick off is also a quantum aspect of normal an electron, but the green and matter, including that of which humans red photons individually do are made. For example, an electron not. It is for this explanation can behave as a wave of wavelength that Einstein actually won the O = h/mv, in which m is its mass and Nobel Prize, not for relativity. v (not to be confused with frequency,

Lecture 20: The Wave-Particle Duality of Light

“Richard Feynman, one of the greatest, most intuitively thinking physicists ever to have lived, said this about quantum mechanics: ‘If you are not bothered and puzzled by it, you haven’t thought about it enough.’ ”

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Q) is its speed relative to the observer. Electrons passing through holes in a screen produce interference effects, just as light does. The large masses of most particles imply that their wavelengths 104

are exceedingly small, making it more dif¿cult to discern their wave-like nature than is the case for light. Many of the greatest minds of physics have struggled with this duality for a century, agreeing that it works but with no intuitive feeling for how. Ŷ

Important Terms Heisenberg uncertainty principle: One form: In any measurement, the product of the uncertainties in energy and time is greater than or equal to Planck’s constant divided by 2S. Another form: In any measurement, the product of the uncertainties in position and momentum is greater than or equal to Planck’s constant divided by 2S. photon: A quantum, or package, of electromagnetic radiation that travels at the speed of light. From highest to lowest energies: gamma rays, X-rays, ultraviolet, optical (visible), infrared, and radio. Planck’s constant: The fundamental constant of quantum physics, h; a very small quantity. rest mass: The mass of an object that is at rest with respect to the observer. The effective mass increases with speed.

Suggested Reading Gribbin, In Search of Schrodinger’s Cat: Quantum Physics and Reality. Hey and Walters, The Quantum Universe. Kirkpatrick and Wheeler, Physics: A World View, 4th ed. Lynch and Livingston, Color and Light in Nature. Minnaert, Light and Color in the Outdoors. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Wolf, Taking the Quantum Leap: The New Physics for Nonscientists.

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Questions to Consider 1. What do you think produces the rings of color seen when sunlight shines on a thin layer of oil? Why do the patterns change with viewing angle and other variables?

2. Describe the behavior of waves and how it differs from the behavior of particles. How can it be possible for light and matter to have both wavelike and particle-like properties?

3. If one photon has 10 times the frequency of another photon, which

Lecture 20: The Wave-Particle Duality of Light

photon is the more energetic and by what factor? What if the ¿rst photon has twice the wavelength of the second photon?

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The Colors of Stars Lecture 21

“When things are glowing due to their own jiggly motions, hot is blue, and cold is red. Hot stars are blue; cold stars are red.”

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n the last lecture, we learned that light is both a wave and a particle. Let’s look brieÀy at why stars emit different colors of light. Stars are huge, opaque, luminous balls of gas held together by the mutual gravitational attraction of their constituent particles. There are about 300 to 400 billion stars in a big galaxy like our own, each of which emits its own color. The hottest stars are bluish in color, and the coldest stars are reddish in color. Stars at intermediate temperatures appear white. Our Sun is a white star.

The colors indicate the temperature of the star’s surface, or photosphere. How? In a gas, particles move around randomly; temperature is a measure of how much these particles move. As the particles bump into each other, they accelerate because they’re changing their speed and direction of motion. Accelerated charged particles—electrons and the nuclei of atoms— emit electromagnetic radiation. When this radiation escapes from a star’s photosphere, it is seen as a particular color. The higher the temperature, the more random motions of particles there are, and the emitted light tends to have shorter wavelengths. The lower the temperature, the smaller the motions, resulting in light having predominantly longer wavelengths. Stars emit thermal radiation because of the random motions of particles inside them. The higher the temperature, the more rapid the motions. Stars are nearly ideal radiators because they emit light in such a way that the mathematical shape of the spectrum—the precise shape of the brightness versus wavelength or color—is dictated only by its temperature, not by its chemical composition or any other of its physical properties. Ideal radiators don’t reÀect light, nor do they transmit light like a window. They only generate light of their own; they are purely thermal emitters. They can also absorb light, thus becoming hotter and increasing the rate at which they emit thermal radiation. In the case of stars, the amount of radiation they absorb from the outside is usually negligible compared with the energy generated inside them. 107

When we discuss the temperature of stars, we use the absolute or Kelvin scale, in which 0 is the lowest possible temperature. On this scale, water freezes at 273 degrees and boils at 373 degrees. If we plot an average star’s brightness against the wavelength of the radiation emitted, we don’t see much in the violet part of the spectrum—short wavelengths. The spectrum peaks at some given wavelength, then drops toward the red. The shape of this emitted spectrum A Second Glance is one of a purely thermal e know that when a stove or emitter. If we plot the spectra coals glow red, they are hot. But of objects having different when a piece of metal glows blue, the temperatures, we can see temperature is even hotter. Given this their main characteristics. example, we might think that ice should Spectra of the hotter objects be hot because it’s bluish in color. peak more in the blue to However, ice’s blue color is not an effect violet range, while spectra of of how much movement its particles are the cooler objects peak in the experiencing but, rather, an effect of red to orange range. For any the type of light waves it reÀects. Ice object of a given size, a hotter reÀects incoming white light in such a object emits more light at all way that preferentially favors the blue wavelengths. The shapes over the red. of the plotted curves are all alike mathematically and are called Planck curves, after Max Planck, who ¿rst derived the mathematical form of the curve. The product of the temperature (T) and the wavelength of the peak of the spectrum O max is a constant: O max T = 2.9 u 107 Å K. This is known as Wien’s law, and it is consequence of the mathematical properties of Planck curves. People emit thermally at infrared wavelengths (about 105 Å, or 10 Pm , according to Wien’s law); thus, we can be seen with infrared detectors even at night. We are visible at optical wavelengths, however, only because of reÀected light (such as sunlight or light from indoor bulbs), which has nothing to do with the thermal emission produced by our own bodies.

Lecture 21: The Colors of Stars

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At higher temperatures, the area under the Planck curve is much greater for a hot object than for a cold object, indicating that, per unit of emitting area, a hot object emits much more radiation than a cold object. This is known as the 108

Stefan-Boltzmann law, another consequence of Planck curves. According to the Stefan-Boltzmann law, the energy emitted per square centimeter per second is proportional to the fourth power of temperature. We can write E = VT4, in which “We glow ourselves E is the energy emitted per unit area (e.g., due to the jiggly cm2) per second, T is the temperature, and motions, and that’s V is a constant of proportionality (known as in the infrared, but the Stefan-Boltzmann constant). Thus, if two stars have the same surface area, but one is we also reÀect light. twice as hot as the other, the hotter star emits The appearance we 24, or 16 times, more energy per second than have depends on the colder star. whatever dyes we It’s important to remember that reÀected light have, whatever colors differs from light seen as a result of thermal happen to reÀect best emission, though both can happen at the same in our clothes.” time. Planets shine at visible wavelengths because they reÀect sunlight (or the light of other stars, in the case of extrasolar planets). Planets also shine because of their own thermal radiation, glowing at infrared wavelengths (which are invisible) because of their warm temperatures. They are not hot, like optically visible stars. Ŷ

Important Terms extrasolar planet: A planet orbiting a star other than the Sun; an exoplanet. Kelvin: The size of 1 degree on the Kelvin (absolute) temperature scale, in which absolute zero is 0 K, water freezes at 273 K, and water boils at 373 K. To convert from the Kelvin scale to the Celsius (centigrade, C) scale, subtract 273 from the Kelvin-scale value. Degrees Fahrenheit (F) = (9/5)C + 32. Planck curve: The mathematical formula describing the spectrum of light produced by a perfect thermal emitter.

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Stefan-Boltzmann law: Law stating that, per unit of surface area, an opaque object emits energy at a rate proportional to the fourth power of its surface temperature.

Suggested Reading Hey and Walters, The Quantum Universe. Kirkpatrick and Wheeler, Physics: A World View, 4th ed. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. What is the difference between light emitted thermally and reÀected light?

2. In what ways are humans not a good approximation to ideal radiators? Why do astronomers and physicists use the concept of an ideal thermal radiator when, theoretically, such objects are almost nonexistent?

Lecture 21: The Colors of Stars

3. Why do we not see the thermal radiation of planets as we do with stars? 4. What is the surface temperature of a star whose spectrum peaks at a wavelength of about 6000 angstroms? If this star were hotter by a factor of 4, how much more energy would it emit per second?

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The Fingerprints of Atoms Lecture 22

“Each neutral element, and every ionization stage of any particular element has a unique ¿ngerprint of patterns that appears in its spectrum.”

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Let’s look at atoms in general. Atoms have a nucleus consisting of protons and neutrons; a cloud of electrons surrounds the nucleus. The whole structure is about 1 angstrom in size (10–8 centimeters), although the nucleus is much smaller. Each individual proton and neutron is only about 10–13 centimeters. Neutrons are neutral, protons are positively charged, and electrons are negatively charged. The electrons and protons attract one another, making atoms stable. As a consequence of quantum physics, electrons occupy discrete sets of A model of an atom. 111

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tars emit light through thermal radiation, the spectrum of which (the Planck curve) depends only on their surface temperature, not on their chemical makeup or other physical properties. However, because stars are not ideal radiators, their plotted curves deviate from a perfect Planck curve. This allows us to discover information on the stars’ chemical compositions, pressures, densities, and other aspects of their physical nature. In addition to a hot, opaque outer layer, stars also have a cooler, thinner atmosphere, where atoms interact with photons to produce deviations to the Planck curve. Typically, the deviations appear as absorption lines, parts of the spectrum where the light is less bright than in adjacent regions; in other words, there are fewer photons and, therefore, less energy in these regions, which appear as dark lines or depressions in the spectrum. Every element, and every neutral and ionized form of a given element, produces a unique ¿ngerprint in its set of absorption lines (or emission lines; see below).

Lecture 22: The Fingerprints of Atoms

energy levels, sometimes called orbits, though electrons do not really orbit the nucleus the way a planet orbits the Sun. A hydrogen atom in its neutral state has a lone proton in the nucleus and a single electron. That electron can be in its lowest energy level or higher energy levels. In general, the farther away an electron is from the nucleus, the greater its energy. What happens when a photon interacts with an electron? Photons can be absorbed by an electron, causing the electron to jump to a higher energy level. The photon is absorbed, or destroyed, in the process. The energy of the absorbed photon must be exactly equal to the difference between the two energy levels occupied by the electron. If a photon does not equal the energy difference between the two energy levels, it will just go right through the atom without being absorbed. The energy of the photon absorbed is equal to the difference in energy, 'E, between the fourth energy level, E4 (the higher level), and the second energy level, E2 (the lower level). 'E is equal to the energy of the photon, which in turn, must be Planck’s constant multiplied by the frequency of the photon, or Planck’s constant multiplied by the speed of light divided by the wavelength of the photon. Mathematically, this statement reads as follows: Ephoton 'E E4  E2 hQ photon hc / O . Thus, shining white light at a cloud of atoms (of a given element) causes their electrons to absorb or “ignore” the different-colored photons according to each photon’s energy and the atoms’ electronic energy levels. Once the electron is in an excited state, it generally jumps back to a lower energy level after a very short time interval, emitting a photon in any random direction and possibly re-emitting photons in a series of steps across energy levels. In a spectrum, absorbed photons create a de¿cit in their color range, known as an absorption line—also called Fraunhofer lines, after Josef Fraunhofer, who discovered them in the early 1800s. Atoms have many energy levels with many possible absorption lines. The spectrum of a gas cloud viewed without a star in the background can consist of many emission lines having different wavelengths. If you look through the cool cloud of gas at a bright continuum-emitting object, such as a hot star, absorption lines occur because some of the photons from the hot star were absorbed by the cloud of gas. Stars are more complicated than just clouds

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of cool gas because stars are opaque, hot, and have high densities, but many of the same physical principles are still relevant. A suf¿ciently energetic photon can completely dislodge an electron from an atom in a process called ionization. Knowing this also helps us to determine the elemental makeup of stars. Ionization can occur with any photon that has more energy than the minimum required energy to dislodge an electron. The resulting so-called free electron moves at random through the gas, no longer bound in a speci¿c energy level, until it comes close to a lone proton (or other atomic nucleus), latches onto it, and is re-bound to a speci¿c energy level. In so doing, it re-emits a photon because it must get rid of the energy that it previously absorbed. “When we look at This process of recombining with a positively stars and we examine charged nucleus is called recombination. An atom can also be ionized if another atom or an their spectra, lo and energetic electron hits it, forcing the electron behold, we see the away and causing it to wander around through patterns produced the gas in no speci¿c energy state. by hydrogen, and only by hydrogen. Each neutral element, and every ionization stage of any particular element, has a unique Therefore, we know ¿ngerprint of patterns that appears in its that the hydrogen is spectrum as absorption lines. Let’s consider present in the stars.” the case of hydrogen, the simplest (and most common) element. Absorption lines in the ultraviolet range are called Lyman lines and have corresponding Greek designations: alpha (D), beta (E), gamma (J), delta (G), epsilon (H), and so on, which refer to the electronic transitions. Absorption lines in the visible range of the spectrum are called Balmer lines, also with their associated Greek designations. Absorption lines in the infrared region of the spectrum are called Paschen lines, with their associated Greek designations. If you look at the spectrum of light going through hydrogen, for example, from the ultraviolet all the way to the infrared, you see a continuum. Superimposed on that continuum are these unique absorption lines. Thus, we can tell which element made them. If we obtain and analyze the spectra of stars—a process called spectroscopy— we can discern their patterns and know which elements produced them, thus giving us the chemical compositions of very distant stars. Ŷ 113

Important Terms absorption line: A wavelength (or small range of wavelengths) at which the brightness of a spectrum is less than it is at neighboring wavelengths. emission line: A wavelength (or small range of wavelengths) at which the brightness of a spectrum is more than it is at neighboring wavelengths. ionized: Having lost at least one electron. Atoms become ionized primarily by the absorption of energetic photons and by collisions with other particles. recombination: Process by which electrons combine with protons and other atomic nuclei to form neutral atoms; believed to have ¿rst occurred about 380,000 years after the Big Bang.

Suggested Reading Bova, The Beauty of Light. Hearnshaw, The Analysis of Starlight: One Hundred and Fifty Years of Astronomical Spectroscopy. Hey and Walters, The Quantum Universe. Lecture 22: The Fingerprints of Atoms

Kirkpatrick and Wheeler, Physics: A World View, 4th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. If someone were to say that we cannot know the composition of distant stars because there is no way to perform experiments on them in terrestrial laboratories, how would you respond?

2. What determines the various absorption lines (e.g., Lyman, Balmer, Paschen in the case of hydrogen) created by white light that is shining through a cloud of gas?

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3. An electron of an atom of an imaginary element has three energy levels: E 0 , E = 3, and E = 9. Suppose you know that the transition from the highest energy level to the middle energy level emits a photon with wavelength O = 3000 angstroms. What is the wavelength of a photon emitted in the transition from the middle energy level to the lowest energy level?

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Modern Telescopes Lecture 23

“Our atmosphere has many layers that are moving to and fro and causing twinkling of light. It also causes a blurring out of the light. For a long time, there was no way to overcome this problem. A telescope didn’t give you any additional clarity because the atmosphere got in the way.”

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Lecture 23: Modern Telescopes

tudies of light are what allow astronomers to gather information about the Universe. How do we collect and analyze light? Telescopes can magnify the apparent size of objects, as we discussed in Lecture 6. Magni¿cation depends on the focal lengths of both the primary lens and the eyepiece lens. Professional astronomers, however, rarely look through telescopes anymore because they can gather data using electronic detectors at the focal plane; no eyepiece is needed to magnify the image. Today, the primary purpose of telescopes is to gather light and make faint objects look brighter. The bigger the collecting area (the size of the mirror or lens), the more light can be captured and the brighter a given object will appear. Special detectors can collect even more light and store it or even create a digital image. The human eye sees a new image roughly every 1/30 of a second, refreshing an image in your brain 30 times a second. Exposing ¿lm with a telescope, on the other hand, allows us to collect light over a longer time; therefore, cumulatively, we would be able to see fainter stars. Photographic plates can store a lot of information over a wide area of the sky, but they also have some disadvantages. Like the human eye, they actually detect only about 1% or 2% of the incoming light. They also can’t record both bright objects and faint objects simultaneously. Photographic plates are non-linear; thus, if you expose them 10 times as long, the star doesn’t look 10 times brighter. Further, stars that are 10 times brighter than other stars don’t look 10 times brighter in a quantitative way. Modern electronic detectors are much better than photographic plates mounted on telescopes. Modern detectors can capture about 80% of the light from incoming photons, store it, and produce data in a digital format.

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At optical wavelengths, typically, a device known as a CCD, a chargecoupled device, is used. Digital cameras and camcorders use less expensive versions of CCDs. CCDs have what are called pixels, or picture elements. A star’s image might fall on a group of pixels, each of which registers a certain amount of light; central pixels in a star’s image register the most light. The CCDs have a linear response, so the brightness of a star can be quantitatively and accurately measured. CCDs have a wide dynamic range—very faint and bright stars can be measured in a given image. Unfortunately, CCDs have small ¿elds of view. The ¿eld of view can be increased by bunching together several or many silicon chips, but this can be expensive.

Did You Know?

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he diameter of a typical large telescope is 6 meters. The dilated human eye is about 6 millimeters, or 6/1000 of a meter, in diameter. Recall that the formula for the area of a circle is ʌr2 = ʌD2/4, in which r is the radius and D is the diameter. The ratio of light-collecting areas of a typical telescope (with diameter D2) and an eye (with diameter D1) is, therefore, given by A2/A1 = D22/D12 = (D2/D1)2. (Equivalently, you could square the ratio of the telescope radii.) If D1 is 6 × 10–3 m (the dilated human eye) and D2 is 6 meters (a large telescope), then A2/A1 = (103)2 = 106. Thus, all other things being equal, the telescope can detect stars that are about 1 million times fainter than those that can be detected by the human eye. Telescopes are important for collecting light, but they also provide higher resolution or clarity in order to detect ¿ner details. Any point-like object looks blurry at some level. Two objects, such as stars, spaced more closely together than their blur circles, will merge together. But as the diameter of the light-collecting lens or mirror increases, the stars’ clarity also increases. Quantitatively, we use angular measure to describe the resolution of a telescope. A full circle is divided into 360 degrees (360°). The Moon and the Sun each subtend (cover) about 1/2°. Each degree consists of 60 arc minutes (60’). Each minute of arc consists of 60 arc seconds (60”). A second of arc is small, approximately the angle subtended by a dime viewed from a distance of 3.7 kilometers. Optical telescopes can be made with an intrinsic resolution 117

of less than 1 arc second. The angular size of a blur circle in seconds of arc = 0.002 × O/D, in which O is the observation wavelength in angstroms and D is the diameter of the lens or mirror in centimeters. Turbulence in our atmosphere can blur light. Today, there are ways to partially overcome this problem, but for a long time, a ground-based telescope above 10 centimeters in diameter didn’t offer additional clarity. Larger refracting telescopes were built to gather more light, but they became unwieldy because of their size; supporting them at their edges causes them to sag in the middle. In addition, the lenses are dif¿cult to fabricate, and they absorb some of the incoming light. They also suffer from chromatic aberration, in which incoming light focuses at different points depending on its color.

Lecture 23: Modern Telescopes

To compensate for the problems associated with refracting telescopes, reÀecting telescopes were invented. You recall from Lecture 6 that these telescopes use mirrors to reÀect light. The simplest curved mirror to construct is a section of a sphere, but it suffers from spherical aberration: Parallel rays of light are reÀected to different foci depending on their distance from the “The whole [telescope] is center of the mirror, producing a fuzzy like some sort of an animal image. One solution is to make the working together to keep mirror parabolic or hyperbolic to get a single focus. the shape exactly the way it is. If you looked at it microscopically, it would be almost as though it’s alive. This technique of actively shaping the mirror in real time is called active optics, and it really works.”

ReÀecting telescopes can be very large. The observer can sit in a cage at the prime focus, making sure the telescope is pointing in exactly the right place and taking long exposures of objects. However, one quickly becomes cold and hungry while in the prime focus cage. Today, we often use Cassegrain telescopes, in which the light comes in from the stars, hits the primary mirror, goes back to a secondary mirror, then enters a hole in the primary mirror, going either to an eyepiece or to equipment that analyzes the light.

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For many decades, the world’s largest Recall that the size of the telescope was the Palomar 200-inch, or 5-meter, Hale telescope, completed blur circle is proportional in 1948. We didn’t need to build bigger to the wavelength of light telescopes because we continually divided by the diameter improved the detectors, culminating of the mirror. At radio with CCDs. By the 1990s, CCDs wavelengths, the blur circle became so ef¿cient that they were detecting up to 90% of the light. To is large and the resolution get more than 90% light, even larger is poor. Thus, radio telescopes had to be built. Mauna Kea telescopes tend to be very volcano in Hawaii has a collection of large so that the ratio of the some of the world’s biggest telescopes, including the twin Keck telescopes, 10 wavelength divided by the meters in diameter. These consist of diameter is relatively small, many individual, relatively inexpensive allowing for good clarity. hexagonal segments aligned in a honeycomb structure. Thin monolithic mirrors, up to 8 meters in diameter, can be made without the need for numerous segments, as in the honeycomb structure. Because they are lightweight, they don’t need massive support structures. Ŷ

Important Terms charge-coupled device (CCD): A solid-state imaging chip whose properties include high sensitivity, large dynamic range, and linearity. resolution: The clarity of detail produced by a given optical system (such as a telescope).

Suggested Reading Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Preston, First Light: The Search for the Edge of the Universe. 119

Watson, Stargazer: The Life and Times of the Telescope. Zirker, An Acre of Glass: A History and Forecast of the Telescope.

Questions to Consider 1. What is the light-gathering power of a telescope that is 3 meters in diameter relative to a 1-meter telescope?

2. Describe the relationship between the diameter of a telescope’s mirror and the clarity of a planet viewed through the telescope. Would you expect the clarity to be greater if the planet is viewed through a blue ¿lter (which transmits blue light) or a red ¿lter?

3. Is it a coincidence that major improvements in astronomical detectors

Lecture 23: Modern Telescopes

were made at nearly the same time as the electronics and computer revolution that began in the late 1970s?

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A Better Set of Eyes Lecture 24

“This technique of interferometry works quite well at radio wavelengths because the atmosphere is pretty stable and distorts them in a way that we can compensate. But recently we’ve extended this technique to infrared wavelengths on ground-based optical/infrared telescopes.”

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e continue our discussion of telescopes, ¿rst looking at how radio telescopes work. The size of a telescope’s blur circle—the clarity with which a star is viewed—depends on both the wavelength at which it is viewed and the diameter of the telescope. The blur grows in proportion to the observed wavelength divided by the diameter of the telescope. Because radio wavelengths are long, they A Second Glance produce large blur circles, ecall from Lecture 20 that light even when the radio telescope waves in phase—when each is as big as 330 meters in of their troughs meet and each of diameter. To compensate for their peaks meet—combine to create this problem, we use several a larger amplitude wave. This is radio telescopes together over constructive interference. Destructive a wide area, which all act as interference occurs where troughs a single large telescope. This meet up with peaks to cancel each collection of radio telescopes other out, producing no light. Also can gather light in an recall from Lecture 20 that light interferometric fashion, taking passing through two holes in a screen advantage of the property of will create a speci¿c interference light that it constructively pattern. In a similar way, two radio and destructively interferes telescopes can act as two holes, in a with itself. sense, to gather and analyze light and its particular interference pattern. Radio telescopes can be positioned in numerous ways to record the different patterns of interference, reconstruct the shape of the image, and provide a detailed picture of celestial objects. The so-called Very Large Array, a set of 27 dishes in Socorro, NM, has many different baselines

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in order to probe the structure of celestial objects on a variety of scales and at different angular resolutions. The University of California at Berkeley, in conjunction with the Search for Extra-Terrestrial Intelligence (SETI) Institute, is currently building an array of 350 radio telescopes, in part to search for possible signals from extraterrestrial beings. The telescopes will also be used for other, more conventional types of astronomical investigations.

© Comstock Images/Thinkstock

Lecture 24: A Better Set of Eyes

Radio telescopes can be set up across a whole continent to achieve a resolution of a 2500- or 3000-mile baseline. These telescopes can also be put on different continents to increase the effective diameter of the telescope even more and get an even smaller blur circle. Because a particular interference pattern depends precisely on the separation of the different telescopes, changes in the separation can be measured very accurately. In this way, we can measure continental drift, the slow movement of continents.

The Very Large Array of radio telescopes in New Mexico surveys the sky.

Interferometry works well at radio wavelengths because the atmosphere is stable and distorts the wavelengths in a way that we can compensate for. This technique has also been extended to infrared wavelengths on ground-based 122

optical/infrared telescopes, such as the pair of Keck telescopes on Mauna Kea Volcano in Hawaii and a set of four 8-meter telescopes (the Very Large Telescope) on a mountaintop in Chile. The overall image can be improved by building a group of smaller outrigger telescopes around two main telescopes, which gives more baselines. Let’s consider atmospheric turbulence. Atmospheric turbulence can make stars appear to twinkle. In a similar way, it can make stars appear blurry when viewed through a telescope. Astronomers have developed a method, called adaptive optics, to correct for distortion due to atmospheric turbulence. A small deformable mirror, whose shape can be changed quickly, can negate the distortions to produce plane-parallel waves. By monitoring the light from a bright star many times per second, we can correct for distortions to make that star appear less blurred. In addition, the appearance of any objects close to that star will also be corrected to show a clear, accurate view. When no bright star appears next to an object we want to view, we can create a fake star using a laser beam. The laser excites sodium atoms about 90 or 100 kilometers above the Earth’s surface. We can correct for those distortions of the fake star and the nearby object we want to view. One limitation of this technique is that it produces a limited ¿eld of view, only about 30 arc seconds in radius, though with promising new technology, the ¿eld of view will increase. Another limitation is that the technology works well at nearinfrared wavelengths but not yet at visible wavelengths. Despite advances in telescopes and their instruments, ground-based observations still have some limitations. As already mentioned, high clarity with adaptive optics is currently being achieved only over small patches of the sky and only at infrared wavelengths. Light pollution causes the sky to glow, which makes viewing celestial objects more dif¿cult. The sky is especially bright at infrared wavelengths. We can’t see much beyond the optical window into the ultraviolet and infrared wavelengths because of absorption by ozone and water vapor (respectively) in Earth’s atmosphere. In addition, x-rays and gamma rays are blocked by certain molecules in the atmosphere. How, then, do we avoid the atmosphere to observe some of these wavelengths? Airplanes mounted with telescopes and infrared detectors can travel above the 2- to 10-kilometer water layer in the Earth’s atmosphere. 123

However, we need spacecraft to get above most of the molecules to detect gamma rays and x-rays.

STScI/NASA

Lecture 24: A Better Set of Eyes

We take a look now at some space telescopes. Throughout the 1990s, NASA’s Compton Gamma Ray Observatory provided great data at gammaray wavelengths from high above Earth’s atmosphere. The Hubble Space Telescope (HST) is named after Edwin Hubble, who discovered the expansion of the Universe. Developed by NASA and launched into nearEarth orbit in 1990, it has a 2.4-meter-diameter mirror polished to a very smooth surface. HST received some bad press when it was discovered that its mirror was slightly the wrong global shape, creating spherical aberration that blurred images. In 1993, Space Shuttle astronauts were able to ¿t HST with corrective optics, which then produced fantastic images from space. HST is still operating as of mid-2006. Discoveries made with the HST have greatly advanced the ¿eld of astronomy. In some topics, the textbooks have essentially been rewritten.

The Hubble Space Telescope orbits Earth.

NASA’s Chandra X-Ray Observatory also orbits high above the Earth’s atmosphere. Chandra gives clear views of the Universe at x-ray wavelengths, probing some of the most energetic processes in the Universe. X-ray telescopes have to be constructed so that light is bounced off mirrors at a 124

glancing angle. In this way, light is focused by a nested set of paraboloids and hyperboloids to achieve a blur circle of about 1 arc second. NASA’s Spitzer Space Telescope observes infrared wavelengths; thus, it is sensitive to dust particles heated to a modest temperature by nearby stars. Spitzer can peer into regions where stars are currently forming. The Swift gammaray observatory has detected so-called gamma-ray bursts, which are star explosions that give rise to high-energy electromagnetic radiation. These sharp bursts of gamma rays last from a few seconds to a few minutes. We hope to continue developing the James Webb Space Telescope, to be completed by 2012 or 2013, a successor to the Hubble Space Telescope but optimized for infrared wavelengths. Ŷ

Name to Know Hubble, Edwin (18891953). American astronomer, after whom the Hubble Space Telescope is named. He proved that “spiral nebulae” are galaxies far outside our own Milky Way and discovered the expansion of the Universe (Hubble’s law) by recognizing that the redshift of a galaxy is proportional to its distance. He also proposed a widely used morphological classi¿cation scheme for galaxies.

Important Terms adaptive optics: Optical systems providing rapid corrections to counteract atmospheric blurring. gamma-ray burst (GRB): A brief burst of gamma rays in the sky, now known to generally come from exceedingly powerful, distant objects.

Suggested Reading Center for Adaptive Optics, UC Santa Cruz, cfao.ucolick.org/. Cristensen, Fosbury, and Kornmesser, Hubble: 15 Years of Discovery. Kerrod, Hubble: The Mirror on the Universe. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. 125

Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Petersen and Brandt, Hubble Vision: Astronomy with the Hubble Space Telescope.

Questions to Consider 1. Was the Hubble Space Telescope worth the roughly $2 billion that it cost? Reconsider this question after ¿nishing the video course.

2. Why is it sometimes better to use a small telescope in orbit around the Earth than it is to use a large telescope on a mountaintop? Conversely, why is it better for some purposes to use a large telescope on a mountain instead of a small telescope in space?

3. What mirror diameter gives 1 arc second resolution for radio radiation of wavelength 1 m? Compare this with the size of existing optical telescopes.

4. Why are optical and radio telescopes sometimes built in groups,

Lecture 24: A Better Set of Eyes

or arrays?

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Our Sun, the Nearest Star Lecture 25

“I discussed a few lectures ago how electrons can be knocked off when things collide with atoms. To get iron to be 13 times ionized, you have to collide with very high speeds. That’s what a high temperature means; it means that particles are moving with a very high speed.”

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With the proper equipment, we can view many of the Sun’s features, including sunspots, prominences, energetic eruptions called Àares, and the corona during an eclipse. Spectra taken of the Sun reveal that its outermost parts are composed mostly of hydrogen. For every million atoms of hydrogen, the Sun has about 85,000 atoms of helium, 850 atoms of oxygen, 400 atoms of carbon, 120 of neon, 100 of nitrogen, and 47 of iron. The Sun also has other trace elements. Earth has silicon, oxygen, carbon, and some hydrogen, among other elements. The Universe Extreme Ultraviolet Imaging Telescope (EIT) is mostly hydrogen. By mass, image of a huge, handle-shaped prominence the Sun is 73% hydrogen, taken on Sept. 14,1999. 25% helium, and only 2% elements heavier than helium. Helium was ¿rst discovered in spectra of the Sun. It was not known here on Earth before the Sun was studied.

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ith this lecture, we enter the second and largest section of the course (Lectures 25 through 70), during which we will study the enormous variety of objects in the Universe. The next 12 lectures are devoted to objects in our Solar System—beginning with our Sun.

Let’s look at a cross-section of the Sun. The Sun’s core is about 15 million degrees on the absolute Kelvin temperature scale. This is where nuclear reactions generate the Sun’s energy. Surrounding the Sun’s core are the radiative zone and the convective zone; these terms describe how energy moves from the core to the surface. Radiation is the transport of energy from a light-emitting object; for example, a candle radiates visible light and heat (infrared rays), which can warm up a nearby thermometer. The Sun’s gases are so dense and packed with so many moving electrons that the progress of light is impeded. Thus, photons bounce off electrons and atomic nuclei, eventually making their way from the hot interior to the cooler outer regions. This process is similar to conduction, in which a spoon, for example, heated at one end will conduct heat to the other end as a result of atoms colliding with one another, transferring their energy. In this way, the Sun’s energy moves through the radiative zone through a combination of radiation and conduction generally called radiative diffusion.

Lecture 25: Our Sun, the Nearest Star

The convective zone surrounds the radiative zone. Convection is the process by which a bubble of gas or liquid is heated, then expands to becomes less dense and more buoyant. As it rises, it deposits energy to the surrounding area above. Bright specks called granules on the Sun’s surface indicate that it undergoes convection. The specks are hot pockets of gas that have risen to the surface, radiating energy to their surroundings before cooling and returning to the interior, where they heat up again. Now let’s look at the Sun’s surface phenomena. The photosphere is the visible surface of the Sun; here, gas becomes suf¿ciently hot and dense to appear opaque rather than transparent. The photosphere temperature is 5800 degrees Kelvin (K). Photons don’t travel freely through opaque regions. Instead, they bounce around and collide with each other. A thin layer called the chromosphere surrounds the photosphere; it is about 10,000 kilometers thick and 10,000 K. The chromosphere looks pink because electrons in hydrogen atoms in the chromosphere are moving from the third to the second energy level, creating a pink hue. The corona surrounds the chromosphere and is visible to the naked eye during a solar eclipse. The corona is shaped from charged particles traveling along magnetic ¿elds. The magnetic ¿elds of the Sun change with time, changing the corona’s shape. The corona has a temperature of about 2 million K in some parts and a little cooler in other 128

parts. We know it is hot because it emits a lot of x-rays and it has highly ionized atoms. Oddly, though the corona’s particles are moving at high speeds, its density is very low. Therefore, a sentient body immersed in the corona could theoretically freeze to death (ignoring light coming from the photosphere) because that body would radiate energy at a faster rate than it would receive energy from particles colliding with it. The corona merges with an outer extension called the solar wind, where particles escape into space at a variety of speeds, typically less than 1000 kilometers per second. Eruptions on the Sun’s surface are called prominences. These occur when chromospheric gas has been ejected from the Sun at temperatures around 10,000 K. Prominences can be studied in great detail from spacecraft positioned between the Earth and the Sun at one of the so-called Lagrange points to allow a continuous view of the Sun. Two such spacecraft are the Transition Region and Coronal Explorer (TRACE) and the Solar and Heliospheric Observatory (SOHO). Prominences are gentle eruptions; more energetic eruptions are called solar Àares, which emit huge amounts of particles at speeds approaching 5% of the speed of light. Prominences and Àares take up regions of space on the Sun’s surface that are much bigger than Earth itself. Coronal mass ejections (similar to Àares) occur when large amounts of material burst The Sun’s from the Sun. Some of these appear to be associated with speci¿c solar Àares, while others seem to occur magnetic poles at random. Coronal mass ejections are not readily switch every understood but might be related to large pockets of 11 years for especially strong magnetic ¿elds that tangle together reasons that and release their magnetic energy in one burst. are still not fully What are sunspots and how are they formed? understood. Sunspots are dark blotches on the Sun’s photosphere, consisting of a central dark region called the umbra and a lighter region called the penumbra. Their shapes change with time; sometimes they appear in large groups and sometimes more or less individually. Sunspots appear dark because they represent cooler regions on the photosphere that don’t emit as much light. Against a dark sky, however, a 129

Lecture 25: Our Sun, the Nearest Star

sunspot would actually glow brightly. Sunspots are about 2000 K cooler than the surrounding photosphere. Per unit of time and per unit area, a sunspot emits about 20% as much energy as the surrounding photosphere. Sunspots are cooler because they have strong magnetic ¿elds, which appear like the magnetic ¿elds of a bar magnet, or the superposition of several bar magnets (producing a more tangled magnetic ¿eld). Strong magnetic ¿elds inhibit or restrain the Àow of hot, charged particles from the Sun’s interior as they move upward because these charged particles tend not to cross magnetic ¿eld lines. As charged particles try to move up through the process of convection and become restrained, the gas cools and is not replenished with fresh hot gas. The Sun’s rotation rate can be measured by monitoring the movement of sunspots. The Sun’s average rotation takes about one month. The number of sunspots and the number of Àares, prominences, and other instances of solar activity varies with time. This so-called solar activity cycle lasts about 11 years. When sunspots are more active, the Sun has more prominences, more Àares, more coronal mass ejections, and more activity in general. Let’s now examine the Sun’s magnetic ¿eld and some of its other characteristics. The Sun’s magnetic ¿eld reverses itself every 11 years, switching the Sun’s north and south poles with each other and resulting in an overall sunspot cycle (including the reversing polarity) that is 22 years long. The magnetic ¿eld, and the reversal of its polarity, may occur as a result of convection, which generates electromagnetic currents within the Sun. If the core temperature is very hot compared to the surface, convection increases and a strong magnetic ¿eld is created. If the core temperature is cooler relative to the surface, convection decreases and a weaker magnetic ¿eld is created. The Sun rotates more quickly at its equator (26 days) than at its poles (36 days). At the equator, the magnetic ¿eld lines become stretched and tangled. This tangling effect may lead to the strong magnetic ¿elds we see in sunspots. Sunspots tend to appear in pairs. In the northern hemisphere, the pairs are aligned with north at the left and south at the right; it’s the reverse in the southern hemisphere. The Sun also vibrates, or oscillates in size, getting a little bit bigger, then a little bit smaller over short intervals of time. Study of these solar oscillations can tells us about the Sun’s interior. If our Sun is a typical star, then much of what we learn from its magnetic activity cycle, sunspots, Àares, solar oscillations, and so on should be applicable to our study of other stars, too. Ŷ 130

Important Terms convection: Process by which bubbles of gas or liquid repeatedly heat and expand, rise and give off energy, and fall again; seen in the stars and in Earth’s core. core: In a main-sequence star, roughly the central 10% by mass. In an evolved star, usually refers to the degenerate central region.

Suggested Reading Bhatnagar and Livingston, Fundamentals of Solar Astronomy. Golub and Pasachoff, Nearest Star: The Surprising Science of Our Sun. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Zirker, Journey from the Center of the Sun.

Questions to Consider 1. Consider a sunspot viewed through a dark ¿lter or reasonably thick fog. If the sunspot is barely visible to the unaided eye (which has a resolution of about 1 or 2 arc minutes), and the Sun’s diameter is 30 arc minutes, physically how large is the sunspot relative to the Earth?

2. If the solar corona is much hotter than the photosphere, why isn’t it much brighter than the photosphere, per unit area?

3. Suppose the temperature of a sunspot is 4000 K and that of the surrounding photosphere is about 6000 K. Per unit area, about how much energy does the sunspot emit per second compared with the photosphere?

4. What is the process of convection? Give an example from everyday life. 131

The Earth, Third Rock from the Sun Lecture 26

“We begin our study of planets in our Solar System with the four innermost or terrestrial planets: Mercury, Venus, Earth, and Mars. ‘Terrestrial,’ in Latin, means Earth or Earth-like—so, all four of these planets are much like the Earth in their overall characteristics.”

Lecture 26: The Earth, Third Rock from the Sun

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hat does Earth’s structure look like? Earth has a solid iron-nickel core surrounded by a liquid nickel-iron core, which in turn, is surrounded by a thick mantle, separated into the lower mantle and upper mantle. The lower mantle is somewhat viscous, continually Àowing, and to some degree, the upper mantle moves as well. A solid crust Àoats on top of the upper mantle. By studying seismic waves, or earthquake waves, and how they travel through the Earth, we can discern its basic structure. There are a number of different types of waves, but the three main kinds are P, K, and S waves. The P and K waves are longitudinal, moving up and down and compressing in the same direction as the direction along which the waves move. They travel through Earth’s layers and bend as each layer’s density changes. S waves, or sheer waves, move transversely through rock; they don’t travel through liquid very well. We know that at least part of Earth’s core is liquid because sheer waves don’t travel through that core. Earth began as a molten substance, undergoing a process called differentiation, in which dense matter—such as iron—sank to the core, and lighter matter— silicates and other substances—moved to the surface. As the crust cooled, it became solid, though parts of the mantle are still liquid because it retains some heat. We think the Earth was formed by the coalescence of dust particles, rock, gas, and other matter. The matter gravitationally attracted more and more material, which—in the process of colliding—released energy in the form of heat and produced an early, molten Earth. The radioactive elements in the matter decayed into stable isotopes. The decaying process freed more energetic particles, which in turn, released heat energy, further contributing to a molten state. Earth remains partially molten because of the continual, long-term decay of radioactive elements.

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The Earth’s crust Àoats on the soft, slowly churning mantle, which produces a phenomenon called continental drift. More generally, we call this phenomenon plate tectonics because the crust is divided into different units, or plates, that move relative to one another. The idea of plate tectonics was ¿rst articulated by Alfred Wegener in 1912, when he noticed that Africa’s west coast looked as if it ¿t with South America’s east coast, like a jigsaw puzzle. Other continents exhibited similar features, and indeed, fossil evidence shows similarities in species between these matching coasts. Wegener theorized that Earth’s continents had all been connected at one time and slowly drifted apart. Today, scientists believe his theory is correct. About 200 to 250 million years ago, there was probably one single supercontinent that we call Pangaea. About 180 million years ago, it split into two subcontinents that we call Gondwanaland and Laurasia. Further subdivisions occurred thereafter. “The very high Other supercontinents may have existed before abundance or Pangaea—such as Pannotia 600 hundred million years ago or Rodinia 1.1 billion years ago. This proportion of breaking apart and coming together of continents oxygen in our appears to have been common on Earth throughout atmosphere most of its history. demands an explanation. When Earth’s plates collide, they form mountains and volcanoes along the collision boundaries. That explanation When they slide suddenly relative to one another, is life itself.” earthquakes occur, their magnitude related to how much energy is released. A so-called Ring of Fire exists around the Paci¿c plate through Japan, the Philippines, and the west coast of North America, where Earth experiences many earthquakes and volcanoes. The movement of Earth’s mantle drives continental drift; this movement occurs by convection, when a pocket of material gains enough heat to become buoyant and rise. As the mantle material in the Earth is heated, it expands and rises toward the surface, giving off heat. As the heat is lost, the material becomes dense and sinks again, and the process repeats. Some of this superheated liquid erupts from Earth’s core in volcanoes as magma. Mars, with only about half the size of Earth, lost most of its heat long ago and no longer experiences convection to a degree that would move

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plates relative to one another. Instead, the crust of Mars has frozen to a single solid plate. Earth has a 6400-kilometer radius, yet its atmosphere is only about 100 kilometers thick. The thin atmosphere extends from Earth’s surface to a region called the ionosphere, where its constituents are mostly ionized. We live in the Earth’s troposphere, and most weather phenomena take place within about 18 kilometers or so from the surface of the Earth. About 20% of the atmosphere is oxygen, while 79% is nitrogen. This proportion of oxygen is relatively high. Earth’s atmosphere may have begun without any appreciable oxygen. But as plant material began to form, oxygen was produced in the process of photosynthesis. Beginning a few billion years ago, the oxygen content gradually increased to what it is now. Because the complete decay of organisms uses up as much oxygen as the organisms produced when alive, to have a net excess of oxygen today, full decay of these early organisms could not have been possible. Massive sediments likely covered these organisms, preventing them from completely decaying. They now have formed into coal and petroleum, which of course, when burned, complete the process of decay, consuming oxygen. Oxygen in our atmosphere usually occurs in diatomic molecules, O2. Another form of oxygen molecule is called ozone, O3, which is poisonous to humans. At altitudes of 20 to 40 kilometers, however, ozone protects us from the Sun’s harmful ultraviolet radiation. Ozone also protects the water vapor in our atmosphere, allowing rain to fall by preventing water vapor molecules from being broken apart by the Sun’s ultraviolet rays. Like the Sun, Earth’s magnetic ¿eld resembles that of a bar magnet, with a north and south pole and well-ordered ¿eld lines around it. The magnetic ¿eld reverses itself from north pole to south pole roughly every 300,000 years, varying from a few tens of thousands of years to a few tens of millions of years. The poles were last reversed about 700,000 years ago, and we don’t know when the reversal will occur again. When reversals occur, the ¿eld is weak, increasing the number of charged particles reaching us from the Sun because the particles don’t get trapped by Earth’s magnetic ¿eld. Evidence in molten rock turned solid over millennia preserves a record of magnetic orientation, proving that reversals occur. Though we’re not certain, the magnetic ¿eld may exist because as Earth rotates, its partially liquid core produces electric currents, which produce magnetic ¿elds. A hotter 134

The Earth’s tides are a consequence of differential forces, mostly caused by the Moon. The side of Earth closest to the Moon feels a An image of Earth taken from space. greater gravitational force than the Earth’s center, which in turn, feels a greater force than the side farthest from the Moon. This is called a differential force, or a tidal force. Thus, relative to Earth’s center, the near side of Earth feels a force toward the Moon, while the far side of Earth feels a force away from the Moon, consequently “stretching” the Earth on both sides. Water Àows in the direction of the pull, resulting in a bulge toward and away from the Moon and a de¿cit of water in other regions. As Earth rotates about its axis during 24 hours, it experiences two high tides and two low tides. One tide is usually bigger than the other because of the tilt of Earth’s axis. The Sun also affects tides but not as much as the Moon because the Sun is so far away. Tides tend to be extreme (very high and very low) when the Sun, Earth, and Moon are aligned. These are known as spring tides, but the term has nothing to do with the season. Differences between high and low tides are smaller when the Sun, Earth, and Moon form a 90-degree (right) triangle. These are known as neap tides. Ŷ

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core produces a stronger magnetic ¿eld because in order for energy to move outward from the core, a higher degree of convection must take place. More convection drives more electric currents, which produce the magnetic ¿eld. Charged particles from solar eruptions can sometimes hit the magnetic ¿eld of the Earth, get trapped, and excite electrons in atoms and molecules of nitrogen and oxygen in our atmosphere to jump to higher energy levels. When the electrons jump back down to lower levels, releasing this energy, the result is the display of the northern and southern lights—the auroras.

Important Terms isotopes: Atomic nuclei having the same number of protons but different numbers of neutrons. tidal force: The difference between the gravitational force exerted by one body on the near and far sides of another body.

Suggested Reading Hartmann and Miller, The History of the Earth: An Illustrated Chronicle of an Evolving Planet. Lang, The Cambridge Guide to the Solar System. McFadden, Weissman, and Johnson, eds., Encyclopedia of the Solar System. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Lecture 26: The Earth, Third Rock from the Sun

Sagan, Pale Blue Dot: A Vision of the Human Future in Space.

Questions to Consider 1. Look at a globe and make a list or sketches of which pieces of the various continents probably lined up with each other before the continents drifted apart.

2. Explain why there are typically two high tides and two low tides per 24-hour day at a given coastal location. Also, if the Moon were farther away from the Earth than it actually is, how would tides be affected?

3. Discuss the structure of Earth’s interior, the various physical processes occurring within it, and the methods by which we learn about the Earth’s interior.

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Our Moon, Earth’s Nearest Neighbor Lecture 27

“In the famous Pink Floyd CD, Dark Side of the Moon, they must have been referring to the dark side at any given time because there’s no perpetually dark side of the Moon.”

J

ust as the Moon is the primary cause of tides on Earth, so, too, does the Earth cause tidal forces on the Moon. Though different phases of the Moon illuminate different parts, from Earth, we still see only one face as a result of the Moon’s synchronous rotation. Synchronous rotation means that the Moon’s orbit around Earth takes place at the same rate as its rotation about its own axis. We believe that initially, the Moon rotated about its axis much more quickly than its orbital time around Earth, gradually slowing due to an effect known as tidal friction. In the same way that the Moon’s pull on Earth leads to bulging and the phenomenon of ocean tides, the Earth has been pulling on the Moon over time, changing its shape. As the Moon stretched, rocks rubbed against each other, causing friction and releasing energy that gradually slowed the Moon’s rotation. Ultimately, the Moon’s rotation slowed down to a rate equal to that of its revolution (orbit) around the Earth, ¿xing its orientation relative to Earth. The Earth’s rotation is also slowing because of the Moon’s tidal pull; as the oceans move, they dissipate energy in the same way that the changing shape of the Moon did. Thus, Earth’s 24-hour day slows by about 1 second every 100,000 years. Because of this complex interaction, the Moon is gradually moving away from the Earth at a rate of about 3.8 centimeters per year. In half a billion years, the Moon will be too small to fully cover the photosphere of the Sun, so total solar eclipses won’t occur. The Moon doesn’t have a perpetually dark side. In fact, nearly 15 days of continuous daylight occur on any given spot on the Moon, followed by 15 days of darkness because of its motion around Earth and its synchronous rotation. During its days of light, the Moon’s temperature increases to 130° C; during its nights in darkness, temperatures plummet to about –110° C. Without an atmosphere, the Moon can’t trap heat, as the Earth does. 137

There’s very little erosion on the Moon and no water or atmosphere. The Moon has craters within craters; Crater 308 on the moon, taken by the Apollo 11 thus, we can tell the crew from orbit. relative ages of features simply by observing what features are on top of other features. Areas with more craters are likely older than those regions without many craters (the maria). But to determine absolute ages, we have to sample the Moon’s rocks using a process called radioactive dating. A radioactive element, such as uranium, decays “For a long time, into daughter products (e.g., lead) with a certain half-life. After a time interval of one half-life, there was a debate: half of the original quantity of the substance Are the craters remains; after two such time intervals, oneimpact craters, or quarter of the original quantity remains, and so are they of volcanic on. If the rock is solid, the daughter and parent products cannot mix with their surroundings origin? Their shape and become diluted. By measuring the ratios gives one clue.” 138

NASA

Lecture 27: Our Moon, Earth’s Nearest Neighbor

Through lunar studies, we have learned much about the Moon and its history. Evidence suggests that the Moon has frozen water at the bottom of some craters, possibly deposited by comets hitting it billions of years ago. The Moon has lots of craters, as well as wide basins known as maria, which is Latin for “seas.” We now know that maria are really frozen lava Àows. Evidence shows that most of the Moon’s craters are not volcanic but, rather, formed from the impact of space debris, which causes a characteristic peak in the crater’s center.

of parent and daughter products, the ages of the rocks (that is, the time since they were last molten) can be determined.

NASA/JPL/Caltech

A glorious time in the history of space exploration was the era of the lunar landings of Apollo 11 through Apollo 17 (19691972). The astronauts did a number of experiments on the Moon. They also left equipment (e.g., seismographs, radar reÀectors). Moon rocks from various regions were returned to Earth. G. The Moon’s oldest rocks are about 4.4 billion years old. The heavily cratered highlands are 3.9 to 4.3 billion years old. Rocks from the maria are between 3.1 and 3.9 billion years old. Because the lava Àows (maria) have fewer craters, we know that most of the Moon’s craters were formed more than 3 billion years ago. Indeed, the bombardment of the Moon was heavy shortly after its formation, about 4.5 or 4.6 billion years ago. However, the Moon does have a few “recent” craters, which were formed 1 to 1.5 billion years ago, such as Tycho and Copernicus. The early era of bombardment of the Moon was probably the last stage of the formation of the Solar System.

Edwin (Buzz) Aldrin Jr. deploys passive seismic equipment.

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Lecture 27: Our Moon, Earth’s Nearest Neighbor

Let’s consider the Moon’s overall structure, size, and origin. The Moon has a small iron core surrounded by a region in which moonquakes occur, on top of which is the upper mantle, and ¿nally, a crust. The Moon experiences little internal motion and is, to a large extent, geologically dead. The Moon’s far side—the side that’s perpetually away from the Earth—looks distinctly different from the near side. Its far side has comparatively few lava Àows and many more cratered regions. For this reason, it must have formed early in the history of the Moon. The far side may also have a thicker crust than the near side, perhaps accounting for the lower number of lava Àows; if the crust were thicker, then there wouldn’t be as many weak spots through which lava could Àow from the interior. The mass of the Moon is about 1/80 of the mass of the Earth, and the radius is about 1/4 (actually, 1/3.7) of the Earth’s radius. What would we weigh on the Moon? The gravitational force per unit mass on the Moon’s surface, GM/R2 (in which M is the mass of the Moon and R is its radius), is (1/80)/(1/3.7)2 | 1/6 times that on the Earth’s surface. Because the weight of an object is a measure of the gravitational force on it, objects weigh about 1/6 as much on the Moon as they do on Earth. The Apollo astronauts were able to jump relatively far, though inhibited by their bulky space suits. The Moon is about 1/4 of Earth’s size. If we compare this size ratio to that of other planets and their associated moons, our Moon is relatively large. Because such a large moon orbits Earth, the inclination of Earth’s rotation axis is stable. A smaller moon would allow the Earth’s rotation axis to chaotically change every few million or tens of millions of years because of the gravitational pull of Jupiter and other planets. Thus, the seasons would change every few million years. Four hypotheses attempt to describe how the Moon was formed. One hypothesis is that the Moon formed through ¿ssion; that is, it broke off from Earth. Another is that the Moon initially came from far away and was “captured” by Earth. A third is that the Moon essentially condensed out of the material of which the Solar System was made at the same time that Earth condensed. The fourth hypothesis is that a large object, roughly the size of Mars or larger, collided with Earth, expelling some of Earth’s material and forming a disk around the Earth. The Moon subsequently formed from the coalescence of this material. We think this is the most likely explanation because lunar material is very much like that of Earth’s mantle in composition. Ŷ 140

Important Terms synchronous rotation: The rotation of a body having the same period as its orbit. weight: The force of the gravitational pull on a mass.

Suggested Reading Chaikin, A Man on the Moon. Hockey, The Book of the Moon: A Lunar Introduction to Astronomy, Geology, Space Physics, and Space Travel. McFadden, Weissman, and Johnson, eds., Encyclopedia of the Solar System. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Sagan, Pale Blue Dot: A Vision of the Human Future in Space.

Questions to Consider 1. It is sometimes said that the U.S. mission to the Moon was entirely motivated by the Soviet Union’s launch of the Sputnik satellite in 1957. Do you think the scienti¿c bene¿ts of lunar landings would have been suf¿cient reason to take the risks and spend the funds?

2. What effect did the heavy cratering of the Earth during the ¿rst half billion years of its existence (as determined by the ages of lunar craters) probably have on the development of life on Earth?

3. Why are we more likely to learn about the early history of the Earth by studying the rocks from the Moon than those on the Earth?

4. Calculate your weight if you were standing on the Moon. 141

Mercury and Venus Lecture 28

“Though broadly similar in nature to the Earth—they are, after all, terrestrial planets—they differ quite a bit in detail, especially Venus, which was thought to be Earth’s sister planet.”

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Lecture 28: Mercury and Venus

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et’s ¿rst explore Mercury. It’s dif¿cult to study Mercury from Earth because Mercury is nearly always in the same direction as the Sun. As we saw with Venus in a previous lecture, Mercury also transits the face of the Sun a few times per decade. But because it is dif¿cult to see surface details on Mercury, for a long time, its rotation rate was not known. Mercury’s rotation period was eventually measured using the Doppler effect, which we will discuss in more detail in a later lecture. This effect is an enormously important tool for determining the radial velocity of an object—that is, its speed as it moves toward you or away from you. Essentially, the Doppler effect is seen when we measure the wavelengths of absorption or emission lines in a spectrum. If a source that is emitting light or sound waves is moving relative to an observer, then along the direction of motion, the Mercury as seen by Mariner 10 on March 29, 1974. source partially keeps up with its most recently emitted wave crest before it emits another wave, causing the crests to bunch up. If we stood in front of an approaching source and measured its emitted waves’ lengths, we would ¿nd that they are shorter than waves trailing behind the source (if we stood behind the source as it moved away from us).

In a similar way, we can shine a radio wave—radar—at two edges of a rotating planet. If the planet is rotating counterclockwise as seen by us, then the side approaching us will reÀect the radio wave toward us with a higher frequency—shorter wavelength. ReÀected waves from the edge that recedes from us will have a lower frequency—longer wavelength. From the amount of this shift, the rotation rate and, hence, the period of Mercury’s rotation could be determined. Mercury rotates about its axis in 59 days, or three times for every two times that it orbits the Sun. This so-called 3:2 resonance occurred because the Sun exerts tidal forces on Mercury, slowing down its initially more rapid rotation. Mercury has a 176-day day/night cycle: Nighttime and daytime each lasts for a consecutive 88 days. Moreover, Mercury has an almost negligible atmosphere. Thus, Mercury heats up a great deal during the day (430° C) and plummets to very low temperatures at night (–170° C). This is similar to, but more extreme than, the temperature range on the Moon. Mercury’s gravity at its surface is only about 40% that of Earth. Mercury’s surface is heavily cratered; most of these craters formed more than 4 billion years ago. As we saw on the Moon, some craters near Mercury’s poles appear to contain frozen water that came from comets. Venus is the second planet from the Sun. Much of Venus is covered in clouds made of sulfuric acid. The clouds cause a high degree of reÀectivity; this high reÀection fraction is called a high albedo in astronomical terms. Despite its proximity to the Sun, the fact that Venus has an atmosphere led people at one time to believe that it might be habitable. In fact, the planet is not habitable because of its high temperatures and high atmospheric pressure, 90 times that of Earth. Venus displays mountains, valleys, craters, and plains. It has only one thick crust with no plates, though it does have some high parts that we call continents—two main continents. Venus may have had global lava Àows as recently as half a billion years ago. There also appear to be a few semi-active volcanoes now that emit some sulfur dioxide fumes. Venus’s surface temperature is 480° C all the time, everywhere. Given its distance from the Sun and assuming that it has a transparent atmosphere, Venus’s surface temperature should be only about 100° C. How did the temperature become so high? Venus suffered a runaway greenhouse effect. Its atmosphere consists of 96% carbon dioxide and about 4% nitrogen. Venus is illuminated by sunlight, but much of that light 143

Lecture 28: Mercury and Venus

Earth would be about 60° F cooler with no greenhouse effect. In addition, Earth has a very effective way of recycling its greenhouse gases, primarily carbon dioxide and water vapor. Why does Venus not have such an ef¿cient system as “There is an operating Earth’s? Venus may have once had oceans, but greenhouse effect without enough rain to remove atmospheric carbon dioxide (as Earth has), carbon dioxide here on Earth. People would build up from volcanic vents. This say, ‘Oh, that’s caused any water to evaporate more quickly, bad, a greenhouse which in turn, would have increased the water effect, something to vapor content of Venus’s atmosphere. Instead be feared!’ No—in of raining down, Venus’s water vapor rose to an altitude at which ultraviolet radiation from moderation, it’s a the Sun could break it apart. The hydrogen, good thing.” being light, escaped from Venus, but the

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reÀects off the high clouds, back into space. Some visible sunlight penetrates and heats the surface, exciting the constituent particles of the surface, which then emit infrared radiation. This radiation is absorbed by the carbon dioxide in the atmosphere of Venus, thereby warming the atmosphere, which in turn, reheats the surface of the planet, increasing its temperature. The Venus as seen from Mariner 10. amount of infrared rays leaking out of Venus’s atmosphere is balanced by the amount of visible light coming in. Venus has reached an equilibrium temperature, which is much higher than it would have been if carbon dioxide allowed infrared light to escape. Though this trapping of heat on Venus is called the greenhouse effect, this is a misnomer because true greenhouses operate differently: Air in a true greenhouse is heated inside, and the structure itself prevents that hot air from mixing with the cooler surroundings.

carbon combined with oxygen to form more carbon dioxide in the atmosphere, creating a runaway greenhouse effect. What can we learn from Venus? Though not entirely unanimous, there is scienti¿c consensus that Earth is warming at an alarming rate. If global warming is occurring, are people to blame? Our burning of fossil fuels does create an increased amount of carbon dioxide in the atmosphere. The carbon dioxide content in CO2 molecules per million molecules of air from the 1950s to 2005 shows seasonal oscillations. But there has also been a dramatic increase, which—probably not coincidentally—started around the time of the industrial revolution. Some scientists argue that an increase in carbon dioxide will lead to more water vapor in the atmosphere, creating clouds, which would offset global warming by blocking more of the Sun’s radiation from reaching Earth. Other scientists believe that an increase in the water vapor increases greenhouse heating and more than compensates for the extra sunlight reÀection off the clouds. An extreme runaway greenhouse effect, like that on Venus, almost certainly won’t occur on Earth for various reasons; however, it is widely acknowledged that even a rise in temperature of a few degrees could cause devastation on Earth. Global warming is a serious concern, and more extensive studies are necessary to determine its effects. In any case, we should do what we can to maintain the atmospheric content of Earth because we don’t yet know what could happen by changing it. Ŷ

Important Terms greenhouse effect: The effect by which the atmosphere of a planet heats up above its normal equilibrium temperature because it absorbs infrared radiation from the surface of the planet. radial velocity: The speed of an object along the line of sight to the observer.

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Suggested Reading Beatty, Petersen, and Chaikin, eds., The New Solar System, 4th ed. Hodge, Higher Than Everest: An Adventurer’s Guide to the Solar System. Lang, The Cambridge Guide to the Solar System. McFadden, Weissman, and Johnson, eds., Encyclopedia of the Solar System. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Sagan, Pale Blue Dot: A Vision of the Human Future in Space.

Questions to Consider 1. Do you think the evidence for human-induced global warming of Earth is strong? Will it be too late to reverse the trend, if and when the effect becomes so large that its presence is unambiguous?

2. Suppose a planet had an atmosphere that was opaque in the visible but transparent in the infrared. Describe how the effect of this type of atmosphere on the planet’s temperature differs from the greenhouse effect. Lecture 28: Mercury and Venus

3. If you increased the albedo (reÀectivity) of Mercury, would its surface temperature increase or decrease?

4. Why do radar observations of Venus provide more data about its surface structure than a Àyby with optical cameras outside Venus’s atmosphere?

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Of Mars and Martians Lecture 29

“Though there are some other interesting features on Mars that sometimes appear as though they are produced by intelligence, we are unlikely to receive a Martian valentine entitled ‘From Mars, with love,’ despite heart-shaped craters that do look like they were perhaps carved by some sort of intelligence.”

I

Let’s look at some of the basic characteristics of Mars. Mars is about half the diameter of the Earth, though somewhat larger than Mercury. It has two small moons, Phobos and Deimos, which are only about 20 kilometers in diameter. Mars has polar ice caps, predominantly made of frozen carbon dioxide—or dry ice—that grow and shrink with the seasons. However, water does lie underneath the dry-ice caps. Mars’s seasons are similar to Earth’s because the tilt of its rotation axis is 25.2 degrees relative to the Solar System axis. Earth’s axis is tilted 23.5 degrees. Mars also has a 24.5-hour day/night cycle. Earth has an exceptionally clear view of Mars every two years when it comes close to our planet. Called opposition, the con¿guration is such that Earth comes between Viking 2 site on the surface of Mars. Mars and the Sun. 147

NASA

n addition to Mercury, Venus, and Earth, the fourth and ¿nal terrestrial planet is Mars, about 1.5 times farther from the Sun than Earth is. For a long time, humans have been intrigued by the so-called Red Planet. Mars is named after the god of war, largely because of its reddish-orange color. We now know that its color comes from iron oxides—that is, rust. Additionally, Mars’s surface is more yellowish-brown than red, though when viewed from Earth, it has a distinctly reddish-orange color.

Lecture 29: Of Mars and Martians

Mars has a thin atmosphere, only about 1% of the thickness of Earth’s atmosphere. It consists of 90% carbon dioxide. But because it’s such a thin atmosphere and because Mars is signi¿cantly farther from the Sun than Earth, it goes through extreme temperatures: from –130° C to (rarely) about 30° C. Mars’s atmosphere supports ferocious winds, which sometimes create huge dust storms. In addition, Mars has craters, volcanoes, canyons, and dunes, but it no longer has plates—there is only one thick crust. The planet’s most striking feature is Valles Marinaris, a giant canyon, which if placed on North America, “Unlike our Grand would stretch from coast to coast. Most of the Canyon, which was canyon was created as a gash as a result of tectonic motions early in the history of Mars. carved by the action The main canyon was a rupture in the plate. of water, most of Valles Marineris In addition to the tributaries of Valles was created as a Marinaris, Mars shows other evidence that liquid water once existed on the planet. Mars gash due to tectonic has ancient riverbeds and Àood plains. Some motions early in the impact craters have a teardrop shape, formed as history of Mars.” a result of erosion, further indicating that water once Àowed on the surface. Photographs show what look like ancient dry riverbeds, as well as evidence of sedimentation and melting permafrost, which may have created the gullies we see. The Mars Odyssey spacecraft measured neutrons coming from the surface of Mars as a result of interactions with charged particles from the Sun. It found a de¿cit, which—by inference—is associated with the presence of hydrogen atoms that block neutrons dislodged from the soil. Presumably, the hydrogen is in the form of water. The presence of ¿ne sediments may indicate water, and so might the existence of a substance called hematite, which forms in the presence of water. Moreover, a mineral called jarosite has been identi¿ed on Mars, a hydrated sulfate, which contains water and forms in its presence. If Mars used to have liquid water, why doesn’t it exist anymore? Mars’s atmosphere is too thin to support liquid water; its atmospheric pressure is only 1% that of Earth’s, and a much higher pressure is needed to support liquid water. The strong evidence for the long-ago existence of liquid water suggests that Mars’s atmosphere must have been thick at one time. We think 148

that, indeed, Mars did have a lush atmosphere for the Astronomy in History ¿rst half billion to billion art of our fascination with Mars was years of its existence. What fueled by the Italian astronomer happened to Mars’s thick Giovanni Schiaparelli, who in 1877, atmosphere? There are two reported seeing canali on Mars. In main hypotheses. If Mars Italian, this word means “channels,” experienced a cooling trend, but it was improperly translated to then some of its atmospheric “canals” in English. People thought carbon dioxide would that the canals might have been built freeze, decreasing the degree by intelligent life forms. Percival of greenhouse warming. In Lowell subsequently made detailed turn, this would lead to lower telescopic observations of Mars, temperatures, more freezing also reporting a network of straightof carbon dioxide, and even lined canals crisscrossing the planet. less greenhouse heating, As telescopes improved, it became and so on. This is called an obvious that Lowell’s observations inverse greenhouse effect were Àawed. Further, missions to Mars and is the opposite of what have proved that there are no canals as seems to have happened on such on Mars. Venus. Another suggestion is that because Mars is small and lost its heat early in its history, its magnetic ¿eld was weak. Without a strong magnetic ¿eld, the intense solar wind from the young Sun could help blow away Mars’s atmosphere, accounting for the thin atmosphere. At this point, an inverse greenhouse effect could have taken over.

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Did Mars ever support life and could it support life now? Investigations of Martian soil samples by the Viking spacecraft in the mid-1970s failed to prove that some form of life exists on Mars. In fact, no organic compounds whatsoever were found in soil analyses. The lack of evidence thus far, however, doesn’t mean that life never existed on Mars; indeed, life may exist deeper in the soil, but there is still no clear evidence for it. The most intriguing evidence for Martian life comes from a 4.5-billion-year-old chunk of rock from Mars that hit Earth and landed in Antarctica about 13,000 years ago. An analysis of this meteorite found that it contains carbonate globules, which generally form in liquid water. Polycyclic aromatic hydrocarbons 149

(PAHs) were also found. Though PAHs can be formed in ways other than by life, the ones found in the meteorite are relatively unusual. The Martian meteorite contains magnetite, a mineral produced by some types of bacteria. In addition, it has tube-like organisms that resemble nanobacteria on Earth. However, they are much smaller than the nanobacteria found on Earth. Most researchers feel that the evidence for microbial life in the Martian meteorite is not compelling. All of the observed phenomena have more conventional non-biological explanations. The results are highly controversial, and additional tests are necessary. It is conceivable that if Mars did have primitive bacteria and microbes early in its history, and if a meteorite from Mars landed on Earth a very long time ago, this could have “polluted” the Earth with life for the ¿rst time. Then, through evolution, all of the modern life forms came about. If so, we may be the descendants of Martians. Though this is a highly speculative idea, it’s not impossible. Ŷ

Important Term terrestrial planets: Rocky, earth-like planets. In our Solar System: Mercury, Venus, Earth, and Mars.

Suggested Reading

Lecture 29: Of Mars and Martians

Beatty, Petersen, and Chaikin, eds., The New Solar System, 4th ed. Boyce, The Smithsonian Book of Mars. Goldsmith, The Hunt for Life on Mars. Hartmann and Miller, The Grand Tour: A Traveler’s Guide to the Solar System, 3rd ed. Kargel, Mars—A Warmer, Wetter Planet. McFadden, Weissman, and Johnson, eds., Encyclopedia of the Solar System.

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Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Squyres, Roving Mars: Spirit, Opportunity, and the Exploration of the Red Planet.

Questions to Consider 1. Plan a set of experiments or observations that you, as a Martian scientist, would have an un-crewed spacecraft carry out on Earth to ¿nd out if life exists here. What data would your spacecraft radio back if it landed in a corn¿eld, in the Sahara, in the Antarctic, or in New York’s Times Square?

2. How likely do you think it is that humans will eventually “terraform” Mars so that its climate becomes suitable for humans?

3. What evidence exists that there is, or has been, liquid water on Mars? Where is some of that water now?

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Jupiter and Its Amazing Moons Lecture 30

“What a wonderful system Jupiter presents, with a whole variety of moons, each having a personality of its own, and lots of cool features to study.”

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Lecture 30: Jupiter and Its Amazing Moons

e now move from the small terrestrial planets in our Solar System to the gas, liquid giants—the Jovian planets—beginning with a look at Jupiter. Jupiter, named after Jove—the king of the gods— is 11 times the diameter of the Earth and about 320 times its mass. It is the largest planet in our Solar System, being roughly 1/10 the Sun’s radius. It is about 5 AU from the Sun and takes 12 years to revolve around the Sun. Jupiter is somewhat squashed, or oblate, because of its rapid rotation. Despite its size, Jupiter rotates fully about its axis in only 10 hours, causing its equatorial region to bulge signi¿cantly. Jupiter consists mostly of hydrogen and helium; thus, its composition is much more representative of the Universe than Earth’s and close to the composition of our Sun. The planet is about 86% hydrogen and 14% helium (by number of atoms) but includes small quantities of other elements, mostly in such compounds as methane and ammonia. Jupiter has a rocky core, resembling Earth’s, surrounded by an icy layer, which is itself surrounded by a layer of extremely compressed hydrogen known as metallic hydrogen. Above the layer of metallic hydrogen is molecular hydrogen, where hydrogen forms a diatomic (two-atomic) molecule. It also has a strong magnetic ¿eld—10 times stronger than Earth’s—probably caused by the rapid rotation of the conducting layer of metallic hydrogen. Thus, Jupiter has polar auroras because its magnetic ¿eld is highly ef¿cient at trapping charged particles from the Sun. It is easy to understand why the giant planets, such as Jupiter, retained so much hydrogen and helium, whereas the terrestrial planets did not. Because the giant planets are much farther from the Sun, they are heated less. Hydrogen and helium move less rapidly and, therefore, were retained by the planets’ gravitational ¿elds. Jupiter’s surface is gaseous, as opposed to our own solid surface on Earth. In this sense, its surface is like the Sun’s photosphere—a place beyond which the gases become thick enough to be opaque. 152

Unlike the Sun’s photosphere, however, Jupiter’s surface reÀects visible sunlight. Because it doesn’t generate visible energy from within, it doesn’t glow visibly from within, though it does glow from within at infrared wavelengths. Jupiter’s colorful bands are seen predominantly parallel to the equator, but they do twist and form oval shapes. The various colors are caused by slight differences in composition, including more methane, ammonia, and sulfur compounds. Jupiter’s most famous landmark is the socalled Great Red Spot, which has been seen for more than 300 years. The Red Spot is two to three times the size of Earth and is like a giant hurricane. Unlike hurricanes, however, which are low-pressure systems on Earth, Jupiter’s Great Red Spot is a high-pressure system. Jupiter is still contracting on the inside. This contraction liberates energy and is the likely explanation for the planet’s stormy atmosphere. The liberated energy heats Jupiter’s interior before escaping from the hot core to the cooler surface, creating “Some of these things convection currents. Convection, coupled with Jupiter’s rapid rotation, you could hardly even call causes the complex and active surface moons. They’re smaller storms. Spacecraft, such as the Pioneer than 4 kilometers in missions, the two Voyagers, Galileo, diameter. They’re captured and Cassini, have provided a wealth of information about Jupiter and asteroids, things like that. its moons. There might be hundreds or even thousands of Jupiter has four main moons, called the moons. Some of them are Galilean satellites in honor of Galileo pretty interesting. None are Galilei, whose observations in 1610 advanced the Copernican revolution. quite as interesting as the These moons are easily seen through four main moons.” amateur telescopes and sometimes create eclipses (or even double eclipses) of the Sun. Three of Jupiter’s moons are larger than Earth’s Moon and one is larger than the planet Mercury. The moon Io is the most geologically active body in our Solar System, with erupting volcanoes spewing sulfur compounds. The magma differs from that on Earth, but clearly, Io’s interior is molten because of tidal forces caused by Jupiter. Tidal forces stretch Io just as Earth’s Moon stretches our oceans to create tides. Io is close to Jupiter, 153

NASA/JPL/Caltech

Lecture 30: Jupiter and Its Amazing Moons

orbiting in only about two days, and Jupiter’s mass is enormous, so the tides are extreme. In addition, because of a gravitational interaction with the other Galilean satellites, Io’s orbit is forced to be quite eccentric; that is, at one end of its orbit, it comes close to Jupiter, and at the other end, it’s farther away. Thus, Jupiter’s tidal force causes Io to become more stretched when it’s close to Jupiter and more round in shape at the farther end of its orbit. This constant change in Io’s shape creates friction in its interior and causes heat to build up, melting the material. Magma then penetrates weak spots in the crust, erupting in volcanoes.

Io is the most geologically active body in our Solar System.

Another moon, Europa, has a relatively smooth, icy surface with some fractures. We know this moon is young because it doesn’t have many craters. When craters form on ice and the ice is not too hard, the craters will be destroyed over time because of the shifting of the ice. Europa also shows ridges, similar to those found on a frozen layer of water with slushy water 154

Farther out, Ganymede is even less affected by changing tidal forces than Europa, and thus, its interior is less molten. Ganymede A close-up of Jupiter’s moon Europa shows has some grooved terrain its ridges. that may have been produced in the last billion years or so. Most of the terrain, however, is covered with craters that are perhaps 2 to 4 billion years old and remain preserved because of little tectonic activity or erosion. Callisto, the outermost of Jupiter’s Galilean moons, has perhaps the oldest surface in the Solar System, heavily pockmarked with craters that formed 4 billion years ago. Jupiter has many more moons; about 60 are known now and more are being discovered all the time. Many are very small, less than 4 kilometers in diameter; these are probably captured asteroids. Jupiter has a thin ring, discovered by the Voyager spacecraft, about 1.8 Jupiter radii from its center. Ŷ

Important Terms asteroid: Chunk of rock, smaller than a planet, that generally orbits the Sun between Mars and Jupiter. Galilean satellites: The four large moons of Jupiter (Io, Europa, Ganymede, Callisto).

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underneath that continues to shift and fracture. Europa is partially molten inside because it, too, suffers from a changing tidal effect, though not as extreme as that of Io because Europa is farther away from Jupiter than Io is. With liquid water, or at least a slush, under its frozen surface, Europa is a prime candidate for the search for life elsewhere in our Solar System.

Suggested Reading Beatty, Petersen, and Chaikin, eds., The New Solar System, 4th ed. Beebe, Jupiter: The Giant Planet. Fischer, Mission Jupiter: The Spectacular Journey of the Galileo Spacecraft. Hartmann and Miller, The Grand Tour: A Traveler’s Guide to the Solar System, 3rd ed. McFadden, Weissman, and Johnson, eds., Encyclopedia of the Solar System. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. Given that Jupiter’s diameter is 11.2 times that of Earth, about how many Earths could ¿t inside of Jupiter? (Neglect the empty spaces that exist between closely packed spheres.)

2. Do you think it is possible to determine Jupiter’s mass by measuring the Lecture 30: Jupiter and Its Amazing Moons

orbital properties of its moons?

3. How can we determine the approximate age of a moon’s surface from the number of visible craters per unit area? (Assume the cratering rate as a function of time was similar to that on Earth’s Moon.)

4. Through a telescope on Earth, can you sometimes see Jupiter in its crescent phase, just as the Moon is sometimes a crescent? Why or why not?

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Magni¿cent Saturn Lecture 31

“The decades ahead promise a lot for the further study of Saturn, to see how this system developed and to determine whether it, too, may have formed life as we know it.”

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aturn is the sixth planet from the Sun and is much like Jupiter but smaller. It is 9.5 AU away from the Sun. Saturn is mostly hydrogen and helium, with an Earth-like core. Its average density is only 0.7 g/cm3, less than that of water. It could Àoat in a bathtub of water on Earth, if Earth (and the bathtub) were big enough. Saturn’s internal structure resembles that of Jupiter, with a rock and ice core surrounded by a layer of metallic hydrogen (though not as thick as Jupiter’s), in turn surrounded by a vast layer of molecular hydrogen. Saturn has an outer atmosphere similar to Jupiter’s. It has bands and spots, but there is less energy driving Saturn’s storms. The different colors are the result of different amounts of ammonia, methane, and other trace contaminants. Saturn has a moderately strong magnetic ¿eld that causes auroras, the glowing polar lights. Saturn’s most notable feature is its magni¿cent rings, though all four of the giant planets have some rings. The rings are about 20 meters thick; compared to the extent of Saturn’s size, the ratio of ring thickness to ring diameter is similar to a CD with normal thickness but 30 kilometers in diameter. The rings are made of chunks of ice and rock, which may have been a moon that never formed or, perhaps, a weakly structured moon or comet that came too close to Saturn and was torn apart. How could this occur? Every planet is surrounded by a region called the Roche limit, where tidal forces are suf¿ciently strong to prevent an object from coalescing due to the gravitational interactions of all the minor particles. The rings of Saturn are within this Roche limit. If a strong rock reaches the Roche limit, it won’t be broken apart because it’s held together by its internal strength. Why haven’t Saturn’s rings dissipated with time? If they formed 4.5 billion years ago, when Saturn formed, they should have disappeared long ago because collisions among the particles tend to dissipate the rings with time. 157

There may be some physical effect we don’t know of that holds the rings in place. More likely, the rings are a fairly young phenomenon, only about 100 million years old. There might be a system of moons holding the rings’ particles in place, but we don’t really know why the rings are still there.

NASA/JPL/Caltech

Lecture 31: Magni¿cent Saturn

Saturn rotates on its axis tilted at 27 degrees, compared to Earth’s tilt of 23.5 degrees. Because of this tilt and the planet’s orbit, from Earth, we view Saturn’s rings from a different perspective as the years pass. Sometimes, we see the rings as if looking down on them; about seven years later (roughly a quarter of Saturn’s orbital period around the Sun), we see the rings edge-on. Seven years later, we see the underside of the rings, relatively face-on, and so on. Thus, twice per 30-year revolution around the Sun, the rings come into view edge-on, appearing as a thin dark line on the face of the planet.

An image of Saturn’s rings taken by Voyager 2 at a distance of 8.9 million km on August 17, 1981.

Let’s take a closer look at Saturn’s rings. From Earth, only two to four rings are visible. The main two rings (A and B) are separated by a dark gap called Cassini’s Division, discovered in 1675. The faint ring C is interior 158

to ring B. In ring A, there’s another gap called Encke’s Division, but that is hard to see. Cassini’s Division is caused by what we think is a resonance between one of Saturn’s moons, Mimas, and the particles that would have been in the location of the gap. Those particles orbit Saturn twice for every one time that Mimas orbits Saturn. Mimas repeatedly exerts a gravitational tug on the particles, causing them to wander away from that location. This repeated gravitational tug clears out a region of Saturn’s ring corresponding to Cassini’s Division. We think that some of the other gaps are caused by resonances with other moons. Saturn has more than 100,000 individual minor ringlets; some appear in groups. But within major rings, there are many other “Saturn, to me, is the smaller subdivisions. In fact, even Cassini’s most beautiful planet Division has a few minor ringlets within it. It is also possible that small moonlets occur other than Earth. I within the rings, clearing away the rings’ gaps know beauty is in the that we see through gravitational tugs. eye of the beholder, but nevertheless, One of Saturn’s main moons is called Titan, discovered in 1655 by Christian Huygens. who could not Titan has a thick nitrogen atmosphere, just as say that Saturn is Earth does (though 1/5 of Earth’s atmosphere beautiful?” is oxygen). Reactions within that nitrogen atmosphere—for example, when lightning occurs—form hydrocarbons, particulate matter, and other compounds. Titan has smog and haze, which along with possible hydrocarbons raining out of the atmosphere, led to the theory that Titan could have hydrocarbons on its surface, possibly dissolved in methane lakes. Titan’s thick atmosphere, along with some greenhouse warming, could make it a relatively warm planet compared to its neighbors, the frozen giants. Using radar, we have mapped Titan’s terrain and know that it has high areas and valley-like features. Some darker areas could possibly be methane lakes, but we have no direct evidence for this so far. The Huygens probe sent to Titan from the Cassini spacecraft revealed what appeared to be a shoreline with rivers emptying into a lake or what was once a lake. Again, we have no direct evidence that these features now contain liquid, yet the images are intriguing. The probe also saw boulders on what appears to be a Àood plain.

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Saturn has other interesting moons, including one called Enceladus. Enceladus has a high albedo, or reÀectivity, in some parts where there are few craters, suggesting that it’s a young surface. Some other parts have many craters. The Cassini spacecraft also found plumes of particles and gas arising from certain regions of this moon, and studies showed that they are waterice and water vapor. The source of the plumes was traced back to striated regions on the surface. Temperature measurements of those regions showed that, though much of the area is cold (75 K), other parts are signi¿cantly warmer by as much as 15 K. The warmer regions coincide with ¿ssures or valleys within this striated region. The current hypothesis is that Enceladus is covered by cold water-ice, below which may be pressurized liquid water at roughly the melting point of ice, 273 K. Through these ¿ssures, water can Àow and turn into vapor and ice, causing the plumes.

Lecture 31: Magni¿cent Saturn

In the same way that Jupiter’s tidal forces heat Io’s interior, Enceladus has changing tidal forces that occur during its elliptical orbit around Saturn. The liquid water on Enceladus may be very close to the surface, and there’s a chance that a probe sent to this moon someday could dig down into one of those ¿ssures and take a sample of water, in search of life. The moon Iapetus has one very bright side and one dark side, as though its bright side has some freshly fallen snow, probably methane, ethane, or maybe some water-ice. The moon Mimas is highly pockmarked with craters, including one giant one. Rhea also has a very old surface, highly pockmarked with impact craters. Saturn has dozens of other moons, many of which are probably captured asteroids or, perhaps, remnants of former bigger moons that collided with each other and broke apart. Ŷ

Important Term Roche limit: The distance from the center of a planet at which the planet’s tidal forces prevent particles from forming a moon through their mutual gravitational attraction.

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Suggested Reading Beatty, Petersen, and Chaikin, eds., The New Solar System, 4th ed. Hartmann and Miller, The Grand Tour: A Traveler’s Guide to the Solar System, 3rd ed. Hodge, Higher Than Everest: An Adventurer’s Guide to the Solar System. McFadden, Weissman, and Johnson, eds., Encyclopedia of the Solar System. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. Why are the chemical compositions of Jupiter and Saturn so close to that of the Sun but those of the terrestrial planets are not?

2. How do studies of other planets and moons in the Solar System potentially help us understand various aspects of Earth better, such as its climate, surface features, interior, and history?

3. Using a ground-based telescope equipped with a spectrograph, how might you deduce that Saturn’s rings are rotating, and how would you measure the rotation speed as a function of distance from the planet’s center?

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Uranus and Neptune, the Small Giants Lecture 32

“Uranus and Neptune were not known to the ancients. The ancients knew about the Sun, the Moon, Mercury, Venus, Mars, Jupiter, and Saturn.”

Lecture 32: Uranus and Neptune, the Small Giants

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oth Uranus and Neptune are considered the outer giant planets. Uranus and Neptune are only about 4 times the diameter of the Earth, which is smaller than Jupiter (11 times Earth’s diameter) and Saturn (9.5 times Earth’s diameter). Uranus and Neptune are more closely aligned with Jupiter and Saturn in their overall characteristics than they are with the terrestrial planets. For example, they consist mostly of hydrogen and helium, and they have rocky and icy cores. Their masses are only about 14.5 times (Uranus) and 17 times (Neptune) that of Earth. Because they have less mass, Uranus and Neptune never compress hydrogen into the metallic form; molecular hydrogen is the most compressed form of hydrogen on these planets. A much larger portion of their masses is made up of a rocky, Earth-like core with an icy layer around it. The ice is water-ice, as well as frozen carbon dioxide, methane, ammonia, and other compounds. For some reason, Uranus and Neptune have considerably less hydrogen and helium than Jupiter and Saturn. Let’s look at Uranus ¿rst in greater detail. Its correct pronunciation is YOURuh-nus. Uranus is named after the mythological father of the god Saturn, who in turn, is the father of the god Jupiter. Uranus was discovered by Sir William Herschel in 1781. Uranus is the seventh planet from the Sun, about 20 AU away, and takes about 84 years to orbit the Sun. It’s composed mostly of hydrogen and helium but has outer layers of methane and ammonia. Methane reÀects blues and greens well, giving the planet a bluish-green tinge. Uranus’s axis of rotation is tilted 98 degrees relative to the perpendicular to its orbital plane. Thus, its axis of rotation is nearly coincident with the orbital plane, resulting in 21-year-long seasons having extreme conditions, in terms of the lengths of the day and night. We don’t know what causes this extreme tilting, but perhaps the planet collided with a large object early in its history. Uranus’s extreme tilt isn’t unique: Venus tilts 177 degrees (actually spinning 162

Given Uranus’s large tilt toward the Sun, we might expect that the heating of its surface would be extreme from season to season and that it would experience many storms. However, its atmosphere shows little activity, and its surface was essentially devoid of features in the ¿rst detailed photographs obtained with the Voyager An image of Uranus and its satellites. spacecraft. Some storms have recently been observed with ground-based telescopes equipped with adaptive optics. Nevertheless, the amount of atmospheric activity is less than that of the other giant planets. The planet’s magnetic ¿eld is tipped by 60 degrees relative to the axis of rotation, and it is offset by a large amount from the center of the planet. In most planets, the magnetic ¿eld and the axis of rotation are relatively aligned, and the offset from the planet’s center is small. The peculiarities of the magnetic ¿eld likely were not caused by a collision with another celestial object because Neptune has a similarly strange magnetic ¿eld, yet its axis of rotation is nearly perpendicular to its orbital plane. Rings were discovered around Uranus in 1977, when Uranus passed in front of a bright star; these rings blocked the star’s light for a short time. The narrow rings are only about 10 kilometers wide, and there are about 10 of them. Astrophysicists theorized that shepherd moons on either side of each 163

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on its axis opposite its motion around the Sun). Pluto’s axis is tilted 120 degrees (though, as we will see in the next lecture, Pluto is now considered to be only a dwarf planet).

Lecture 32: Uranus and Neptune, the Small Giants

ring may keep the ring particles in place through a complex gravitational interaction. For example, if a particle tries to move toward an outer shepherd moon, that moon absorbs some of the particle’s energy and forces the particle back. A particle that tries to move toward an inner shepherd moon gains some energy as that moon passes it up, and that energy Àings the particle back toward the rings. Indeed, spacecraft have con¿rmed the presence of shepherd moons orbiting Uranus’s rings; two such moons are Cordelia and Ophelia. Uranus has 27 known moons, the most interesting of which is Miranda. It’s a relatively small moon but still has many surface features, including striations, craters, canyons, and what look like fault blocks. Now we turn to Neptune, roughly the same size as Uranus and consisting mostly of hydrogen and helium. Neptune was discovered in 1846 and is named for the Roman god of the sea, a son of Saturn. Interestingly, Galileo actually saw Neptune in late 1612 and early 1613, drawing what he thought was a ¿xed star—but even noting that its position had moved some time later. If we use the known position of Jupiter at the time that Galileo made his measurements and take his plotted position of Neptune relative to Jupiter, we can re¿ne our knowledge of Neptune’s orbit. The discovery of Neptune was one of the great triumphs of celestial mechanics. The predicted and observed orbits of Uranus disagreed in detail. Urbain Leverrier and John C. Adams independently concluded that another planet must perturb Uranus, and they calculated its expected location. Johann Galle searched around the predicted position and found Neptune. In 1989, the Voyager spacecraft took pictures of Neptune, capturing such features as icy methane clouds skirting above the main part of the atmosphere, as well as storms, such as the Great Dark Spot, reminiscent of Jupiter’s Great Red Spot. Neptune’s atmosphere is much more dynamic than Uranus’s, which is unusual given that Neptune is farther from the Sun and, therefore, heated less. Neptune has rings as well, although they are full of clumps. There is some material between the clumps. One hypothesis is that the material in the clumpy rings is from a moon that was relatively recently torn apart by the tidal gravitational force of Neptune. As in the case of Uranus, Neptune’s magnetic ¿eld is offset from the center of the planet and tilted by 55 degrees relative to the rotation axis, which is odd. But Neptune’s rotation axis is tipped by only 30 degrees relative to the perpendicular to its orbital plane. 164

Neptune has a notable moon, Triton, which is larger than our own Moon and has a thin nitrogen and methane atmosphere. Triton moves backward around Neptune, whereas its other moons orbit in the same general direction An image of Triton, Neptune’s largest moon. as Neptune’s orbit around the Sun. This may indicate that Triton did not form out of a disk of gas from which Neptune itself formed; rather, Triton was probably another body captured by Neptune long ago. The capture probably occurred in such a way as to initially give Triton an elliptical, highly eccentric orbit around Neptune. (Tidal “It really does look forces later made the orbit become circular.) like Neptune’s This initially eccentric orbit means that Triton moon, Triton, should have been subjected to large variations in the tidal forces; its interior was initially had a geologically molten. Thus, there could be signs of activity active history on its surface. Indeed, Voyager’s images of in the relatively Triton captured some signi¿cant features, such recent past.” as a series of depressions about 30 kilometers in diameter, crisscrossed with various ridges, possibly faults similar to fault blocks on Earth. Triton’s surface also shows dark streaks thought to be the result of icy volcanoes that may spew nitrogen gas from below the surface. Ŷ

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NASA

We don’t really know what causes this offset magnetic ¿eld, but it may be due to a circulation of charged particles—that is, currents—in a shell around the rocky, icy core of both Uranus and Neptune.

Suggested Reading Beatty, Petersen, and Chaikin, eds., The New Solar System, 4th ed. Hartmann and Miller, The Grand Tour: A Traveler’s Guide to the Solar System, 3rd ed. Hodge, Higher Than Everest: An Adventurer’s Guide to the Solar System. McFadden, Weissman, and Johnson, eds., Encyclopedia of the Solar System. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. What fraction of its orbit has Neptune traversed since it was discovered and since it was last seen by Galileo?

Lecture 32: Uranus and Neptune, the Small Giants

2. Compare the rings of Jupiter, Saturn, Uranus, and Neptune. 3. Given that we have already learned so much about the Jovian planets with un-crewed spacecraft, should we next send humans to them, or do you think using un-crewed spacecraft and robots (such as the Spirit and Opportunity rovers on Mars) makes more sense?

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Pluto and Its Cousins Lecture 33

“Pluto is named after the brother of Jupiter and Neptune, the Roman god of the underworld. That’s kind of appropriate because Pluto is way out there. Moreover, the god of the underworld had this ability to render himself invisible for some periods of time; so that’s really an appropriate name.”

F

or more than 75 years, the ninth known planet was Pluto, an odd body that is actually a member of a much larger cloud of incipient comets. It was recently (in August 2006) demoted to the status of a dwarf planet, rather than a genuine planet. The existence of Pluto, originally known as “Planet X,” was suspected because of an apparent discrepancy between the observed and predicted orbits of Uranus, even after taking Neptune into account. The additional planet would gravitationally affect the orbit of Uranus, and Percival Lowell made detailed calculations about its probable location. Clyde Tombaugh, a 23-year-old amateur astronomer, was hired by the Lowell Observatory in 1929 to search for Planet X, long after Lowell’s death (1916) and despite the fact that some previous astronomers elsewhere had failed to ¿nd the planet. He used a blink comparator to discover Pluto in 1930, close to the position predicted by Lowell. He compared two photographs taken a week apart and noticed that one faint object had moved substantially, indicating that it was not a star. However, it is now known that Pluto’s mass is far too small to have produced the perceived discrepancy in Uranus’s orbit. Moreover, the discrepancy wasn’t real: The wrong mass had been assumed for Neptune when predicting the orbit of Uranus. Thus, Pluto just happened to be in the predicted part of the sky! Tombaugh was lucky, but he was also a skillful and thorough observer; Pluto was a very faint dot among tens of thousands of stars in the photographs that he examined. Pluto is named for the Roman god of the underworld, the brother of Jupiter and Neptune, able to make himself disappear or remain hidden for long periods of time. The name was suggested by an 11-year-old British schoolgirl, Venetia Burney. The name Pluto begins with the letters PL, and can be thought of as a tribute to Percival Lowell. Because it has an eccentric 167

Lecture 33: Pluto and Its Cousins

orbit (eccentricity 0.25), Pluto actually comes closer than Neptune to the Sun for 20 years of its 250-year orbit. This happened most recently during 1979– 1999. The relative tilts in the orbits of Pluto and Neptune, together with the fact that Neptune orbits the Sun three times for every two of Pluto’s orbits (a 3:2 resonance), prevent the collision of the two planets; they are never “For a long time, people in the same place at the same time. didn’t know about the KBOs Pluto’s semimajor axis is 40 AU, and that are scattered way out because of this distance, its features of the plane because people are dif¿cult to view, even with the Hubble Telescope. didn’t look outside the plane of the other planets The determination of Pluto’s mass orbiting the sun; everyone and radius was made possible with just looked in the ecliptic. the 1978 discovery of Pluto’s moon— Charon—that orbits Pluto in 6.4 days, But if you scan the sky the same time it takes Pluto to rotate far away from the plane, on its own axis. Because Pluto’s axis you can come up with of rotation is 120 degrees relative to unexpected objects.” the perpendicular to its orbital plane, occasionally, Pluto and Charon eclipse each other as viewed from Earth. This happens twice every 250 years for a 6-year period each time. By measuring these eclipse cycles, we can determine the masses and radii of Pluto and Charon. Charon is nearly half the diameter of Pluto; therefore, some astronomers have suggested calling it a double planet. Pluto is 1/500 the mass of Earth and about 1/5 of Earth’s radius. Before it was discovered, Lowell had predicted Pluto to be 6.6 times the mass of Earth, thereby earning it planet status. In 2005, two additional moons of Pluto—Nix and Hydra—were discovered, but those moons are very small compared with Charon. Pluto is a mixture of ice and rock, unlike the terrestrial planets (mostly rocky with an iron core) and the giant planets (mostly liquid with gaseous outer regions). Because it doesn’t seem to ¿t with the other planets in our Solar System, astronomers began to wonder if Pluto should be considered a planet at all. To further understand Pluto’s characteristics, we must look at TransNeptunian objects (TNOs) in the Kuiper belt. In 1951, Gerard Kuiper 168

Another odd KBO, called 2003 EL61 (and nicknamed “Santa”), is oblong and spins about its axis in just 4 hours. This object is thought to be mostly a rocky system, but its high reÀectivity (albedo) An illustration of Quaoar’s orbit. suggests that it has a crust or a thin layer of ice that reÀects much of the incoming sunlight. Its oblong shape, high albedo, and rapid spin might be attributable to a collision with another KBO. Perhaps even its two moons were produced during the collision.

169

NASA and A. Feild (STScI)

suggested the existence of a swarm of icy, rocky bodies orbiting at and beyond Neptune’s orbit, which he thought was the source of some shortperiod comets. At least two other astronomers had previously postulated the presence of such a region, but it is now known as the Kuiper belt. Ironically, Kuiper didn’t think there were many objects in this belt. In 1992, astronomers found the ¿rst Kuiper-belt object (KBO) by taking very deep photographs of the sky—deep meaning that they enabled observation of faint objects. A series of photographs of the same part of the sky over the course of one night or several nights can record the potential movement of any KBOs, indicating that an object is something other than a star. More than 1000 KBOs, most of them quite faint, have been discovered. Many of them have a 3:2 resonance with the orbit of Neptune—that is, Neptune orbits three times for every two times that the KBO orbits. Others have a 1:2 resonance or no resonance. Some KBOs travel far beyond most of the others, which could mean that they were scattered (gravitationally Àung) to eccentric orbits; they are not con¿ned to the plane of our Solar System. Some KBOs are quite large, such as Quaoar, discovered in 2002, which is somewhat over half the size of Pluto. Other KBOs at least half the diameter of Pluto have also been found. Many KBOs, especially the large ones, have moons.

In 2005, a KBO was found that is 10% to 30% larger than Pluto itself. Initially given the formal designation 2003 UB313, it was informally known as Xena until August of 2006, when it was of¿cially named Eris, after the goddess of chaos and strife. It has a semimajor axis of 97 AU and has a highly eccentric orbit that is tilted 45 degrees relative to the plane of the Solar System, dwar¿ng Pluto’s already strange inclination of 17 degrees. It even has a moon, nicknamed Gabrielle until it was of¿cially named Dysnomia, after the daughter of Eris and the spirit of lawlessness. Some astronomers believe that Eris should be designated our Solar System’s 10th planet. Many if not most astronomers would not call Pluto or Eris genuine planets because they are both part of a swarm. Indeed, in August 2006, Pluto was demoted to a dwarf planet. We will discuss this in further detail in the next lecture. Sedna, another bizarre rocky, icy body, was discovered in 2003 and named for the Inuit goddess of the ocean. Sedna’s orbital period is 11,000 years, and the orbital plane is tilted 12 degrees to the plane of the Solar System. Right now, it is 90 AU from the Sun, but it has an eccentric orbit, at times reaching a distance of about 1000 AU from the Sun. Probably not a true KBO, Sedna could be the innermost scattered member of the more distant Oort cloud, in a sense, an escapee from the Oort cloud. The discovery of Sedna suggests that at least the innermost part of the Oort cloud is within our realm of exploration. Ŷ

Lecture 33: Pluto and Its Cousins

Important Term Kuiper belt: A reservoir of perhaps millions of Solar-System objects, orbiting the Sun generally outside the orbit of Neptune. Eris and Pluto are the two largest known Kuiper-belt objects, though some astronomers consider them to be planets.

Suggested Reading Beatty, Peterson, and Chaikin, The New Solar System, 4th ed. Hartmann and Miller, The Grand Tour: A Traveler’s Guide to the Solar System, 3rd ed. Hodge, Higher Than Everest: An Adventurer’s Guide to the Solar System. 170

McFadden, Weissman, and Johnson, eds., Encyclopedia of the Solar System. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. Compare Pluto to the terrestrial planets and the Jovian planets. Consider as many physical properties as you can.

2. What are Kuiper-belt objects, and how is Pluto thought to be related to them?

3. What fraction of Pluto’s orbit has Pluto traversed since its discovery in 1930?

171

Asteroids and Dwarf Planets Lecture 34

“The Kuiper-belt objects (KBOs) constitute a swarm of planetary debris. The asteroid belt is a similar family of small bodies. How do these objects call into question the de¿nition of a planet?”

W

Lecture 34: Asteroids and Dwarf Planets

e begin with a look at asteroids. Based on an empirical description of the planets’ spacing, a planet was expected to exist somewhere between Mars and Jupiter, in addition to those already known. Thus, astronomers searched the skies for such a planet and discovered the asteroid Ceres in 1801. For a short time, Ceres was called a planet. However, within a few years, several more asteroids were discovered. Moreover, it was realized that Ceres is very small, much smaller than Mercury. Ceres and its brethren were subsequently designated asteroids or minor planets (which were not considered true planets). There are several hundred thousand known asteroids, the four largest being Ceres, Pallas, Vesta, and Hygiea. About 5000 new ones are discovered each month. It is estimated that there are 1 to 2 million asteroids with diameters greater than 1 kilometer and even more with diameters less than 1 kilometer. Together, all of the asteroids have a mass smaller than that of our Moon. Asteroids come in three main types: the stony, rocky ones made of silicates; iron-nickel ones, which are dense; and carbon-rich asteroids. Asteroids probably came from bodies that had tried to form planets, and some became partially differentiated; that is, the iron core sank to the middle, as on Earth, with rocky regions surrounding the core. Jupiter’s gravitational force likely caused the various newly forming bodies to have more eccentric orbits, thereby causing violent collisions that tended to break these bodies apart. Asteroids are ancient objects that might provide clues to the origin of the Solar System and the formation of planets. Not all asteroids are con¿ned between the orbits of Mars and Jupiter. A family of so-called Trojan asteroids occupies the same orbit as Jupiter—about 5 AU from the Sun—but they are 60 degrees away from Jupiter, as viewed from the Sun, in both the east and west directions. Jupiter forces objects to 172

congregate at these locations. Some asteroids have orbits that bring them fairly close to Earth; they are called the near-Earth asteroids. Spacecraft have visited a few of them, and one even crash-landed on the asteroid Eros. As in the case of KBOs, some asteroids have moons, such as Ida and its diminutive moon Dactyl. Collisions can shape asteroids, and some have been shattered by collisions; these are no longer solid objects but rubble piles, rather loosely held together by gravity. Another class of objects, neither asteroids nor KBOs, is called centaurs, which occupy the space between the orbits of Saturn and Neptune. Chiron, the ¿rst known centaur, was discovered in 1977. We believe they escaped from the Kuiper belt, but no one is certain. Our study of asteroids, KBOs, and centaurs leads us to consider the interesting question: What is a planet? A more concrete de¿nition for a planet would be easier to articulate if there were no objects in the gray area: KBOs, asteroids, and centaurs. Part of the reason why the ¿rst known asteroid, Ceres, was demoted from planethood is that several asteroids were discovered in a relatively short amount of time. They share similar characteristics that were easy to classify over the short time span of their discoveries, without having to give them planet status. Pluto, on the other hand, was known for more than 70 years before other similar objects were discovered. The KBO Eris is larger than Pluto; thus, technically, Eris should be called a planet if Pluto were a planet. After the discovery of Eris, many astronomers argued “Remarkably, that Pluto is simply another KBO and shouldn’t astronomers don’t deserve planet status. If astronomers had known have a consistent, how small Pluto was at the time of its discovery well-de¿ned, and had other KBOs been discovered near the same time, Pluto would likely not have been given planet status.

generally accepted de¿nition for what a planet is.”

What characteristics might constitute a planet? Perhaps a planet should be an object that is larger than 300–400 kilometers in diameter, thus achieving a relatively spherical shape due to its suf¿ciently strong gravity, and is itself not orbiting another body (the Sun excluded). We know of at least seven “planets” among the asteroid belt larger than 300 kilometers in diameter, in addition to at least six KBOs that qualify as planets by the above de¿nition. Probably many 173

more KBOs at least this large will be found in the next few years. Even 2003 EL61 (“Santa”), which is oblong shaped, would qualify because its odd shape is caused by its rapid rotation. If it didn’t rotate so quickly, it would be spherical. Thus, we would have at least 14 additional planets.

Lecture 34: Asteroids and Dwarf Planets

In August 2006, the International Astronomical Union (IAU) met in Prague for its triennial meeting. How to de¿ne a planet had been a growing issue ever since the discovery of the ¿rst KBOs. An initial proposal at the 2006 meeting de¿ned a planet as follows: It primarily orbits the Sun and is roughly spherical, and the center of mass in a binary system has to be outside the primary object’s surface (otherwise, it’s a moon, not a planet). A counterproposal reached only on the last day of the 10-day conference replaced the center-of-mass criterion with the idea that a planet gravitationally clears its path. Although the IAU has almost 10,000 members, only about 400 astronomers were still in attendance by the time the de¿nition came to a vote. The de¿nition sanctioned by the IAU in August 2006 was technically Àawed. Even many genuine planets, such as Neptune, Jupiter, Mars, and the Earth, have not gravitationally cleared out their respective paths, though each is dynamically dominant (that is, has by far the largest mass) within that path. The de¿nition offered no guidance about other solar systems, much less planetary objects that have escaped from their planetary systems or planets that formed in the absence of a sun. The de¿nition did not preclude nuclear fusion from having occurred; that is, it did not even preclude stars. The term dwarf planet was offered as a double noun, but it sounded, confusingly, like an adjective plus a noun. A term such as mesoplanet (coined by Isaac Asimov) might have been clearer. Pluto’s demotion makes sense, scienti¿cally. Changing the classi¿cation of objects based on new knowledge is part of the process of science. Nevertheless, a large number of astronomers are upset with Pluto’s demotion, regardless of whether it is primarily a KBO. They are also unhappy with the voting process that was used or with the technical details of the new de¿nition of a planet. It would not be surprising if the demotion were overturned in the next few years. At the very least, a more rigorous de¿nition of a planet will probably be formulated. 174

We conclude our discussion of asteroids and minor planets with a look at meteoroids. Meteoroids are chunks of asteroids that have broken off from asteroid collisions. They could also be material left over from the formation of the Solar System that didn’t happen to be in the family of asteroid orbits or other centaur-type orbits. Most meteoroids are small (less than 10 meters) and have random trajectories. Some of them come from disintegrating comets. When meteoroids enter Earth’s atmosphere, they slow down because of friction. As they enter the atmosphere, they heat up and the air in front of them is so compressed that they simply disintegrate. We sometimes call meteors “shooting stars” or “falling stars,” though they have nothing to do with stars. A meteoroid that penetrates the atmosphere is called a meteor—that’s the visible phenomenon—and, in some cases, is large enough to land on Earth. Those that do land are called meteorites. Many meteorites are found in Antarctica, but only because such rocks stand out on the ice of Antarctica, as opposed to those that land in places where we expect to see rocks. Chemical analysis can tell us about their origins. A few came from the Moon and from Mars. At 4.6 billion years old, many meteorites are among the oldest objects known in the Solar System—even older than rocks found on the Moon. They are thought to be primitive remains from the birth of the Solar System. Ŷ

Important Terms meteoroid: An interplanetary rock that is not in the asteroid belt. minor planets: Asteroids. Some astronomers now reserve this term for the largest asteroids and Kuiper belt objects. nuclear fusion: Reactions in which low-mass atomic nuclei combine to form a more massive nucleus.

Suggested Reading Bell and Mitton, eds., Asteroid Rendezvous: NEAR Shoemaker’s Adventures at EROS.

175

Hutchison and Graham, Meteorites. Kowal, Asteroids: Their Nature and Utilization. McFadden, Weissman, and Johnson, eds., Encyclopedia of the Solar System. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. Asteroids are among the oldest, most primitive objects known in the Solar System. However, given that there are three main types (stony, iron-nickel, and carbon-rich), is it fair to say that all asteroids consist of original, completely unprocessed (raw) material?

2. Now that many objects, some of them quite large, have been discovered in the Kuiper belt, do you think Pluto should still be called a planet?

3. Do you think Ceres would have retained its planetary status all the

Lecture 34: Asteroids and Dwarf Planets

way until the 21st century, as Pluto did, if other asteroids had not been discovered shortly after the discovery of Ceres?

4. What is the physical nature of a shooting star or falling star?

176

Comets—Gorgeous Primordial Snowballs Lecture 35

“ ‘Comet’ comes from the Greek aster kometes, which means ‘longhaired star.’ To the Greeks, it appeared that these were stars that had these beards, or mustaches, or hair sticking out from them.”

I

n addition to the planets of the Solar System, there are various nomads, such as the KBOs, asteroids, centaur-type objects, and random meteoroids. Let’s now look at comets. Comets appear as diffuse, luminous patches in the sky, sometimes with long tails that can stretch over many tens of degrees in the sky. Really bright comets appear only about once per decade. Comets are what we might call dirty snowballs that evaporate as they approach the Sun. Sunlight and the solar wind push the comet’s gases away, which in turn, reÀect the sunlight, forming the comet’s tail. Comets vary in their ice and rock composition, but some ice is present in the form of water-ice, carbon dioxide, ammonia, methane, and other substances. The evaporated gases are pushed away from the comet by the Sun’s radiation pressure—the photons—and by electrons, protons, and atomic nuclei in the solar wind. The evaporating gases reÀect light to form the tail, which always Àows in a direction away from the Sun, regardless of whether the comet is approaching the Sun or moving away from it during the comet’s trajectory. A comet usually has two tails, a dust tail and an ion tail. The ion tail consists of charged particles—ions—coming from the nucleus, pushed away by the solar wind at a very high speed. The ion tail tends to be long and straight. The dust tail consists of particles that are heavier than ions, so they lag behind and curve away. Periodic comets circle the Sun once per orbital period. According to Kepler’s second law (equal areas are swept out in equal times), periodic comets spend less time near the Sun and more time away from it. Comets are only about 10–11 of the Sun’s mass. Each time one passes near the Sun, it loses a little bit of that mass. For example, Halley’s Comet loses mass every 76 years, when it comes around the Sun. It will take some tens of thousands of years before it disintegrates. Short-period comets (less than about 200 years) in the plane of the Solar System come predominantly from 177

Lecture 35: Comets—Gorgeous Primordial Snowballs

the Kuiper belt. Collisions and gravitational interactions among objects in the Kuiper belt occasionally send comets careening toward the Sun. Others might escape from the Solar System. Large planets, such as Jupiter and Saturn, can alter these comets’ orbits, capturing them and turning their initially long periods into short ones. Longer-period comets are believed to arise from the Oort cloud, some 50,000 AU from the Sun. If a planet does not alter the trajectory of such a comet, it will pass by the Sun before disappearing again. Sedna, as we discussed in the previous lecture, could have been a comet that was altered by a passing star and sent into a much shorter-period orbit. Spectra of comets show that some contain many organic compounds. If they crashed into Earth early in its history, they may have brought some of the organic “We don’t know how compounds that later provided the seeds for much of today’s life on Earth. Water on Earth may have come largely from comets. water came from comets, but certainly Comets are made of primitive, cold material at least some of it whose properties were not affected by planet probably did.” formation. They therefore offer clues to physical conditions in the early Solar System, and we are very interested in studying them. The Stardust mission visited the Comet Wild 2 in 2004 and collected dust particles. Some of these particles turned out to be large, a few hundred micrometers in diameter. Another way to study comets is to force collisions. On July 4, 2005, a projectile from the spacecraft Deep Impact collided with a comet called Tempel 1. The collision excavated some material, which could then be studied by cameras and spectrometers aboard the satellite. Before the impact, the comet had already experienced outbursts of activity, during which chunks broke off. The data are still being analyzed, but the comet’s density and size were determined. Its density is so low that it must be at least 75% empty space; it is porous like a sponge. Studies also found comparatively little water in this comet but a fair amount of organic compounds. We can also study the breakup of comets in a natural way—that is, not by hitting them with a projectile. As a comet breaks up on its own, we can study the spectra of its constituent pieces to ¿nd out what they are made of.

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NASA

When a comet breaks up, a swarm of particles can intersect the Earth during its trajectory around the Sun, causing a meteor shower. As we said in the previous lecture, we often see sporadic meteors. But occasionally, we notice that several meteors appear to come from a particular area in the sky. Meteor showers occur when Earth passes through the debris of a long-dead or stilldisintegrating comet. This happens at the same time each year for a given shower. During a shower, the meteors appear to come from a common point in the sky, known as the radiant. This is the vanishing point of the essentially parallel trajectories of the individual chunks of debris.

Halley’s comet.

The Leonid meteor shower occurs in November, with the individual meteors coming from the direction of the constellation Leo. The Perseids come from the direction of the constellation Perseus in August. A weak meteor shower occurs when Earth passes through a part of the comet’s orbit that doesn’t have much debris. But every 33 years or so, thanks to Comet Temple-Tuttle, the Leonid meteor shower turns into a meteor storm. This occurs when Earth intersects the comet’s orbit near its head, where a clump of debris still remains. There was a spectacular Leonid meteor storm in 1966 and a minor 179

one in 1999. In 1833, Earth traveled through a large clump of Temple-Tuttle’s debris, leading people to believe that the sky was literally falling. In general, most comets and meteoroids are nothing to worry about. However, as we will see in the next lecture, occasionally, there are meteoroids or comets that we do have to watch out for: They are on a collision course with Earth. Ŷ

Suggested Reading Beatty, Peterson, and Chaikin, The New Solar System, 4th ed. McFadden, Weissman, and Johnson, eds., Encyclopedia of the Solar System. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Lecture 35: Comets—Gorgeous Primordial Snowballs

Questions to Consider 1. Use Kepler’s third law and the known orbital period of Halley’s Comet (about 76 years) to deduce its semimajor axis. Which planet has a comparable semimajor axis?

2. What creates the tail of a comet? Is something chemically burning? 3. How far is the Oort comet cloud from the Sun relative to the distance from the Sun to Pluto?

4. Why might some meteor showers last only a day while others can last several weeks?

180

Catastrophic Collisions Lecture 36

“You’d need a really massive object hitting us really hard to cause the Earth to break apart. That’s not going to happen. But the crater that forms, the dust thrown into the atmosphere, the ¿res that result, and everything else can cause much of life on Earth to be extinguished—so you have to watch out.”

S

ome groups of asteroids, called near-Earth asteroids, have orbits that cross Earth’s orbit. In the prehistoric past, they have hit Earth, causing signi¿cant destruction and at least one mass extinction. The Apollo asteroids are the best known; we know of about 2000 relatively large Apollo asteroids (greater than 100 meters in diameter). Icarus is an example of an asteroid that crosses Earth’s orbit, but usually an asteroid and Earth are not at the same place at the same time. The Barringer meteor crater in Arizona is about 1 kilometer in diameter and was formed by the impact of an ironrich meteorite—perhaps only 50 meters in diameter—about 50,000 years ago. The Tunguska event was recorded in 1908 in Siberia, where an object might have broken up in Earth’s atmosphere before actually hitting the surface. It leveled 2000 square kilometers of forest with an estimated force of the equivalent of 15 megatons of trinitrotoluene, TNT. For comparison, the largest hydrogen bomb ever exploded had an energy of 60 megatons. Throughout the Moon’s early history, mostly in the ¿rst few hundred million years, meteorites have pockmarked the surface. Most of the resulting craters have been preserved; there is little erosion. As a result of erosion on Earth, craters tend to be obliterated after a relatively short time, though we do know of about 180 craters on Earth that have survived. When a meteorite hits Earth, the material surrounding the point of impact is vaporized. Material at a greater distance from the impact is excavated, creating the crater, which is always much bigger than the meteorite itself. For example, a 1-kilometer projectile hitting Earth could form a crater 10 or 20 kilometers in diameter, depending on the projectile’s composition and speed. We know of more than 800 near-Earth asteroids whose size is greater than 1 kilometer, though we think that the total is about 1100. We expect a 181

© Jupiterimages/Photos.com/Thinkstock

Lecture 36: Catastrophic Collisions

meteoroid of this size to collide with Earth every million years or so; the explosive energy released would be equivalent to about 105 to 106 megatons of TNT. Smaller meteoroids (with diameters greater than 100 meters) could also collide with Earth, and we know of perhaps 100,000 of them. We would expect a collision with a smaller meteoroid to occur every 10,000 years or so, producing an explosion equivalent to 102 to 103 megatons of TNT. Even smaller blasts, like the Tunguska event of 1908, happen roughly every 1000 years, or maybe even every few hundred years, on average.

The Barringer meteor crater in Arizona.

Given that Earth stands to collide with meteoroids and comets, should we be worried? Statistically, averaged over 100 million years, we are as likely to die from a cosmic collision as from an airplane crash, a Àood, or a tornado. An Earth impact from a meteoroid larger than 10 kilometers in diameter could cause the end of human civilization. An object of this size would produce an energy equivalent of about 108 to 109 megatons of TNT. Such a collision and the subsequent ¿ery aftermath would lead to what is called an impact winter. So much dust would ¿ll the atmosphere that sunlight would be prevented from reaching Earth’s surface. Temperatures would plummet, 182

killing plants, then herbivores, and eventually, those at the top of the food chain. The atmospheric particulates would eventually come down as acid rain. Elevated levels of carbon dioxide in the atmosphere would cause high temperatures for up to thousands of years—the greenhouse effect. Some scientists believe that mass extinctions, regardless of their cause, are periodic, resulting in the destruction of life on Earth roughly every 62 million years. The evidence for periodic impacts of large objects is not very strong. As far as we know, such impacts are fairly random, but the average is every 100 million years or so. The last large extinction that we know of—the Cretaceous/Tertiary (K/T) extinction 65 million years ago—was probably caused by a cosmic collision with an object greater than 10 kilometers in diameter, killing the dinosaurs and other life on Earth at the time, including small marine creatures called foramonifera. Fossil records show the sudden death of two-thirds of all living species on Earth during the K/T extinction and an abundance of iridium in the Earth strata from that era. Iridium is attracted to iron, and when Earth was young and molten, iridium attached itself to iron, which sank to the Earth’s core during the process of differentiation. Thus, Earth’s surface layers are relatively de¿cient in iridium. But when a celestial body collides with Earth, dispersing its material over the surface, a thin layer with an anomalously high concentration of iridium will appear. The probable impact site of the K/T extinction event was found off the coast of the Yucatan peninsula, called the Chicxulub crater. It is now covered by 500 meters of sediment, although through measurements of the local gravity, we know there is a deformation there. The crater has been dated to 65 million years. The crater is about 200 kilometers in diameter, comparable to what would have been produced by a comet with a diameter of 10 or 20 kilometers hitting the Earth. Evidence of huge tsunamis along the Gulf Coast 65 million years ago further supports the hypothesis for this impact crater. In addition, there are vast deposits of charcoal from forest ¿res at around that time. Recent cosmic collisions demonstrate that such events can be predicted, as in 1994, when Comet Shoemaker-Levy 9 collided with Jupiter. Over the course of a week, about 20 comet fragments hit Jupiter, releasing an estimated equivalent of 40 million megatons of TNT. Some of the 183

Lecture 36: Catastrophic Collisions

individual comet fragments had energies of up to 6 million megatons of TNT, equivalent to about 100,000 of the most powerful nuclear weapons ever made by humans. The amount of energy released was determined largely through studies at infrared wavelengths. We were able to study how the shape of the ejected debris from the impacts changed over time, giving us information about Jupiter’s atmospheric currents. In addition, spectra of the impacted areas showed molecular sulfur, carbon disul¿de, ammonia, and other molecules that were excavated from underneath Jupiter’s surface, providing information about the planet’s composition. The impact with Jupiter gave “Maybe what we really scientists additional impetus to ¿nd all large objects that might hit the Earth. The pace need is a wakeup call of discovery of Earth-crossing asteroids to get all of us to unify is rapidly increasing for those objects less behind a common than 1 kilometer in diameter but leveling cause—that is, saving off for those greater than this size. all of humanity rather Though we don’t know of any imminent than ¿ghting amongst threat, Earth has experienced some ourselves all the time.” relatively close calls. In July 2006, an Apollo asteroid came within 270,000 miles of Earth—only 1.1 times the Moon’s distance from Earth. Toutatis, a well-known asteroid 4.6 kilometers long, came within four lunar distances in 2004. By studying the trajectories of celestial objects, astronomers can predict when Earth is likely to experience a collision. If we know such information, we could send spacecraft to deÀect the threat. Perhaps such a threat might even unify the nations of Earth to work together, rather than ¿ghting among ourselves. Ŷ

Suggested Reading Alvarez, T-Rex and the Crater of Doom. Chapman and Morrison, Cosmic Catastrophes. McFadden, Weissman, and Johnson, eds., Encyclopedia of the Solar System.

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Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Verschuur, Impact! The Threat of Comets and Asteroids.

Questions to Consider 1. Do you worry about asteroid or comet collisions with Earth? What could be done to save the Earth if an asteroid were discovered suf¿ciently far in advance of the collision?

2. Can you argue that the presence of humans on Earth may have impeded the rise of some other animal to a position of great prominence?

3. Some scientists have suggested that the dinosaurs were about to become extinct anyway, without an asteroid or comet collision, because of changes in Earth’s climate and for other reasons. If so, does this detract from the impact theory, in view of evidence that two-thirds of all species perished quite suddenly during the K/T extinction and a large crater having the right age has been found?

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The Formation of Planetary Systems Lecture 37

“We think that most planetary systems formed in about the same way. Although the words ‘solar system’ are technically reserved for our own Solar System, people loosely call other planetary systems ‘solar systems’ as well.”

Lecture 37: The Formation of Planetary Systems

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n this lecture, we discuss the formation model not only for our own Solar System but for others, as well. We think that most planetary systems formed in roughly the same way. Our Solar System has two main characteristics: All the planets orbit the Sun in the same direction, and most of them rotate about their rotation axes in that same direction and with an axis roughly perpendicular to the plane of the Solar System. The Sun also rotates about its axis in the same direction. The Solar System looks like a thin disk, and most of the planets are nearly in the same plane, though they are tilted relative to one another. This thin, spinning disk suggests that our Solar System arose from a rotating structure that may have contracted and formed regions where material accumulated into planets. In such a nebular hypothesis, initially there is a gravitationally contracting, slowly spinning cloud of gas and dust. Occasionally, regions denser than average occur, which become gravitationally unstable and begin to collapse. A passing star can cause the region to rotate somewhat. As the region collapses, its rotation rate increases as the result of a principle called the conservation of angular momentum. Angular momentum (L) is a measure of the total amount of spin of an object or a system: In simple cases, L = mvr, in which L is angular momentum, v is the rotation speed, m is the material’s mass, and r is its size radius. Contracting objects of a given mass become smaller; therefore, the spin rate must increase in order to keep the angular momentum constant. The contracting cloud, in a similar way, spins faster with time. Spinning objects are Àung away from the axis of rotation, experiencing centrifugal force, a manifestation of the rotating frame of reference. For example, we feel this force when riding in a car that turns a corner rapidly. Particles feel more centrifugal force as they contract because of their greater

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spin rate. At some point, they are held “Centrifugal force is a back from contracting further because the centrifugal force balances the ¿ctitious force; it’s not gravity trying to pull them in. On the one of the fundamental other hand, a particle along the axis forces like gravity, or of rotation doesn’t have any distance electromagnetism, or the from the spinning axis; thus, the total amount of angular momentum is zero, forces that hold the nuclei causing that particle to fall. Similarly, of atoms together. It’s a particles away from the axis of rotation force that’s a manifestation fall toward the equatorial plane of the of the rotating frame spinning cloud, but their inward motion of reference.” toward the axis of rotation is inhibited by the centrifugal force. In this way, contraction plus conservation of angular momentum leads to a Àattening of the spinning cloud, eventually forming a disk in which all the particles are balanced and the gravity they feel inward is equal to the centrifugal force outward. Material accumulates in the Àattened disk’s center, and that, presumably, is where a star (a sun) forms. Is there evidence of this nebular hypothesis? We see a giant cloud of gas and dust in the Orion nebula, where a cluster of young stars has formed as a result of gravitational contraction. We see many such nebulae in our Milky Way Galaxy and in other galaxies. When these giant clouds of gas and dust contract, the cloud can fragment into many smaller units that are denser than average. Each of these units contracts and forms a spinning disk with a central region where a star and planetary system can form. As each of these units contracts, the temperature and pressure rise; the individual particles of gas move more rapidly. Eventually, the outward pressure from the hot, rapidly moving particles nearly balances the inward gravitational force, and the object continues to contract very slowly. It is now called a “pre-main-sequence star.” When the temperature in the center of the premain-sequence star becomes suf¿ciently high, nuclear reactions begin to occur, signaling the birth of a star/sun. It is dif¿cult to see this process of star formation in detail at optical wavelengths because the gas and dust become opaque if they’re suf¿ciently dense. However, radio and infrared wavelengths allow us to peer into these central star-forming regions. 187

NASA,ESA, M. Robberto (Space Telescope Science Institute/ESA) and the Hubble Space Telescope Orion Treasury Project Team

Lecture 37: The Formation of Planetary Systems

An optical image of the Orion nebula.

Many of these star-forming regions show debris around a young star or stillforming star. This debris often has a disk-like shape, called a protoplanetary disk, or proplyd for short. Many young stars deep in the heart of nebulae show debris disks surrounding them, providing good evidence for the nebular hypothesis of planetary formation. In addition, Àat debris disks are needed to form planets. Eventually, the remaining debris is blown away by the wind from the young star (the solar wind). With the exception of some asteroids and other small debris, the cleared space is relatively empty, forming what we would call a planetary system (solar system). There are many such disks

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in which we can see these clumps of accumulating debris. However, not all planetary systems will be alike. Let’s look at how planets form, though many of the details are unclear because we don’t yet know enough about the process. In the early stages of a planet’s birth, we believe, particles begin to clump together and grow in size. Clumps can hit each other and grow even bigger, especially if they’re icy, because ice sticks together better than rock. This may be how the outer giants (Jupiter, Saturn, Uranus, and Neptune) in our Solar System formed. Clumps between 1 and 100 km in size are called planetesimals, or little planets. Once a number of planetesimals have formed, their gravitational inÀuence on one another brings them together, and they accumulate into bigger structures, forming the core of a planet. Regions suf¿ciently far from the inner sun are icy and attract other ice clumps, forming large planets. These massive objects can accumulate hydrogen and helium left over in their vicinity. Closer to the center of the Àattened disk, the sun region, temperatures are higher and ices don’t form. Here, it is harder for objects to stick together and form large cores, such as those in the icy giants. Such gases as hydrogen and helium evaporate or are blown away by the solar wind. These regions of the disk are where we expect terrestrial-like planets to form. Beyond a certain distance from the center of the disk, particles don’t collide with each other frequently enough because of the vast distances between them. This region would be like the Kuiper belt in our Solar System. In our own Solar System, much farther out from the Kuiper belt, is the Oort cloud, which we think was formed by a gravitational slingshot effect caused by the large planets. Similar processes could well occur in other planetary systems, though we don’t yet have any direct evidence. If material comes close to a large planet, it can be Àung outward; in the case of the Oort cloud, this material may have been Àung generally perpendicular to the plane of our Solar System. We think that Uranus and Neptune contributed more to the Oort cloud than Jupiter and Saturn. There are more icy rocks near Uranus and Neptune than Jupiter and Saturn. Moreover, Jupiter and Saturn have accumulated into their own masses more of the material in their vicinity, whereas Uranus and Neptune are not as massive and likely ejected more material into the Oort cloud.

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Jupiter formed quickly; its gravitational tugging led to collisions among the planetesimals and the asteroid belt that were too energetic to allow them to stick together. Jupiter also cleared out certain parts of the asteroid belt. For example, there were regions of the asteroid belt where a particle orbited two or three times for every one time that Jupiter orbited. This created additional tugging in the same direction, clearing out that region. The cleared region in the asteroid belt is known as the Kirkwood gaps, which are a form of resonance such that a big planet can affect the amount of material in the region by progressively tugging on it.

Lecture 37: The Formation of Planetary Systems

A competing hypothesis for how big planets formed in our Solar System, and perhaps in others as well, is that in a certain region of the disk, the gas collapsed all at once into a giant planet. Currently, however, the evidence for this suggestion is not strong. There are certain impediments to the formation of disks around stars. Some bright stars can emit so much radiation that they effectively evaporate the surrounding cloud of gas and dust. Luminous stars outside of gas clouds can also evaporate those clouds. Another problem is that the spinning cloud must expend angular momentum. We think that the angular momentum is taken away through bipolar outÀows, jets of material streaming away from the star perpendicular to the axis of rotation, like spinning bullets shot from a riÀe. Though we don’t yet have all the details, we’ve come a long way in understanding at least some of the methods by which stars and their associated planetary systems form. Ŷ

Important Terms angular momentum: A measure of the amount of spin of an object; dependent on the object’s rotation rate, mass, and mass distribution. bipolar outÀow: A phenomenon in which streams of matter are ejected from the poles of a rotating object.

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centrifugal force: The outward force felt by an object in a rotating frame of reference. nebular hypothesis: Theory of the formation of the Solar System, asserting that spinning clouds of interstellar matter gradually contracted and allowed for the formation of the Sun and the planets. planetesimals: Small bodies, such as meteoroids and comets, into which the solar nebula condensed and from which the planets subsequently formed. protoplanetary disks: Also called proplyds; concentrations of matter around newly formed or still forming stars out of which planets may form.

Suggested Reading Cohen, In Darkness Born: The Story of Star Formation. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Smith, The Origin of Stars.

Questions to Consider 1. A solitary star that is still forming must expend its angular momentum through the ejection of spinning jets (and, to some extent, by storing it in planets that form in the disk). Is there as much of a problem for a cloud from which a double star forms?

2. Do you expect to ¿nd massive planets, consisting mostly of gases and liquids, in the inner regions of other planetary systems?

3. In what way do the Kuiper belt and the Oort cloud provide clues to the origin and early history of our Solar System?

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The Quest for Other Planetary Systems Lecture 38

“Other worlds—what do they look like? Our imaginations run wild. Someday, we hope to have actual pictures of these planets, but it was a challenge just to detect them.”

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Lecture 38: The Quest for Other Planetary Systems

e have seen ample evidence for the existence of other solar systems, and though ¿nding other planets has been challenging, we have succeeded in doing so. We can say without any doubt that there are planets around many other stars in our Galaxy and, presumably, in other galaxies. We call these extra-solar planets, or exoplanets. We don’t yet have actual pictures of exoplanets because just discovering them was a challenge. The main problem in detecting these planets is that the glare of the star they orbit is so much greater than the amount of light the planet reÀects. The key is to measure the slight reÀex motion of the star induced by the orbit of a planet around it. Planets do not orbit a perfectly stationary star; the star actually wobbles some in response to the planets’ motions. Two objects, such as a star and a planet, orbit each other around their common center of gravity, or center of mass. The general equation is as follows: The mass of one object multiplied by its distance from the center of mass is equal to the mass of the other object multiplied by its distance from the center of mass, or M1 R1 M 2 R2 , in which 1 and 2 simply denote the two objects. This formula applies in general for two objects being held together by their mutual gravitational force, F GM1M 2 d 2, in which M is the mass of each object and d is the distance between them. The star, with its larger mass, orbits closer to the common center of mass than the less massive object, the planet. A very massive star and a relatively low-mass planet will have a common center of mass that occurs nearly at the center of the star itself. This reÀex motion can be detected through a series of photographs of the star over the course of time. Measurements of positions of stars and their motion is a sub¿eld of astronomy known as astrometry. However, no extra-solar planets have been discovered thus far with this technique.

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Another way to detect reÀex motion is to examine the star’s light and search for a periodic shift in the wavelength of the absorption lines in the spectrum. The shift is caused by the Doppler effect, which we discussed in a previous lecture. Remember that a stationary emitter of waves sends out spherical wavefronts with a well-de¿ned, measurable wavelength. But if an object is moving, the waves in front of it are “squished” (creating a blueshift, or shorter wavelengths) and the waves in back are more elongated (creating a redshift, or longer wavelengths). If we look at a star from our position near the Sun and the star is moving perpendicular to our line of sight, then an absorption line in the star’s spectrum will show no shift. The formula for the Doppler shift is 'OeO = v/c, in which v is the speed of the object relative to the observer, c is the speed of light, and 'O = O í O (O being the rest wavelength of the line, as measured in a gas at rest relative to the observer, and O is the observed wavelength of the line).

Application of the Doppler Shift Formula 'OeO = v/c Given O observed wavelength) = 6,565 Å O rest wavelength) = 6,563 Å c (speed of light) § 3 × 105 km/s Find v (speed of object relative to observer) 'O(shift in wavelength) = O– O= 6,565 Å – 6,563 Å = 2 Å 'OeO = 2 Å / 6,563 Å § 3 × 10–4 Å v/c = 3 × 10–4 Å v = c(3 × 10–4 Å) § (3 × 105 km/s) (3 × 10–4 Å) § 90 km/s

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Lecture 38: The Quest for Other Planetary Systems

How can we detect exoplanets? If an unseen planet is orbiting a star, the star itself moves, too, because they both orbit their common center of mass. If the star is moving toward us, its spectrum will show a blueshift; if it’s moving away from us, its spectrum will show a redshift. We look for a periodically changing shift of the absorption lines in the star’s spectrum; this is known as the Doppler wobble. If a planet’s mass is large and its distance from the star is small, the planet causes the star to move around the common center of gravity more quickly. If the planet’s mass is smaller, its gravitational inÀuence is less, and the star moves less—its wobble (reÀex motion) is less. The farther apart a star and planet are, the less the star wobbles, too. Knowing the period and amplitude (maximum change in radial velocity) of the Doppler wobble, the mass of the detected planet can be calculated by using Newton’s form of Kepler’s third law. Actually, one gets a minimum mass for the planet, because the inclination of the orbit is generally not known. The measured radial velocity of the star is only part of the total orbital velocity unless the orbital plane is perpendicular to the line of sight (i.e., edge-on). The planets in our Solar System cause our Sun to wobble, and each has a slightly different effect on the Sun according to each planet’s mass and distance from the Sun. Until 1995, we had not found other planets. But using this technique of measuring reÀex motion, astronomers have since found about 200 exoplanets. The ¿rst discovery in 1995 was detected by a wobble in what is called 51 Pegasi, a star in the constellation Pegasus. Michel Mayor and Didier Queloz found the planet, and their discovery was quickly con¿rmed by Geoff Marcy and Paul Butler. Marcy and Butler used the 3-meter telescope at Lick Observatory to measure the spectrum of 51 Pegasi to con¿rm the results of Mayor and Queloz. The ¿nd was unexpected because the large planet had an orbital period of only 4.2 days, and the reÀex motion of the star was about 50 meters per second. Typically, such large planets are much farther from their stars and, therefore, take much longer to orbit. As an example, remember that Jupiter’s orbital period is 12 years, and the Sun’s reÀex motion is only about 10 meters per second. The star 51 Pegasi was originally misclassi¿ed as being not sun-like in its properties, which meant that Marcy and Butler had not included it in their extensive search for companion planets.

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Among the ¿rst dozen discovered exoplanets, we see some interesting trends. First, they are all massive, ranging in size from half the mass of Jupiter to 10 times Jupiter’s mass. The fact that we are ¿nding only big planets, however, doesn’t mean that there are no smaller planets to be found. Larger planets are simply easier to detect. Second, some of these exoplanets are very close to their respective stars, some even less than 1/10 AU away. Again, these planets are easier to detect because the closer they are to their stars, the greater the stars’ wobble, and the easier it is to detect. Third, some of these exoplanets have very eccentric orbits, not circular like that of 51 Pegasi. A good example is 16 Cygni B. We did not anticipate that so many planets would have such eccentric orbits. These discoveries proved that some of our assumptions about other solar systems were wrong, as we will see in the next lecture. Ŷ

Important Terms astrometry: Measurement of the position and motion of the stars in the plane of the sky. Doppler shift: The change in wavelength or frequency produced when a source of waves and the observer move relative to each other. Blueshifts (to shorter wavelengths) and redshifts (to longer wavelengths) are associated with approach and recession, respectively. redshift: De¿ned to be z = (O  O0)/O0, where O0 is the rest wavelength of a given spectral line and O is its (longer) observed wavelength. The wavelength shift may be caused by recession of the source from the observer or by the propagation of light out of a gravitational ¿eld. rest wavelength: The wavelength radiation would have if its emitter were not moving with respect to the observer.

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Suggested Reading California and Carnegie Planet Search, www.exoplanets.org. Croswell, Planet Quest: The Epic Discovery of Alien Solar Systems. Dorminey, Distant Wanderers: The Search for Planets beyond the Solar System. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Goldsmith, Worlds Unnumbered: The Search for Extrasolar Planets.

Questions to Consider 1. Under what conditions can we measure the true mass of an extra-solar planet, not just its minimum mass, with the Doppler wobble technique?

Lecture 38: The Quest for Other Planetary Systems

2. Does the Doppler wobble method for deducing the existence of a planet orbiting a star depend on the star’s distance from Earth? (Assume the star’s apparent brightness is independent of distance.)

3. It turns out that the ratio of the speed of a planet to the speed of the star it orbits is equal to the inverse of the ratio of their masses. If Earth orbits the Sun with a speed of 30 km/s, what is the Sun’s corresponding orbital speed (that is, its reÀex motion, induced by the Earth’s motion)? Considering this, is the current precision of the optical Doppler techniques (about 1 m/s) close to suf¿cient for a detection of Earth-like planets orbiting other stars?

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Extra-Solar Planets Galore! Lecture 39

“Quite a few exoplanets have highly eccentric orbits. In our Solar System, the orbits are circular or nearly circular.”

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s we saw in the last lecture, many of the exoplanets discovered so far are very close to their central stars and have short orbital periods. These large exoplanets, known as hot Jupiters, range from about 0.3 AU to less than 0.1 AU from the stars they orbit. It is dif¿cult to understand how such planets could form so close to their stars because these planets have large amounts of gas. Gas tends not to get gravitationally bound to a planet so close to a hot star; the thermal motions of the gas are too fast. Hot Jupiters could have formed farther away from their stars, where conditions were colder. Through gravitational accretion, their iron-rockice cores could then gather surrounding gas. Most stars are at least 98% hydrogen and helium. The remaining 2% (or less) is composed of heavy elements, such as iron, carbon, and nitrogen. Stars with more than 2% heavy elements tend to have more exoplanets. Stars with a low percentage of heavy elements tend to not have planets. Both the stars and their exoplanets formed from the same gas and dust. Clouds having relatively large amounts of heavy elements were more likely to form iron-rock-ice cores than those having small amounts of heavy elements. Thus, it seems likely that large Jupiter-like planets ¿rst formed iron-rock-ice cores, accreting more heavy matter until they were gravitationally strong enough to attract hydrogen and helium. One hypothesis is that planets farther out encountered a lot of material, rubbing against it and creating frictional drag. Gradually, the planets spiraled toward their stars. Or the planets could have formed farther out, and gravitational interactions among them sent some careening toward the star in an elliptical orbit. Through tidal effects, the elliptical orbit gradually became circular. Passing stars could also have perturbed some planets that were initially far out, sending them into closer orbits with their stars. Another common trait among exoplanets is that many have highly eccentric (elliptical) orbits, while others have nearly circular orbits. The planets with elliptical orbits tend to be 197

farther from their stars than those with circular orbits. It’s possible that these planets were relatively close together and interacted gravitationally, with some planets being ejected, while others rebounded with a kick that gave them eccentric orbits. The hot Jupiters that are close in don’t have elliptical orbits because when a planet is close to its star, subtle tidal effects eventually create circular orbits.

Lecture 39: Extra-Solar Planets Galore!

Let’s take a look at some of the planets that have been found. In 1999, astronomers found a multi-planet system around Upsilon Andromedae, the ¿rst of its kind to be found. Now, about 20 such multiple systems are known. This three-planet system has one planet close to the star, another that orbits as if it were between Venus and Earth, and a third much farther away at 3 AU from the star. Another system, called 55 Cancri, was believed to have three planets until a fourth was discovered in 2004. This star has two planets with a Mercury-like orbit and one big planet roughly where Jupiter would be; the fourth is close to the star, with only a 2.8-day orbital period. Two planets were discovered orbiting the star Gliese 876. They had masses of about 0.6 of Jupiter and 1.9 times Jupiter, with orbital periods of about 30 and 60 days, respectively. In 2005, a third planet was discovered, but it was much smaller than many of the other hot Jupiters we had been ¿nding—only 7.5 times Earth’s mass. Ultimately, we would like to ¿nd planets about Earth’s size and more Earthlike, but this is dif¿cult using the Doppler wobble technique. How do we ¿nd them? The Doppler wobble technique isn’t suf¿cient for detecting Earth-like planets because at Earth’s distance from the Sun, Earth induces only a 10 cm/s motion in the Sun—not very fast. The current precision limits for the Doppler technique are about 1 m/s. In addition, certain fundamental properties of stars may inherently limit the precision of the Doppler technique, such as turbulence in the star’s atmosphere causing motions of gas that obscure the tiny Doppler wobble. Another technique used involves planetary transits, as we saw in two previous lectures when we discussed the transit of Venus. Occasionally, a planet will appear to cross the face of its star as seen from Earth. As the planet transits, it will block part of the star’s light, causing the star to dim. We can

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measure the star’s brightness as a function of time (that is, its light curve) to obtain information on the planet’s size. If rings or moons are present, these may also show up in the light curve. During the transit of a planet around the star HD 209458, an atmosphere was detected around the planet. Photons from the star were absorbed by sodium in the planet’s atmosphere, which appeared as sodium absorption lines in the star’s spectrum. A big planet, such as Jupiter, produces a signi¿cant dip in the star’s light curve; a small planet, such as Earth, produces a small dip. Earth is 1/109 of the Sun’s diameter, and its area in the sky is about (1/100)2 of the Sun’s disk area. If Earth were to pass across the Sun, the Sun’s light curve would show a dip of about 0.01%. We can detect terrestrial planets around other stars by looking for minute dips of this sort. One problem with measuring small dips is that presumably other stars, like our Sun, have sunspots. As these spots traverse a rotating star, the star will dim or brighten in a non-periodic way. Therefore, a star varies slightly in brightness, regardless of whether a planet traverses its face or not. By monitoring stars over a long time, we would presumably begin to see dips in the light spectra occurring in a periodic way, indicating the presence of a planet, not just spots. Another problem with measuring transits is that the odds of our “NASA hopes to build viewing a planetary transit of a monitored an instrument called star are only 0.5% Most planetary systems are not viewed suf¿ciently edge-on. To the Terrestrial Planet improve these odds, NASA will launch the Finder, which would Kepler spacecraft in 2009. It will monitor be launched sometime 100,000 stars continuously for four years. between 2020 and Another way to ¿nd planets is by 2030, to take images of measuring the apparent brightness of stars terrestrial [exo]planets.” at infrared wavelengths over the course of time. At infrared wavelengths, we can see the planet’s emitted light; this is the thermal emission from the planet. When a planet moves behind its star, the star blocks some of the planet’s light. If the planet is not blocked by the star, the total brightness of the star plus the planet is greater than when the planet is blocked.

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A ¿nal way to detect planets is through gravitational microlensing. To understand this technique, recall that the Sun bends light because of the warping of space and time. If a star comes between Earth and a background star along our line of sight, a focusing (lensing) effect occurs of the star’s light onto the Earth—the background star appears slightly brighter than it would in the absence of the passing star and its planet. When the planet is perfectly aligned with the background star and Earth, a temporary spike—a short brightening— of the background star’s light occurs because of the microlensing effect of the planet. In 2005, a planet was detected for the ¿rst time using this gravitational microlensing technique. The planet is only 5 times the mass of Earth, even lower than the least massive of the planets discovered by the Doppler wobble technique. Ŷ

Important Terms light curve: A plot of an object’s brightness as a function of time. planetary transit: The passage of a planet directly along a star’s line of sight, causing a momentary dimming of the star’s light; can be used to detect planets in other solar systems.

Lecture 39: Extra-Solar Planets Galore!

Suggested Reading California and Carnegie Planet Search, www.exoplanets.org. Dorminey, Distant Wanderers: The Search for Planets beyond the Solar System. Goldsmith, Worlds Unnumbered: The Search for Extrasolar Planets. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. What are the pros and cons of the different techniques used (or potentially used) to detect and study extra-solar planets?

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2. If a transiting exoplanet has 10% of the diameter of the star it orbits, by what percentage will the observed brightness of the star decrease during the transit?

3. How would you expect the radial velocity of a star to change with time if more than one exoplanet orbits it?

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Life Beyond the Earth Lecture 40

“Headlines like, ‘The Birth of Planets’ and ‘Scientists Discover New Solar Systems and Rethink the Odds of Life Beyond Earth,’ appear on national magazines because this is the kind of stuff that excites the public’s attention.”

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he recent discovery of exoplanets has rekindled our question of whether life exists beyond planet Earth. To reduce speculation, we will restrict our attention to life as we know it. The emerging ¿eld of astrobiology or exobiology is the pursuit of ¿nding life elsewhere. Vast numbers of galaxies exist beyond the Milky Way, each possibly containing up to 300 to 400 billion stars like our own and planets where life forms could thrive.

Lecture 40: Life Beyond the Earth

Life, as we de¿ne it, must consist of organic compounds. Organic compounds are chains of carbon with hydrogen on the side and occasional molecules of oxygen and nitrogen. We call these amino acids. Long chains of amino acids form proteins, and although hundreds of thousands of such proteins are possible given the various combinations, life on Earth appears to select a relatively small number of proteins. Living organisms have a genetic code that is contained in deoxyribonucleic acid, or DNA, the famous “double helix” and the key to life. We don’t really understand how DNA formed, but we do know that it is an extremely long and complex structure built to self-replicate and evolve through mutations. [Note: During the lecture, it was erroneously stated that DNA is a protein. Actually, DNA consists of nucleotide bases, not amino acids, with a backbone of phosphates. DNA requires proteins to function, and proteins require DNA to form.] In order for DNA to form proteins, organic compounds must be made. Laboratory experiments have replicated the formation of organic compounds for the simplest amino acids. The most famous experiment, conducted in 1953 by Stanley Miller and Harold Urey, used water vapor, methane, ammonia, and hydrogen—at one time, thought to be the constituents of Earth’s primitive atmosphere. However, we now know that Earth’s primitive atmosphere was 202

mostly carbon dioxide and nitrogen molecules, without much methane and ammonia. In replicating the experiment using nitrogen and carbon dioxide, amino acids are not produced. The experiment, however, was important for demonstrating that complex molecules can form under not-so-farfetched conditions. Such conditions may have existed around some exoplanets or the moons of exoplanets. We know that the formation of amino acids is not that complex because simple amino acids have been found in some carbonaceous meteorites. We also ¿nd amino acids in comets. How, then, was life ¿rst formed? How did cells arise? We don’t know exactly, but we do know that primitive life—microbes and bacteria—must have arisen quite early in Earth’s history. Earth is about 4.6 billion years old, but for at least the ¿rst half billion years or so, it was still pummeled by space debris (planetesimals), making conditions too harsh for life to exist. There is fossil evidence for life (in the form of cyanobacteria called stromatolites) from “We know of 3 billion years ago, and 3.5-billion-yeargeothermal vents on old evidence for cellular life, though this is Earth where there is still controversial. There is also chemical evidence from 3.8 billion years ago for some a source of energy forms of life. that’s not the Sun; it’s, rather, geothermal If life arose in a simple manner on Earth, activity underneath perhaps it could also arise on moons and planets orbiting other stars in galaxies. We the Earth’s crust, and could argue that conditions on Earth were the magma seeps “just right” for life to form. However, there up and heats the are many places on Earth where conditions surrounding regions.” vary drastically and where life exists without seeming to have derived its energy from the Sun, such as geothermal vents deep under the ocean surface. The thermal features of Yellowstone National Park contain bacteria that exist in extremely high temperatures and acidic conditions. Algae exist beneath the surface of Antarctic rocks, thriving on hydrogen generated by a chemical reaction between water and iron silicates in the volcanic rock. Conditions may have been similar on Mars. It is estimated that up to half of the biomass of life on Earth might occur in various microbial forms in extreme conditions. 203

Lecture 40: Life Beyond the Earth

As discussed in a previous lecture, studies of a meteorite from Mars (ALH 84001) initially suggested that the planet could have primitive microbes. Though many scientists now believe that particular evidence to be weak, it still doesn’t prove One of Saturn’s moons, Enceladus, has that life doesn’t exist on a thin layer of surface water ice that came Mars. Life could possibly from geysers. have formed early in Mars’s history because conditions there may have been very favorable at one time, maybe even preceding the time when conditions were good on Earth. It’s possible that microbes did form 4 billion years ago on Mars, and it’s even possible that some meteoroid hit Mars, excavated a crater, and sent debris Àying through the Solar System. That debris could have landed on Earth, releasing microbes and making us descendants of Martians! (The odds for this, however, seem low.) It’s even thought that a particular Martian crater may have been the crater from which the meteorite in question came, although clearly, that meteorite didn’t provide the seeds of life on Earth. 204

NASA/JPL/Space Science Institute

We can look for life elsewhere in our Solar System and Milky Way Galaxy. The discovery of even a single species of life would support the hypothesis that simple life forms easily. We know that whatever life may have formed in the Solar System (other than on Earth), it most likely was primitive—microbes and bacteria. So far, there has been no good evidence for what we call “intelligent” life elsewhere in our Solar System. Analysis of Martian soil has shown no evidence of primitive life, but perhaps there is life under the planet’s surface. Further testing is necessary if we are to ¿nd organic compounds on Mars.

Important Term proteins: Molecules consisting of long chains of amino acids.

Suggested Reading Croswell, Planet Quest: The Epic Discovery of Alien Solar Systems. Goldsmith and Owen, The Search for Life in the Universe, 2nd ed. McKay, “The Origin and Evolution of Life in the Universe,” in The Origin and Evolution of the Universe.

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NASA/JPL/Space Science Institute

Jupiter’s moon Europa is at least partly molten inside. Its surface is covered with cracked and ¿ssured water ice, suggesting that ice sheets Àoat atop a layer of water slush. Such conditions could support primitive life. Saturn’s moon Enceladus also has a layer of surface water ice, but it is much thinner than Europa’s. Erupting geysers release water vapor, and these regions would be a good place to Ice jets send particles streaming into space hundreds of kilometers above the south pole begin the search for life. of Enceladus. Jupiter’s moon Io, with its sulfur compounds and erupting volcanoes, could also produce sulfur-based life forms. Indeed, biologists are studying the possible formation of life deep beneath the Earth’s surface where sulfur compounds and iron silicates are found. Thus, it is conceivable that life exists in other places in our Solar System; all we have to do is search. Ŷ

Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. How restrictive do you think we are being when we consider only “life as we know it”?

2. Do you think gas/liquid giant exoplanets resembling Jupiter are necessarily inhospitable to life? Consider also the moons that might orbit them.

3. Would you support the use of federal funds for the search for

Lecture 40: Life Beyond the Earth

bacteria and primitive microbes on Mars and some of the moons of Jovian planets?

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The Search for Extraterrestrials Lecture 41

“It’s hard to detect life, especially if you don’t go there. Even if you go there, it can be hard. We’ve gone to Mars, and we still don’t really know whether there ever was or is microbial life there.”

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n the preceding lecture, we saw that the existence of life on other planets and moons, at least in our Solar System, is possible. Yet even if we do land probes in such places, detecting life can be dif¿cult, as our studies of Mars have proved. How can we conduct such studies from a distance? An alien looking at the Earth from afar could deduce from the atmospheric composition that there might be extensive life on Earth. For example, a spectrum of Earth would show free oxygen in the atmosphere, which comes from photosynthesis (although this isn’t the sole source of free oxygen). The spectrum would also show free methane, which comes, in part, from decaying organic matter. Methane easily reacts with oxygen to form other compounds, thus basically disappearing. Methane and oxygen together in an atmosphere suggest some process by which the methane is continually replenished. That process could be life. If there weren’t living creatures on Earth, any initial methane in the atmosphere would quickly react with oxygen, leaving no methane. Uranus and Neptune have lots of methane but no free oxygen; there’s nothing for methane to react with, leaving methane in their atmospheres.

In our search for intelligent life, we could look for electromagnetic signals from extraterrestrials, particularly radio waves. Radio waves are inexpensive to produce in vast quantities. Also, radio waves travel through celestial gas and dust essentially unimpeded. Gamma rays and x-rays are expensive to produce and are easily blocked by thick clouds of gas and dust, just as optical or ultraviolet photons are. However, recently, astronomers have been using optical radiation to try to ¿nd evidence for extraterrestrials on planets orbiting nearby stars. They look for sharp pulses of light all having the same wavelength (like from a laser). Most of our radio telescope studies concentrate on detecting unnatural patterns in space signals—that is, patterns that could not have been produced by a rotating star or a disk of gas and dust 207

that might form planets. Instead, we look for signals that have been produced by intelligent beings. The Very Large Array set of radio telescopes in New Mexico collects and analyzes radio signals to search for unusual patterns. We also use the Arecibo radio telescope to collect signals from outer space during times when other science projects are conducted, such as astronomers studying a galaxy and its radio waves.

The Drake Equation

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eveloped by Frank Drake, the Drake equation highlights our sources of uncertainty in an estimate of the number of intelligent, communicating civilizations at any given time. The equation is N Rf s f p ne f1 fi f c L . The number (N) of communicating civilizations is a product of several factors: R = the rate at which stars form fs = the fraction of stars that are good suns fp = the fraction of good stars that have planetary systems

Lecture 41: The Search for Extraterrestrials

ne = the number of planets or moons per star that occur within what is called the ecosphere, the habitable zone fl = the fraction of those habitable planets and moons on which life actually develops fi = the fraction of living species that develop intelligence fc = the fraction of living species that reach the electromagnetic communicative phase L = the lifetime of the communicative phase

We don’t really know how many communicating civilizations there might be in our Milky Way Galaxy, but we can make an educated guess using the Drake equation. A reasonable estimate is R = 10 stars/year. The number is lower now but was higher in the past, when there was more free gas and dust in our Galaxy. What fraction of the stars are actually “good” suns (fs), lasting a reasonable amount of time for life to form and evolve on planets 208

orbiting them, but not having such a low mass that the luminosity and ecosphere are very small? Perhaps 0.1 is a good estimate. The fraction of suitable stars actually having planetary systems (fp) might be 1, or maybe it is only 0.1 (that is, 1 in 10), on average. The number of Earth-like planets or moons per planetary system (ne) could be between 0.1 and 1, or it could be larger (perhaps as high as 10, including the suitable moons). The fraction of Earth-like planets or moons (fl) on which even primitive life can be found is speculative but might be in the range of 103 to 1. The fraction of lifebearing planets on which intelligence actually arises (fi) is perhaps even more speculative, but might be 106 to 1. The fraction of intelligent life that has the ability and desire to communicate with aliens (fc) is also very speculative, so If civilizations don’t let’s guess 103 to 1. The typical lifetime last long while of a communicating civilization (L), or the cumulative lifetime of such civilizations communicating, there on a given planet, might be somewhere won’t be enough at between 100 or 109 years; we really any given time whose don’t know. signals we could Multiplying these factors together, from detect. The longer they the pessimistic view, there is only 1 chance live, the greater is our in a trillion (10–12) that a galaxy like the chance of ¿nding them. Milky Way has intelligent, communicative life forms. In other words, among a trillion galaxies (1012), more than the total number of galaxies in the observable parts of the Universe, our Galaxy is the only one with communicating intelligent life. On the other hand, according to the optimistic view, multiplying the numbers gives us 10 billion communicating civilizations in our Galaxy at any given time. Our two calculations show a vast range, from 1 in a trillion up to 10 billion, which doesn’t tell us how many communicating civilizations are out there. It does, however, show us where the greatest uncertainties are— the lifetime of an intelligent, communicating civilization (L) and the fraction of life-bearing planets on which intelligence develops. It is quite possible that primitive life—bacteria and microbes—are fairly common elsewhere. Intelligence at or above our level, however, may be rare. During Earth’s history, there have been about 10 billion species. 209

Lecture 41: The Search for Extraterrestrials

As far as we can tell, only one, Homo sapiens, has reached this level of intelligence. We arrived only relatively recently on Earth; thus, other life forms could have examined Earth during most of its history and concluded that Earth didn’t have intelligent life. In addition, intelligence at our high level could, in a sense, be “Unless we considered detrimental to species survival. We’re continue trying, the ¿rst species known that has the capability to destroy itself and most other complex lifeforms. it’s almost Other intelligent life, on other planets, may certain that we’ll have existed for a short time but subsequently never detect destroyed itself. other intelligent Many scientists believe that Earth had to meet a civilizations.” number of amazing conditions for it to exhibit the stability needed to develop intelligent, communicative life. For example, if we didn’t have a large orbiting moon, our axis of rotation would undergo chaotic variations, leading to signi¿cant changes in the climate over rapid time scales. If Jupiter were not present, the debris in the Solar System would not have been cleared out, and Earth would still be bombarded by meteoroids, causing extinctions before communicating intelligence had a chance to develop. By the same token, if Jupiter had a highly eccentric orbit rather than a nearly circular one, it would eventually knock the small terrestrial planets out of the Solar System. Finally, life on Earth could be considered a rarity because we needed heavy elements, such as carbon, oxygen, and calcium, from which to form. The earliest stars in our Galaxy did not have those heavy elements because there hadn’t been enough time for other stars to form them and eject them into the cosmos. Ŷ

Important Term luminosity: Power; the total energy emitted by an object per unit of time; intrinsic brightness.

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Suggested Reading Drake and Sobel, Is Anyone Out There? The Search for Extraterrestrial Intelligence. Goldsmith and Owen, The Search for Life in the Universe, 2nd ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Sagan and Shklovskii, Intelligent Life in the Universe. [email protected], seti.berkeley.edu. (Download a program that, as a background task, will analyze data from radio telescopes, searching for signs of extraterrestrial life.) Ward and Brownlee, Rare Earth: Why Complex Life Is Uncommon in the Universe.

Questions to Consider 1. In the Drake equation, use your own preferences for each quantity to derive the number of intelligent, communicating civilizations in our Galaxy. Discuss the importance of the value of L, the lifetime of the civilization.

2. If 10% of all stars are of suitable type for life to develop, 30% of all stars have planets, and 20% of planetary systems have a planet or moon at a suitable distance from the star, what fraction of stars have a planet suitable for life? Roughly how many such stars would there be in our Galaxy?

3. Do you think the conclusion that Earth had to be “just right” for intelligence to develop might be too anthropocentric?

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Special Relativity and Interstellar Travel Lecture 42

“We come now to Lecture 42, which, of course, provides the answer to the question of Life, the Universe, and Everything—at least according to The Hitchhiker’s Guide to the Galaxy.”

Lecture 42: Special Relativity and Interstellar Travel

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ur Galaxy is huge, and the distances between the stars are vast. Is interstellar travel possible with the right spacecraft? Interstellar travel is possible at relatively slow speeds. For example, at the escape velocity from Earth (11 km/s), a large spaceship could reach one of Earth’s nearest stars—Sirius, 8.7 light years away—in about 240,000 years. Voyager II is heading toward Sirius in the constellation Canis Major and will pass close to it in about 160,000 years. On average, it is traveling a bit faster than 11 km/s. Voyager I is heading toward the constellation Camelopardalis (the Giraffe) and will pass close to a star there in about 300,000 years. The Pioneer spacecraft, which passed Jupiter in the early 1970s, are heading toward other stars and will reach them in about 2 to 3 million years. Is it possible to travel to another star within our lifetime? We turn to Albert Einstein’s special theory of relativity to see how it could be done. At the time Einstein was working on his special theory of relativity, other physicists were working on similar concepts, namely Poincaré and Lorentz. However, Einstein received the credit because he brought it all together in a consistent physical framework, rather than just developing mathematical equations. Einstein concluded that Maxwell’s equations of electromagnetism were incompatible with Newtonian mechanics, which was based on Galileo’s observations. One of the problems in Maxwell’s equations was that the speed of light, c, was always the same, regardless of one’s reference frame. In Newtonian mechanics, velocities add up in a linear way, which didn’t seem compatible with electromagnetism. Einstein concluded that there was a problem with Newtonian mechanics, not electromagnetism. Experimental evidence showed that the speed of light is a constant regardless of the motion of the source or the observer. We are uncertain whether Einstein knew about that result or how much he was inÀuenced by it if he did. 212

The special theory of relativity is “special” because it deals with constant speeds and no gravitational ¿eld. Later, we will discuss Einstein’s general theory of relativity, which differs. Einstein made two fundamental assumptions in developing his theory. The ¿rst was the principle of relativity, which states that the laws of physics are the same for all observers moving at constant speeds relative to one another. More simply, if you are moving with uniform speed and direction relative to your surroundings, you cannot tell that you are moving; rather, your surroundings seem to be moving past you. It is similar to Àying in a jumbo jet, where we feel like we’re not moving (in the absence of turbulent air), but the ground, instead, is moving beneath us. The second assumption states that the speed of light is measured to be the same for all observers, regardless of their state of motion. This is consistent with electromagnetism. There are four important consequences to Einstein’s two fundamental assumptions. The ¿rst consequence is called time dilation; moving clocks slow down as viewed by an observer at rest. For example, consider a particular kind of clock at rest in which a light pulse emitted from a source takes time t0 2 L c to make a round trip (from the source to a mirror and back to the source). Here, L is the distance between the source and the mirror, and c is the speed of light. If the clock is moving relative to a stationary observer, then the observer sees the light travel a longer distance along a diagonal path, from the source to the mirror and back again. Thus, the length of the second line, t1—or time required—is longer than t0: t1 = Ȗ t0, and J 1/ 1  v 2 / c 2 . The second consequence is called length contraction; moving objects contract in the direction of motion. If a meter stick moves past us, it will look shorter than it really is by a factor of 1 J . Thus, L1 L0 / J . The third consequence is called lack of simultaneity; people in different reference frames will not necessarily see two events as being simultaneous. Einstein considered a “thought experiment” (that is, a hypothetical experiment whose results can be deduced through logical thinking, not an actual measurement) in which one train passes another at rest. When the trains are exactly aligned, an explosion ignites on each end of the resting train. To a person on the moving train, the explosion at the end of the train in the direction of travel would appear to ignite before the explosion at the other

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end. However, the person on the stationary train would see both explosions igniting at the same time.

Lecture 42: Special Relativity and Interstellar Travel

Finally, and most famously, Einstein came up with the equation E = mc2. More correctly, E = mc2 = Ȗm0c2, in which E is energy and m0 is the mass of an object at rest, known as its rest mass. If an object moves, its mass will change by a factor of Ȗ. We simply use E = mc2, in which it is understood that m = Ȗm0. As one considers progressively higher speeds, initially, the factor of Ȗ increases only slightly. But as the speed approaches that of light, Ȗ increases quickly. Indeed, as v/c approaches 1, Ȗ approaches in¿nity. We can’t travel at the speed of light, but if we could, time would slow down so much that it would essentially stop. If we could travel faster than the speed of light, time would actually go backward! However, it is impossible for us to travel at the “Interstellar travel, though speed of light because of the equation E = mc2. If E = Ȗm0c2 and Ȗ approaches possible in principle, in¿nity as the speed approaches c (the is very, very dif¿cult in speed of light), then the energy required practice. It’s conceivable to actually reach the speed of light that the reason we is in¿nite. have not seen any Let’s consider an example illustrating the evidence for intelligent essence of relativity. Relativity is well extraterrestrials demonstrated by an experiment using traversing vast distances a particle called a muon (a negatively is that neither we nor they charged particle somewhat like an electron but 209 times more massive), have ¿gured out how to which is unstable and decays at rest in do it.” 2.2 microseconds, or 2.2 millionths of a second. A muon traveling at 99% of the speed of light for 2.2 microseconds should be able to travel only 0.653 km before decaying into other kinds of particles. Thus, a muon emitted at one end of a laboratory 3 km long will not reach the other end. However, time for the muon slows down by a factor of 7.09, according to the laboratory observer. That is, the muon, which is at rest relative to itself (the principle 214

of relativity), thinks that it lived only 2.2 microseconds, but laboratory observers see the traveling muon experience a lifetime 7.09 times longer, or about 15.6 microseconds. In that amount of time, the muon could travel 4.63 km and, hence, will reach the other end of the laboratory. According to the muon, on the other hand, the laboratory is moving past it at 99% of the speed of light, and hence, its length gets contracted by a factor of 7.09, from 3 km to only 0.423 km. In 2.2 microseconds, the laboratory would have moved 0.653 km, more than its apparent length. Thus, the muon thinks that it was emitted from one end of the lab, and then the other end rushed over and hit it. The time and distance over which the muon (or laboratory) moved depends on our frame of reference. To laboratory observers, the muon moved farther than expected because of time dilation. To the muon, the lab was shorter than expected because of length contraction. They agree on the measurable quantities (muon emitted at one end of the lab and detected at the other end), but they disagree about how this happened. Both are right, because they are in different frames of reference. Now we apply special relativity to interstellar travel. A rocket heading for Sirius at 99.5% the speed of light would take 17.5 years to make a round trip, as experienced by someone remaining on Earth. But at that speed, someone aboard the rocket would experience only 1.75 years and would, thus, age by only 1.75 years, while those on Earth aged 17.5 years. At 99.99% the speed of light, 17.4 years will have passed on Earth, but only 3 months will have passed for the traveler. In principle, if we could approach the speed of light without physical harm, we could make the journey in shorter amounts of time as our speed increased. From the traveler’s point of view, the length of time for the trip is greatly shortened because the traveler experiences rest rather than motion, making it seem as if the Universe is moving by very quickly and, hence, is contracted in length. For a spacecraft to move at speeds approaching the speed of light would require truly vast, almost unfathomable, amounts of energy. Our current technology has not solved this problem; therefore, rapid interstellar travel is, as yet, possible in theory only. Moreover, to avoid serious bodily injury or death, one would need to accelerate to high speeds very slowly and decelerate very slowly upon reaching one’s destination. Thus, for much of the journey, one’s speed would be low, and there would not be substantial savings from time dilation and length contraction. Ŷ 215

Important Terms E = mc2: Einstein’s famous formula for the equivalence of mass and energy. in¿nity: All numbers. A countable in¿nity can be put in one-to-one correspondence with the counting numbers, whereas an uncountable in¿nity cannot. special theory of relativity: Einstein’s 1905 theory of relative motion, gravity excluded. time dilation: According to relativity theory, the slowing of time perceived by an observer watching another object moving rapidly or located in a strong gravitational ¿eld.

Suggested Reading

Lecture 42: Special Relativity and Interstellar Travel

Kirkpatrick and Wheeler, Physics: A World View, 4th ed. Mallove and Matloff, The StarÀight Handbook: A Pioneer’s Guide to Interstellar Travel. Mook and Vargish, Inside Relativity. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. Explain how it is possible, in principle, to travel many light years in a short time interval as measured by the traveler.

2. How long would it take a rocket ship traveling at 100 km/s to reach a star that is 20 light years away?

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3. Suppose you are in a rocket ship that is moving at 97% of the speed of light. If your journey to another star appeared to take 30 years from the perspective of an Earth-bound observer, how long did it take in your frame of reference? How far did you travel in your frame of reference?

4. Do you think humans or their successors (machines?) will ever overcome the enormous barriers to rapid interstellar travel?

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Stars—Distant Suns Lecture 43

“I’ll be discussing stars—their births, their lives, their deaths. What happens to them? How do they produce the elements of the Universe? What kind of compact and weird remains come about when stars die?”

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Lecture 43: Stars—Distant Suns

tars are distant versions of our Sun—glowing, opaque balls of gas held together by gravity. Nuclear reactions occur deep in the core, providing the light that we see. In the next several lectures, we will discuss stars, their births, lives, and deaths. We start by describing how we measure the distances between relatively nearby stars and Earth. There is a seemingly countless number of stars in the Milky Way Galaxy, but the number of stars is, in fact, ¿nite. A big galaxy like our own has roughly 300 to 400 billion stars. Despite the large number of stars, the distances between them are vast. We can measure these distances using a method called triangulation, which is based on the concept of parallax shifts in apparent position of objects (relative to more distant objects) as viewed from different physical locations. We discussed this concept in a previous lecture. First, we photograph a relatively nearby star, then take another photograph 6 months later, after the Earth has moved 2 AU in its orbit around the Sun. We then measure the angular shift with respect to more distant stars whose positions appear relatively stationary. The parallax (p) of a star is half the angular shift produced over a 6-month baseline (2 AU, the diameter of Earth’s orbit). Thus, as viewed from the star, the parallax is simply the angle subtended, or covered, by 1 AU. As the distance of a star increases, the parallax decreases. All known stars have parallax shifts of less than 1 arc second. The distance of a star whose parallax is 1” (1 second of arc) is called 1 parsec (1 pc). One parsec is about 3.26 light years. Recall that a full circle is 360°; 1° = 60 minutes of arc (60’); 1’ = 60 seconds of arc (60”). To illustrate, 1” is the angle subtended by a dime seen from a distance of 3.7 km. Using the parsec unit, the relationship between distance and parallax is simple. A star’s distance, d (in parsecs), is 218

the inverse of its parallax, p (in seconds of arc): d = 1/p. The measurement works because a distant set of stars will shift very little as the Earth orbits the Sun, while nearby stars shift much more. However, it’s dif¿cult to accurately measure a shift of less than 1/100 of an arc second. The most distant stars that we can measure from the ground have distances of about 100 pc; those large distances aren’t very accurate, however. We can accurately measure a star’s shift if its parallax is 1/10 of an arc second, or 10 pc. We know accurately the distances of stars within 10, 20, or 30 pc and less accurately the distances of stars up to about 100 pc. To measure stars more distant than 100 pc, we use satellites. In 1989, the European Space Agency launched a satellite called Hipparcos (in honor of the ancient Greek astronomer) that catalogued about 120,000 stars out to 100 pc in distance, or about 300 light years away. Now let’s look at the surface temperatures of stars. As viewed from Earth, stars in the night sky have different colors. Hot stars appear blue, cool stars appear red, and medium-temperature stars appear white. As discussed in Lecture 21, the spectra of hot, opaque objects glowing on their own—because of the random motions of particles within them—produce Planck curves. Strictly speaking, these curves apply in their precise mathematical form only to objects that are perfect absorbers and emitters of radiation, known as ideal radiators, or black bodies. To review, an ideal radiator (black body) doesn’t reÀect any radiation and doesn’t transmit any radiation. It only absorbs radiation, which causes it to heat up. It is a perfect absorber and a perfect emitter because the spectrum of its emitted light follows a very precisely de¿ned mathematical form, the Planck curve. Stars are roughly—but not ideally—black bodies; they do have some absorption lines, so the spectrum depends a little on variables other than surface temperature. However, the shape of the emitted spectrum depends mostly on the surface temperature. Cool stars peak in the red or infrared parts of the spectrum; hot stars peak in the green, blue, or even violet parts of the spectrum. We describe this mathematically through Wien’s law, which says that the wavelength of the peak of the spectrum multiplied by the surface temperature of the star is a constant: ȜpeakT = a constant, in which the constant is about 2.9 u 107 in units of angstrom-Kelvins. We can calculate a star’s surface temperature by measuring the wavelength of the peak of the star’s spectrum. 219

The main stellar classi¿cation scheme, OBAFGKML , depends on surface temperature. The traditional mnemonic is “Oh, Be A Fine Girl, Kiss Me Lovingly!” O-type stars have surface temperatures Name to Know of more than 25,000 Kelvin (K), while B-type stars are annon, Annie Jump (18631941) from 11,000 to 25,000 K. was an American astronomer. Stars in these two classes She classi¿ed the photographic spectra appear to be bluish. A-type of several hundred thousand stars, stars are between 7500 and demonstrating that the spectra depend 11,000 K, F-type stars are mostly on the stellar surface temperature. between 6000 and 7500 She arranged the spectral types into the K, and G-type stars are sequence OBAFGKM. between 5000 and 6000 K. Stars in these three classes appear white. K-type stars are between 3500 and 5000 K, M-type stars are between 2200 K and 3500 K, and L-type stars (recognized only in the past decade or so) are below 2200 K. These types of stars appear orange or even red. Each main class is divided into 10 subclasses, ranging from 0 (hottest) to 9 (coolest). Our Sun is a G2 star, with a temperature of 5800 K. “How can you remember this sequence? You The surface temperature of a star also largely dictates which absorption lines could say, ‘Oh, Be A Fine are visible in the spectrum. Each star’s Girl; Kiss Me Lovingly— spectrum shows different absorption or Oh, Be A Fine Guy; lines spanning a range of strengths from Kiss Me Lovingly,’ various chemical elements near the star’s depending on your surface. At very high temperatures, hydrogen is ionized and, thus, doesn’t preferences. Some of my produce absorption lines; for this reason, students have a different O-type stars don’t show hydrogen in way of remembering it. their spectra. In cool stars, hydrogen is They say, ‘Oh, Boy, Alex generally in its lowest electronic energy level. As discussed in Lecture 22, the Filippenko Gives Killer resulting absorption lines therefore appear Midterms, Laughing.’ ” in the ultraviolet part of the spectrum

Lecture 43: Stars—Distant Suns

C

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(Lyman series) but not in the visible range (Balmer series). Thus, cool stars also don’t show hydrogen in their visible spectra but for a different reason than hot stars. All other elements can be explained in a similar way. Though a star’s surface temperature mostly sets the strength of the observed absorption lines, for any given temperature, two different stars will have different absorption-line strengths, depending on the abundance of each element near the star’s surface. We assume, to a good ¿rst approximation, that the interior composition is similar to that of the surface. Astronomers have determined that more than 98% of the mass of typical stars consists of hydrogen and helium, elements that were produced early in the Universe, at the time of the Big Bang or shortly thereafter. Ŷ

Important Terms black body: An object that absorbs all radiation that hits it; none is transmitted or reÀected. It emits radiation due to thermal (random) motions of its constituent particles, with a spectrum that depends only on the temperature of the object. parsec: A unit of distance equal to about 3.26 light years (3.086 u 1013 km).

Suggested Reading Cooper and Walker, Getting the Measure of Stars. Hirschfeld, Parallax: The Race to Measure the Cosmos. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. What is the distance of a star whose parallax is 0.3 seconds of arc? What is the parallax of a star whose distance is 40 pc?

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2. Though it would take longer to measure the parallax of a star from Jupiter than from Earth, would you be able to determine the distances more accurately, as well as determine larger distances? (Assume you are above Jupiter’s atmosphere and have a clear view of the sky.)

3. The Sun’s surface temperature is about 5800 K and its spectrum peaks at 5000 Å. An O-type star’s temperature may be 40,000 K. (a) According to Wien’s law, at what wavelength does its spectrum peak? (b) In what part of the spectrum might that peak be? (c) Can the peak be observed with the Keck telescopes?

Lecture 43: Stars—Distant Suns

4. Make up your own mnemonic for spectral types, through type L.

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The Intrinsic Brightnesses of Stars Lecture 44

“An important characteristic of a star is how much energy it produces. That, together with these other fundamental properties of stars that we’ve been discussing, will give us a more complete understanding of the physical way in which stars work, and generate their energy and shine.”

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star’s brightness can be de¿ned in terms of both its observed (apparent) brightness and its intrinsic brightness (luminosity, or power). The most obvious observed fact about stars is that they have different apparent brightnesses. Astronomers use the term apparent magnitude to quantify this observed quality; the term dates back to the ancient Greek astronomer Hipparchus, who ¿rst catalogued the positions and apparent brightnesses of more than 850 stars. Hipparchus categorized the typical brightest stars as magnitude 1. The faintest stars visible to the naked eye were classi¿ed as magnitude 6. Later, astronomers determined quantitatively that a 1st-magnitude star is 100 times brighter than a 6thmagnitude star. That is, per second, 100 times more photons hit our eyes from a 1st-magnitude star than from a 6th-magnitude one. The difference of 5 magnitudes corresponding to a factor of 100 in brightness is due to the fact that our eyes respond according to a logarithmic scale, to a reasonable ¿rst approximation. For every equal factor in brightness, there is a one-step increase or decrease in observed magnitude; every 1 magnitude of difference must correspond to the 5th root of 100 (an irrational number: 2.512…) in brightness. Thus, a 1st-magnitude star is roughly 2.5 times brighter than a 2ndmagnitude star, and so on. In general, for two stars, a and b, with apparent brightnesses Ba and Bb and apparent magnitudes ma and mb , we have Ba / Bb 2.512( mb  ma ) . What are the apparent magnitudes of some common celestial objects? The Sun is –26.8 (apparent magnitudes can be negative); the full Moon is about –12.6, depending on how close it is to Earth; Venus at its brightest is –4.4; Mars at its brightest is –2.8, and Jupiter is comparable. Sirius, the brightest star, is –1.5; Canopus, the second brightest star, is –0.7. Many stars 223

Lecture 44: The Intrinsic Brightnesses of Stars

have magnitudes of 0 or 1. The very faintest ones visible with the naked eye are magnitude 6. The faintest stars observable in long exposures with powerful telescopes, such as the Hubble or the Keck telescopes, are about magnitude 30. If we look at stars through different-colored ¿lters, we can isolate the light in either the blue or the red part of the spectrum or in other parts, as well. Note that in astronomical jargon, a red ¿lter is one that passes (transmits) red light and blocks all other colors, while a blue ¿lter is one that passes blue light and blocks all other colors. Technically, the apparent magnitude of a star depends on which part of the spectrum we are observing. For example, Betelgeuse looks “When you see patterns, red to the naked eye. Thus, through a blue ¿lter, it appears fainter (higher magnitude) you know that there’s than through a red ¿lter. got to be some physics behind those patterns. We de¿ne the intrinsic brightness (power) Watching the patterns of stars as their luminosity. Luminosity can be quanti¿ed as absolute magnitude, and quantifying them which is the apparent magnitude a star allows you to get to that would have at a distance of 10 parsecs ¿rst step of a complete (about 32.6 light years) from Earth. If all physical understanding stars were the same distance from Earth, the of the object that you differences in their apparent brightnesses would correspond to differences in their are studying.” intrinsic powers. If our Sun were 10 pc from Earth instead of 1 AU, it would have a magnitude of 4.8 instead of –26.8. One pc is about 200,000 AU, and 10 pc is about 2 million AU; therefore, the Sun would look much fainter at 10 pc. Remember, the higher the magnitude, the fainter the star. The qualitative relationship between apparent magnitude and absolute magnitude is as follows: m  M 5log(d / 10) , in which m is apparent magnitude, M is absolute magnitude, d is distance in parsecs, and the logarithm is base 10. In this course, we will use the more physical units of apparent brightness (instead of apparent magnitude) and luminosity (instead of absolute magnitude). The apparent brightness, b, is de¿ned in terms of the amount of energy that hits the pupils of our dilated eyes each second. Speci¿cally, the 224

apparent brightness is the amount of energy per second per square centimeter of the collecting device, be it our eyes or some kind of telescope. Apparent brightness is clearly related to the intrinsic (true) brightness, also called the luminosity (power) of a star: The greater its luminosity, all other things being equal, the greater its apparent brightness. But a star’s distance is a factor in its apparent brightness, as well; an intrinsically powerful (luminous) star looks dim when it’s very far away. The relationship between apparent brightness, the luminosity, and the distance is known as the inversesquare law, analogous to the inverse-square law of gravity discussed in Lecture 16. Mathematically, b L (4Sd 2 ) , in which the intrinsic brightness is L (luminosity), and d is the star’s distance from Earth. Using this inverse-square law, we can see how luminosity, brightness, and distance are related in a quantitative way and how we can use this relationship to determine luminosity. Stars emit a great deal of energy; the Sun, for example, emits 4 u 1033 ergs per second. An erg is close to the amount of energy required to lift 0.001 gram a distance of 1 centimeter at the surface of the Earth. [NOTE: During the lecture, the mass was erroneously given as 1 gram instead of 0.001 gram, leading to a value a factor of 1000 too high.] It is roughly equivalent to the amount of energy it takes a Ày to do a pushup. A more convenient unit than ergs is solar luminosity, designated Lsun = 3.83 u 1033 ergs per second, or about 4 u 1033 erg/s. Thus, if a star’s luminosity is 8 u 1033 erg/s, we say it is a 2-solar-luminosity star. Lsun is often denoted by L with a circle subscript, and that subscript has a dot in the middle of it. The dotted circular subscript is the astronomical symbol for the Sun. If we plot stars’ luminosity (vertical axis) against their surface temperature (horizontal axis), we get what is called the Hertzsprung-Russell (H-R) diagram, or the temperature-luminosity diagram. In contrast with the usual convention in graphs, the surface temperature decreases from hot to cool as one goes from left to right. We ¿nd that most stars fall along a well-de¿ned main sequence in the diagram, going from the upper left (hot, luminous stars) down to the lower right (cool, low-luminosity stars). There are some additional regions where stars tend to appear but in smaller numbers. It is striking that certain parts of the diagram contain very few stars. Thus, something about the structure of stars allows them to have only certain 225

combinations of surface temperature and luminosity. These combinations can change as a given star evolves with time. When we observe such speci¿c patterns—not randomly produced—in our studies of the stars, we conclude that some physical explanation accounts for these patterns. This provides the ¿rst step in our understanding of the objects we study. Ŷ

Important Terms absolute magnitude: Logarithmic measurement of the luminosity of stars; assumes all the stars to be at the same distance of 10 parsecs from Earth. Hertzsprung-Russell (H-R) diagram: A plot of the surface temperature (or color) versus luminosity (power, or absolute brightness) for a group of stars. Also known as a temperature-luminosity diagram.

Lecture 44: The Intrinsic Brightnesses of Stars

inverse-square law: Decreasing with the square of increasing distance. For example, the brightness of a star is proportional to the inverse-square of distance, as is the gravitational force between two objects. main sequence: The phase of stellar evolution, lasting about 90% of a star’s life, during which the star fuses hydrogen to helium in its core.

Suggested Reading Cooper and Walker, Getting the Measure of Stars. Dickinson, Nightwatch: A Practical Guide to Viewing the Universe, 3rd ed. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. ———, Peterson First Guide to Astronomy. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

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Questions to Consider 1. Star Albert appears to have the same brightness through red and blue ¿lters. Star Bohr appears brighter in the red than in the blue. Star Curie appears brighter in the blue than in the red. Rank these stars in order of increasing surface temperature.

2. If a star that is 100 light years from us appears to be 10th magnitude, would its absolute magnitude be a larger or a smaller number?

3. If one star has twice the apparent brightness of another star but is a factor of 8 farther away, what is its luminosity relative to the other star?

4. Besides distance and luminosity, what other factor might affect the apparent brightness of a star? (Consider the headlights of an oncoming car viewed through fog and through clear conditions.)

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The Diverse Sizes of Stars Lecture 45

“If you plot the luminosity on the vertical axis versus the surface temperature on the horizontal axis, most stars fall in distinct regions of that temperature-luminosity diagram. … Now let’s see how we can use the diagram to infer the sizes or radii of stars, another fundamental property of stars.”

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Lecture 45: The Diverse Sizes of Stars

et’s review the relationship among temperature, radius, and luminosity before seeing how we can infer a star’s radius. The HertzsprungRussell diagram, or temperature-luminosity diagram, can be described as follows. On the vertical axis, luminosity is listed in units of absolute magnitude, though we will refer to the less arbitrary solar luminosity. On the top horizontal axis, spectral types are listed (O, B, A, F, G, K, M, L), which as we noted previously, are related to surface temperature. On the bottom horizontal axis, surface temperature is given in units of 1000 Kelvin. The main sequence on which most stars fall in this temperature-luminosity diagram crosses diagonally from the upper left-hand side to the lower right-hand side. Remember that stars are nearly perfect emitters of radiation; thus, their spectra are nearly those of a perfect thermal emitter—that is, a Planck curve. The area underneath each curve grows with increasing surface temperature of the star. Recall from Lecture 21 that this phenomenon is quanti¿ed by the Stefan-Boltzmann law. The law says that hotter stars emit more energy per second than cooler stars per unit of emitting area, and the amount they emit is proportional to their surface temperature raised to a power of 4, or T4. Mathematically: E VT 4 , in which E is energy emitted per second per unit surface area, ı is the Stefan-Boltzmann constant, and T is surface temperature. For example, if two stars have equal areas and the surface temperature of one is 6000 K and the other is 3000 K, the ratio of surface temperatures = 6000/3000 = 2, and 24 = 16. Therefore, one star that is twice as hot as another emits 16 times as much energy per second as the cooler star, if they have the same surface area.

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In the Hertzsprung-Russell diagram, the temperatures of stars are plotted against their luminosities. The position of a star in the diagram provides information about its present evolutionary stage and its mass.

The luminosity (power) of a star is equal to the amount of energy emitted per second per unit surface area, multiplied by the total surface area. The surface area of a star can be approximated as 4SR2 (that is, proportional to the square of its radius), because most stars are roughly spherical. Thus, L = 4SR2VT4 for a star of radius R and surface temperature T. O-type main-sequence stars are much more luminous than M-type main-sequence stars, primarily because their surface temperatures are considerably higher than those of M-type stars. The radius of the star—in this case—is not as important along the main sequence. 229

Lecture 45: The Diverse Sizes of Stars

The luminosity of cooler stars can be much greater than that of hotter stars only when the cooler stars are very large. Some stars can be 10,000 to 1 million times more luminous than the Sun yet have roughly the same temperature, only somewhat cooler than the Sun. We call these supergiants or red supergiants because, being somewhat cooler, they tend to be redder than the Sun. If a star is 1 million times as luminous as the Sun but has the same temperature, the radius of the star must be 1000 times greater than the radius of the Sun. The stars Betelgeuse in Orion and Antares in Scorpius are good examples of red supergiants. Stars that are only about 100 times more luminous than the Sun but somewhat cooler are called red giants. Some other stars are about the same temperature as the Sun but emit much less energy per second, typically 1/10,000 that of the Sun. These stars are much smaller than the Sun (about 1/100 of the Sun’s radius) and are called white dwarfs. Sirius B is a good example of a white dwarf. The terminology can “Looking at Betelgeuse sometimes be confusing: Main-sequence stars can be white, and main-sequence stars in the upper-left are also called dwarfs in comparison to shoulder of Orion, we giants and supergiants. However, a white calculate that it should main-sequence star, such as the Sun, is not a be about as big as the white dwarf, even though it is white and it’s a dwarf in comparison to the supergiants. radius of Jupiter’s orbit Remember that white dwarfs have a much around the Sun. Can lower luminosity than the Sun does. you imagine that? If we were orbiting that star, Let’s look at how we can determine the we would be well radii of stars. In the case of relatively nearby stars, we can infer their distance inside it.” from their parallax. We can also measure their apparent brightness, b. This allows us to calculate their luminosity, L = 4Sd 2 b, from the inverse-square law of light. We can also infer their surface temperatures from the wavelength at which their spectrum peaks, using Wien’s law (recall Lecture 21). But above we saw that L = 4SR2VT4. Setting this equal to L = 4Sd 2 b, the only unknown quantity is R, the star’s radius. When calculating radii, it’s important not to 230

confuse the 4SR2 in the Stefan-Boltzmann formula, which is the surface area of the star, with the 4Sd 2 in the inverse-square law of light. In some cases, we can verify the measured radii of stars by taking direct images of those stars that are suf¿ciently large and close. In addition, we can use the technique called interferometry, which we discussed in Lecture 24. This has been done at infrared wavelengths for some stars. Not all stars have a constant radius; some stars vary in their size. This variation in size also causes a variation in luminosity and, hence, in apparent brightness. Mira, in Cetus the Whale, is an example of a star whose size varies. Its apparent magnitude can change from 3 (bright) to 9 (much dimmer) over time. Mira is called a long-period variable star because it takes more than a year to go through a full cycle of changing brightness. Because the star is unstable, or nearing the end of its life, the plot of brightness versus time (the light curve) does not look exactly the same from cycle to cycle. Another type of variable star, called a Cepheid variable, is important for determining the size and age of the Universe—which, as we will see later, are fundamental questions of cosmology. Cepheid variables change from faint to bright rapidly, fading again more slowly to form a distinct and easily recognizable light curve having a period of between 1 Name to Know and 100 days. All Cepheids are quite luminous stars, but those eavitt, Henrietta (18681921) whose average luminosity is was an American astronomer higher have longer periods of who demonstrated a relationship oscillation than those whose between the period and luminosity average luminosity is lower. of Cepheid variable stars. This This period-luminosity relation was done by analysis of Cepheids was proved through studies of clustered together and, therefore, at the same distance, so that the Magellanic Clouds, two differences in brightness indicate satellite galaxies of our Milky luminosity differences. Way, in which the changing apparent brightness of Cepheid variables was noted. In the Magellanic Clouds, all the stars are about the same distance from Earth. Thus, distance becomes irrelevant in comparing apparent brightness,

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and differences in apparent brightness must correspond to differences in luminosity. Knowing a particular Cepheid’s period, we can infer its average luminosity. From its average apparent brightness, we can determine its distance. Because the Cepheids in other galaxies appear very faint yet are intrinsically very luminous, astronomers deduced that those galaxies must be extremely far away. Having determined star sizes, we can now deduce the sizes of some of the exoplanets that orbit them, using the transit technique discussed in Lecture 39. During the transit of an exoplanet, the apparent brightness of a star decreases somewhat because the planet is covering part of the star. This creates a dip in the star’s light curve. By measuring the amount of this dip, we derive the planet’s area relative to that of the star: It is equal to the amount of fractional decrease in the star’s brightness. Knowing the star’s radius, we calculate its area, and hence, we infer the planet’s area and its radius. It is through measurements such as these that we hope to ¿nd and measure the sizes of many terrestrial-like exoplanets with the Kepler spacecraft. Ŷ

Important Terms

Lecture 45: The Diverse Sizes of Stars

Cepheid variable: A type of pulsating star that varies in brightness with a period of 1 to 100 days. cosmology: The study of the overall structure and evolution of the Universe. red giant: The evolutionary phase following the main sequence of a relatively low-mass star, such as the Sun; the star grows in size and luminosity but has a cooler surface. variable star: A star whose apparent brightness changes with time.

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Suggested Reading Cooper and Walker, Getting the Measure of Stars. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. If a red giant has half the Sun’s surface temperature but 100 times its radius, what is the giant’s luminosity relative to that of the Sun?

2. Suppose you were to double the Sun’s surface temperature. What would you need to do to its radius in order for the luminosity to remain unchanged?

3. Consider two stars of the same spectral type and subtype but not necessarily both on the main sequence. Describe whether this information is suf¿cient to tell you how the stars differ in (a) surface temperature, (b) size, and (c) distance.

4. Why do you think the radii of very few exoplanets have been determined thus far?

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Binary Stars and Stellar Masses Lecture 46

“I’ve described how astronomers determine the intrinsic properties of stars—and it turns out that these intrinsic properties are dictated by the mass of the star. In this lecture, I will describe how this key property of stars is determined.”

Lecture 46: Binary Stars and Stellar Masses

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e must realize that many stars are parts of multiple star systems; that is, usually, we ¿nd at least two stars orbiting each other. In almost all cases, the naked eye sees only a single star, because the light from the multiple stars merges together. The two stars in a binary system orbit their common center of mass (center of gravity), or their balance point, as we discussed when we talked about exoplanets and their stars. The high-mass star is closer to the center of mass than the low-mass star. Mathematically, M1r1 = M2r2, in which M1 is the mass of the high-mass star and r1 is its distance from the center of mass; M2 and r2 are the equivalents for the lower-mass star. If the two masses are equal, the center of mass is equidistant from the two stars. The two stars are held together according to Newton’s law of universal gravitation, F = GM1M2/d2. According to Kepler’s second law, when the two stars are close to each other, they move faster than when they are farther apart. Let’s look at some types of binary stars, which can be broadly divided into optical doubles and physical binary stars. Optical doubles, or fake doubles, are two stars that appear to be gravitationally bound, because viewed from Earth, they seem to be close together. However, optical doubles just happen to be along the same line of sight and are not gravitationally bound to each other. A good example is Alcor, the second star from the end of the Big Dipper’s handle, which has an apparent companion called Mizar. Physical binary stars are gravitationally bound to each other. There are four main categories (visual, eclipsing, astrometric, and spectroscopic), though they are not mutually exclusive. Visual binaries are those that appear as one star to the naked eye, but through a telescope, it is obvious that there are two

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stars. Polaris, the North Star, is good example of a binary star system, which is made up of Polaris A (actually two more stars in itself) and Polaris B. Eclipsing binaries appear as single stars through a telescope. Yet when we monitor the brightness of an eclipsing binary star, we notice that the brightness changes with time because of another orbiting star. The two stars orbit around their mutual center of mass, but from Earth’s perspective, one star periodically passes in front of the other, blocking all or part of the other star’s light. The size of the dip in total apparent brightness of the star system depends on whether the hotter star (with a greater amount of emission per unit area) or the fainter star (with a smaller amount of emission per unit area) is blocked. When the hotter star eclipses the cooler star, the light curve (plot of brightness versus time) shows a small a dip in brightness. When the cooler star eclipses the hotter star, the dip is deeper. Astrometric binaries are stars that appear to move slightly backward and forward in the sky over the course of time. This happens when two stars orbit each other, but one star is so faint that we can’t really see it (at least, not easily). We deduce its presence by noting this wobble, or backward-forward motion. Sirius is such a star. It has a faint white dwarf companion (now known as Sirius B), whose presence was ¿rst noted through measurements of its position over time (a process called astrometry). The most common binary stars are the spectroscopic binaries. Even through a telescope, those stars appear as one. The brightness doesn’t appear to change, but when we take multiple spectra of the star over time, we see some unexpected results. In the spectra, we see pairs of absorption lines— two hydrogen lines or two iron lines, for example—closely spaced together and shifting from night to night. In general, each line appears doubled, but they periodically move back and forth toward bluer or redder wavelengths (blueshifted or redshifted due to the Doppler effect). This movement is evidence that two stars are orbiting each other, accounting for the shifting spectral lines. Sometimes, only one set of absorption lines is visible, but these periodically shift back and forth. The second star is simply much fainter than the ¿rst star in such cases.

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Lecture 46: Binary Stars and Stellar Masses

Spectroscopic and eclipsing binary stars can tell us much about the star system; some can be both spectroscopic and eclipsing. We can take all possible measurements of eclipsing spectroscopic binary stars—their orbital periods, light curves, distances from Earth, spectra—and determine the masses, radii, and luminosities of the individual stars. In fact, from these systems, we have deduced the masses of a few hundred stars fairly accurately. What does mass tell us about stars, at least those on the main sequence of the temperature-luminosity diagram? Stars that fall on the main sequence are in their prime of life—stable, fusing hydrogen into helium in their cores. Their luminosities don’t change much with time, nor do their radii. Our Sun is a main-sequence star, as are most stars. It is roughly halfway through its life. The luminosity of a main-sequence star is very roughly proportional to its mass to the 4th power: L v M4, in which M is the star’s mass. Thus, the luminosity is highly dependent on mass. (The dependence is actually not as sensitive to mass at high masses and somewhat more sensitive to mass at low masses.) For example, main-sequence stars that are 10 times as massive as the Sun are roughly 10,000 times as luminous. Conversely, stars that have 1/10 of the Sun’s mass have roughly 1/10,000 of the Sun’s luminosity. This “I know how a rainbow mass-luminosity relationship implies that works, but that doesn’t more massive main-sequence stars have detract from its beauty shorter lifetimes than less massive stars. They live fast and die young because they and wonder. There’s are burning fuel at a much higher rate than still the awe and low-mass stars. mystery of how it all got here, why the laws A star’s main-sequence lifetime is the amount of fuel divided by its luminosity, of physics even exist, which is proportional to M/L. (Although and why they lead to not all of a star’s total mass is available such an interesting and as fuel, most stars have about the same complex Universe, with fraction of their mass available as fuel.) But an essentially in¿nite given that L v M4 (roughly), we ¿nd that the lifetime is very roughly proportional variety of objects.” to M/M4 = 1/M3. Thus, a star twice as 236

massive as the Sun lives only 1/8 as long on the main sequence. A star 10 times as massive as the Sun lives only about 1/1000 as long on the main sequence. The Sun will live about 10 billion years on the main sequence. A 10-solar-mass star would live, accordingly, only about 10 million years on the main sequence. We know that very massive main-sequence stars, such as those in the heart of the Orion nebula, are young (a few million years old); otherwise, they wouldn’t be on the main sequence any more. Such massive stars older than a few million years would have turned into supergiants or blown up as supernovae (exploding stars). To summarize, massive stars are the most luminous main-sequence stars; low-mass stars are the dim main-sequence stars; our Sun is somewhere in the middle. Mass, therefore, is critical to a star’s life. Massive main-sequence stars (O-type and B-type stars) have large radii, high luminosities, and high surface temperatures. All these properties decrease as a star’s mass decreases. Sometimes, facts and ¿gures can seem to take away from the beauty of the heavens; however, by determining these facts, we have been able to ¿gure out how stars work, what makes them shine, and how they change throughout their lifetimes. Knowing such details only enhances our appreciation for celestial wonders and can be a springboard to the greater mysteries of the Universe. Ŷ

Important Terms binary star: Two stars gravitationally bound to (and orbiting) each other. spectroscopic binary stars: Binary stars detected by examining the periodically varying Doppler shift in their absorption lines.

Suggested Reading Cooper and Walker, Getting the Measure of Stars. Kaler, Stars. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed.

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Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. If one main-sequence star is 3 times as massive as another one, what is the ratio of their luminosities? What is the ratio of their main-sequence lifetimes? Physically, why do you think the massive star uses up its fuel much faster than the low-mass one?

2. Do you think that planetary systems are more or less likely to form around binary stars than around single stars?

3. Albireo (ȕ Cygni), the “Cal Star” (that is, the of¿cial star of the

Lecture 46: Binary Stars and Stellar Masses

University of California, Berkeley, because of its colors), is a physical binary system consisting of a bright, yellow (“gold”) star and a fainter, blue star. Can you argue that the gold star is signi¿cantly larger than the blue star?

238

Star Clusters, Ages, and Remote Distances Lecture 47

“The ages of stars are obviously a fundamental aspect of their existence. We want to know how old each star is in order to be able to see how stars evolve as they age.”

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s we have seen, the mass of a star determines its luminosity, radius, and surface temperature. Let’s look at star clusters and learn how we can determine their age. Star clusters are gravitationally bound groupings of stars, and many stars are found in such clusters. Indeed, stars are often born in clusters of hundreds or even thousands. There are two main types of clusters. The ¿rst is an open cluster, consisting of a loosely bound set of stars, from a few dozen up to a few thousand. Also called galactic clusters (not to be confused with clusters of galaxies), they are not bound in a tight sphere. We know of about 1000 open clusters in our Milky Way Galaxy. The best-known example can easily be seen with the naked eye: the Pleiades, or Seven Sisters. Open star clusters are often composed of young stars because, we believe, after they have formed, they are gradually torn apart. Stars escape from the cluster as stars outside the cluster gravitationally tug on them. A gravitational slingshot effect among stars within a cluster can also cause stars to become unbound from the cluster. Open clusters appear in spiral galaxies, usually in the arms of the galaxy, which is where most of the gas and dust are found—substances from which stars are born. The second type of cluster is the globular cluster. These are much more massive clusters, as well as more spherical and denser, consistent with their name. They contain hundreds of thousands to a million stars. In our Milky Way Galaxy, we know of about only 150 to 170 globular clusters. They tend to occur in what is called the halo, or the outer regions surrounding our Galaxy. This suggests that these globular clusters were among the ¿rst structures to form in our Galaxy. Some massive elliptical galaxies have a very large number of globular clusters, about 20,000 in the case of M87. It’s crucial to recognize that all the stars in a given cluster are roughly the same distance from Earth. Certainly, some are farther away than others, but 239

NASA

Lecture 47: Star Clusters, Ages, and Remote Distances

the differences in distance are minor compared to the overall distance of the cluster as a whole. Thus, on the temperature-luminosity diagram, if we plot the apparent brightness (or apparent magnitude) of the stars (instead of their true luminosity or absolute magnitude) on the vertical axis against their surface temperatures on the horizontal axis, we see a well-de¿ned main sequence; the distance, d, is about the same for all stars in the equation L = 4Sd2b. Next, we can compare the main sequence of the cluster stars (apparent magnitudes) to the main sequence of nearby stars of known distances (absolute magnitudes). The difference in apparent magnitude versus absolute magnitude, or the factor by which apparent brightness is less than luminosity, allows us to derive the distance of the whole cluster.

One of the densest of the known globular star clusters in the Milky Way, M80 (NGC 6093), contains hundreds of thousands of stars and is located 28,000 light years from Earth.

We can also determine the ages of stars in the cluster. Stars in the same cluster all formed at the same time from the same cloud of gas (the same collapsing nebula). What differs is each star’s mass. A given cluster will form low-mass stars, intermediate-mass stars, and high-mass stars. We can assume that, 240

initially, a cluster was born with stars having O-type main-sequence stars down to K, M, and L main-sequence stars, which translates to a range of luminosities. We know that the more massive stars use up their fuel quickly and burn out and that the lower-mass stars are more stable and live longer. Therefore, noting the spectral type of the top end of the main sequence in the temperature-luminosity diagram (that is, the turnoff point of the main sequence), we can estimate the approximate age of the cluster. For example, if the main sequence of a cluster is missing the higher-mass stars (O-, B-, and A-type stars), but the F, G, K, M, and L stars are still present, the cluster must be old enough for the more massive stars to have burned out. Clusters that are missing main-sequence stars of type F or G are even older because those stars require more time to burn out. The gradual decrease in the height of a candle is analogous to the declining length of the main sequence. Knowing the initial length of the candle and the rate at which it is burning, we could determine how long it has been burning by measuring its current height. The amount of time it takes each type of main-sequence star to use up its central reservoir of fuel and leave the main sequence is determined from its luminosity and amount of available fuel. Clusters with O-type main-sequence stars are only a few million years old; clusters without G-type main-sequence stars have to be at least 10 billion years old because that’s how long it takes G-type stars to burn out. Our Universe is not yet old enough to have burned out M-type main-sequence stars, which can live more than a hundred billion years, even a trillion years. Most open clusters are young, but some are as old as 5 billion years. Globular clusters are the oldest clusters that we know of and have low main-sequence turnoff points. Because some are as old as 12 or 13 billion years, we know that the Universe is at least that old. It’s much more dif¿cult to determine the ages of individual stars that are not in clusters. We can use the temperature-luminosity diagram to determine the distances of stars that are too far away for the trigonometric parallax method to work. This method is called spectroscopic parallax, in which we use a star’s spectrum to help determine its distance. From the spectrum, we can tell what spectral type of star we are looking at—for example, O, B, A, F, G, K, M, or L. The spectrum can also tell us the star’s luminosity class—whether it is on the main sequence, a red giant, a white dwarf, or a supergiant. Knowing the spectral type and the luminosity class, we can determine where the star 241

Lecture 47: Star Clusters, Ages, and Remote Distances

falls on the temperature-luminosity diagram. Then, by measuring the star’s apparent brightness and knowing its spectral type and luminosity class (and, hence, its luminosity), we can calculate its distance from Earth using the inverse-square law of light. For example, if a star is just like our Sun (a G2 main-sequence star) but appears faint, we can compare it with the known luminosity of the Sun and derive its distance. One complication with this method is that often gas and dust obscure the star’s light in what is called interstellar extinction, causing the star to appear dimmer than it really is. If we don’t account for this light extinction, we will deduce that the star is farther away than it really is. We can measure this extinction because a star that is dimmed by the absorption and scattering of light also appears redder—the overall spectrum becomes de¿cient in blue photons relative to red photons, because the blue photons are preferentially affected. Not to be confused with a redshift (caused by the Doppler effect or the expansion of the Universe), this effect is analogous to that of the setting Sun, which looks not only dim but also red. We know the true color of a given star because we measure its spectral type. “There are stars that Knowing the true color, we can account for completely dwarf the this dimming by observing the amount by Sun. Nevertheless, the which it is reddened, just like the setting Sun is more luminous Sun. Taking account of this dimming effect, and massive than we can get a more accurate distance. the majority of the How typical is our G-type Sun? Our Sun little pipsqueak stars. isn’t typical in that it’s a single star, not part Overall, the Sun is of a binary system. Most of the apparently pretty much a brightest stars in the sky are more luminous than the Sun—however, these are not typical garden-variety star.” stars either. Most of the stars within a given volume around the Earth (say, a radius of 10 or 20 pc) are less luminous than the Sun. Thus, although our Sun is a G-type star in the middle of the main sequence, it’s more massive and luminous than a majority of stars but not as massive and luminous as the most massive and luminous stars. Overall, we consider the Sun to be an average star, with average mass and luminosity. Ŷ 242

Important Terms interstellar extinction: The obscuration of starlight by interstellar gas and dust. globular cluster: A bound, dense, spherically symmetric collection of stars formed at the same time. open cluster: A loosely bound cluster of stars, usually consisting of young stars that eventually break away from the cluster.

Suggested Reading Kaler, Stars. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. Suppose you ¿nd two clusters, one whose main sequence doesn’t have O, B, and A stars and the other whose main sequence doesn’t have any O, B, A, and F stars. Which is older? Why?

2. Massive main-sequence stars are much rarer than low-mass mainsequence stars. Thus, how might one accidentally overestimate the age of a very sparse cluster from its main-sequence turnoff?

3. When the temperature versus apparent brightness (not luminosity) is plotted for the stars in a cluster, why is the result a much cleaner-looking diagram than it is when this is done for random stars (not in a cluster)?

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How Stars Shine—Nature’s Nuclear Reactors Lecture 48

“A main-sequence star is in the prime of its life. It has a stable luminosity, surface temperature, and radius. It just doesn’t change very much. In this lecture, I’ll explain how a star achieves this stability. What is it actually doing while it’s on the main sequence?”

Lecture 48: How Stars Shine—Nature’s Nuclear Reactors

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ebulae are vast clouds of gravitationally unstable gas and dust. Some areas collapse inward and coalesce into denser and denser regions in the centers; this is where stars are born. Larger clouds of gas typically fragment into smaller units, or cores, forming protostars, which themselves collapse and eventually turn into individual stars. These stars are initially gravitationally bound together to form open star clusters or globular clusters. The protostars are essentially in free-fall, and as they fall, or collapse, the particles pick up speed and collide with one another. The energy is converted into thermal energy, which creates pressure that eventually impedes the free-fall collapse. As the pressure and temperature rise, the collapse becomes a slower contraction. When the contraction is suf¿ciently slow and steady, the protostar becomes a pre-main-sequence star, slowly contracting and releasing half of its gravitational energy in the form of photons while the rest is transformed into heating the star, causing the temperature and pressure to rise still further. Eventually, the pressure and temperature become high enough to ignite nuclear fusion, which typically happens at about 10 million K. Fusion occurs at a controlled, non-explosive rate. Once the fusion reactions begin, they occur at the rate necessary to keep what is now a main-sequence star in a stable form, with nearly constant luminosity, radius, and surface temperature. Continually created energy keeps the star hot and pressurized inside, halting gravitational contraction and achieving stability. This mechanical stability is called hydrostatic equilibrium, in which gravity is pulling in and the net pressure is pushing out by an equal amount. The star is also in thermal equilibrium, which means that the nuclear reactions occur at exactly the rate they need to in order to keep the star from 244

getting too hot or too cool. If the star became too hot inside, the nuclear reaction rate would increase, causing the star to expand and cool—making the reaction rate subside. Conversely, if the star were cooled on the inside, its pressure would decrease, causing contraction, which would cause the star to heat up again—making the reaction rate increase. Thus, a star’s core is selfregulating, like a thermostat. What is nuclear fusion, and how does it occur? In the center of a star such as the Sun, the temperature is very high and varies with the star’s mass. The Sun’s temperature is about 15 million K, for example. At such temperatures, hydrogen, helium, and other light atoms are completely ionized; that is, they’ve lost their electrons. The nucleus of a hydrogen atom (H) is simply one proton. We designate it as 1H1, in which the subscript 1 denotes the number of protons and the superscript 1 denotes the total number of protons and neutrons (collectively called nucleons). A helium nucleus is denoted as 2He4, indicating that it has two neutrons and two protons, for a total of four nucleons. In the central part of a star, where temperatures are high, the protons move very “This binding rapidly; these are simply the thermal motions of the protons. Although protons tend to repel one energy seems like another (because they have the same electrical kind of a weird charge), under such high temperatures, they are concept. How is it often able to get reasonably close to each other. produced? Does it At this point, they can sometimes bind together because of the strong nuclear force. have something to do with the nuclei, Eventually, four protons bind together and turn or does it appear into an alpha particle, or a helium nucleus. more commonly Energy is liberated in the process, allowing the star to shine. Two of the protons turn into neutrons in life?” and release particles called positrons, the antiparticles of electrons. When an electron and a positron meet, they annihilate each other, turning into a burst of energy, or photons. The binding process releases additional light in the form of gamma rays (high-energy photons). Further, some released energy takes the form of particles called neutrinos, which don’t contribute to a star’s temperature or pressure, as the positrons and photons do. The fundamental result is that the 245

Lecture 48: How Stars Shine—Nature’s Nuclear Reactors

helium nucleus is more tightly bound than the four original protons of which it was made. This means that the helium nucleus has less mass than the four initial protons. The difference in mass between the original protons and the helium nucleus produces the energy that we see shining from stars. The liberated energy is given by E mc 2 , in which m is the difference in mass. Even though this difference is only 0.7% of the mass of the four original protons, it is enough to create the observed luminosity. Let’s look in more detail at what happens in the nuclear reactions within stars, speci¿cally in the proton-proton chain that occurs in the Sun. The nucleus of a normal hydrogen atom is known as a proton, but hydrogen can occur in different isotopes, or types. For example, the proton could be bound to a neutron and become a deuteron. Two neutrons bound to a proton create a triton. Helium (with two protons) has two isotopes: the most common containing two neutrons, and the other (light helium), only one neutron. In the ¿rst stage of nuclear reactions, two protons combine to form a deuteron, a positron, and a neutrino. This happens twice, forming two deuterons. Each of those deuterons can combine with a proton to form a nucleus of light helium. The two light helium nuclei fuse together to form the heavy, normal isotope of helium. In the process, two of the protons are liberated, so only two of the four protons in the two light helium nuclei are assimilated into the single nucleus of heavy helium. Thus, out of six protons, four are assimilated into the bound helium nucleus and two are left over. This proton-proton chain is the process by which fusion occurs in the core of the Sun and other low-mass main-sequence stars. Our Sun uses nearly 700 million tons of protons every second! This seems like a huge number, but the Sun is 70% hydrogen and its mass is enormous; thus, it has a lot of fuel. Even though only 10% to 15% of the Sun’s mass ever participates in nuclear reactions, we can calculate that the Sun’s mainsequence lifespan is about 10 billion years. The Sun, currently about 4.6 billion years old, is therefore only a middle-aged star. We can now see how more massive stars use up their energy more quickly: Their internal pressures and temperatures are higher in order to maintain hydrostatic equilibrium. Because the fusion rate increases sharply with increasing temperature, the fuel runs out more rapidly.

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All main-sequence stars convert hydrogen into helium in some way. The lower-mass stars (below about 1.1 to 1.2 solar masses) use the protonproton chain. More massive stars use a process called the carbon-nitrogenoxygen cycle (CNO). Basically, the stars begin with a carbon nucleus left over from some long-dead star. This fuses with a proton, forming nitrogen, which decays into another isotope of carbon, releasing a positron and a neutrino. The resulting carbon isotope combines with another proton to form a different nitrogen isotope than before. This combines with a proton to form an oxygen isotope, which decays into another isotope of nitrogen. That nitrogen can combine with a proton to form the most common isotope of carbon (having 6 protons and 6 neutrons) plus helium. The net effect is that the cycle began with a carbon nucleus and ended with a carbon nucleus, but four protons were turned into a helium nucleus plus energy. Ŷ

Important Terms antiparticle: A particle whose charge (if not neutral) and certain other properties are opposite those of a corresponding particle of the same mass. An encounter between a particle and its antiparticle results in mutual annihilation and the production of high-energy photons. deuteron: A deuterium nucleus. fusion: The formation of heavier nuclei from lighter nuclei. neutrino: A nearly massless, uncharged fundamental particle that interacts exceedingly weakly with matter. There are three types: electron, muon, and tau neutrinos. positron: The antiparticle of an electron. proton-proton chain: A set of nuclear reactions by which four hydrogen nuclei (protons) combine to form one helium nucleus, with a resulting release of energy. protostar: A star still in the process of forming in a cloud of gas and dust, collapsing nearly in free fall. 247

solar mass: The mass of the Sun, 1.99 u 1033 grams, about 330,000 times the mass of the Earth. strong nuclear force: The strongest force, it binds protons and neutrons together in a nucleus. Actually, it is the residue of the even stronger color force that binds quarks together in a proton or neutron.

Suggested Reading Kaler, Stars. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Lecture 48: How Stars Shine—Nature’s Nuclear Reactors

Smith, The Origin of Stars.

Questions to Consider 1. Given that individual stars can live for millions or billions of years, how can observations taken at the present time tell us about stellar evolution?

2. At one time, it was thought that the source of the Sun’s energy is gravitational contraction. If this were true, however, the Sun could have a current age of only a few tens of millions of years. With what known facts about Earth would such a number conÀict?

3. Why does nuclear fusion occur only in the central region of stars rather than near their surface?

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Solar Neutrinos—Probes of the Sun’s Core Lecture 49

“The detection of neutrinos and neutrino oscillations is one of the greatest achievements of the past few decades. It affects not just astrophysics, it also affects fundamental particle physics, throwing a giant wrench into the theory, and that’s really exciting.”

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n the previous lecture, we learned that the Sun produces its energy through nuclear fusion. But we can’t actually conduct physical experiments on the core of the Sun, so how do we know nuclear fusion is occurring now? The Sun could not burn from chemical reactions, such as Àames burning paper or wood, because such a reaction couldn’t produce enough energy to power the Sun. Also, we know that temperatures in the Sun are too high for chemical burning in the conventional sense. The Sun cannot burn through gravitational contraction because this process would allow the Sun to live only about 50 million years; the Sun has likely been shining at its present rate for at least 3 billion years. In addition, other studies prove that the Sun is not gravitationally contracting, at least not much. Physicists have concluded that nuclear fusion must be occurring now because there is no other source of energy for the Sun to use. Though earlier concepts about physics couldn’t account for nuclear fusion, the advent of quantum mechanics changed our perception of how particles behave and answered some questions about nuclear fusion in the Sun. Still, we cannot physically test the Sun for nuclear fusion reactions. We do know that photons emerge from the Sun, though this fact still doesn’t prove that nuclear fusion occurs. Why not? When a photon is produced in the middle of the Sun, it encounters an opaque gas on its way to the Sun’s surface (photosphere). This causes photons to move randomly on their way out, which on average, takes about 100,000 years. If nuclear fusion reactions in the Sun stopped right now, we wouldn’t know it for 100,000 years because photons are already on their way to the surface. Thus, we can’t rely on photons to tell us that nuclear fusion is occurring right now. We must rely on ghostly particles called neutrinos, which are produced during fusion reactions. Neutrinos have only a slight mass and hardly interact with other 249

matter. It takes about 2 seconds for a neutrino to go from the core of the Sun to its surface and another 8.3 minutes to reach Earth. If we could detect neutrinos coming in great numbers from the Sun, we could prove that nuclear fusion is occurring right now.

Lecture 49: Solar Neutrinos—Probes of the Sun’s Core

Where do these neutrinos come from and how do they interact? Recall the ¿rst step of the proton-proton chain, in which two protons combine to form a deuteron. In the process, one of the protons turns into a neutron, a positron—an antielectron—and a neutrino. The positron annihilates an electron and produces photons. In the proton-proton chain, the neutrino— called an electron neutrino because it is associated with processes that form electrons and antielectrons—simply exits the Sun at a high speed. Every square centimeter of the Earth, every second, is bathed by about 60 billion such neutrinos from the Sun. With such high concentrations of neutrinos all around us, surely some would react with earthly elements and we could detect them. In fact, neutrinos can combine with a neutron in an atomic nucleus, turning it into a proton and an electron. Speci¿cally, a nucleus of chlorine can occasionally absorb an electron neutrino, turning it into a radioactive form of argon, which can be detected with a Geiger counter or some other device that detects radioactivity. One such experiment was conducted by Ray Davis, whose amazingly precise methodology allowed for the detection of a single radioactive argon nucleus in a 100,000-gallon tank of dry-cleaning solution. Another experiment by Masatoshi Koshiba made a similar discovery. Koshiba could actually con¿rm that the neutrinos were coming from the Sun rather than some other source. The detection of neutrinos was a great breakthrough, but there was another puzzle. Davis’s experiment detected only about one-third of the expected number of neutrinos, suggesting that our theory about the Sun was incorrect or that something else was at work. For example, perhaps the temperature in the Sun’s core wasn’t quite as high as we thought. Or maybe the Sun simply wasn’t fusing much at all at the present time. Alternatively, perhaps the electron neutrinos turned into some other kind—of¿cially known as “Àavor”—of neutrinos, such as muon neutrinos or tau neutrinos.

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A 1998 experiment measured muon neutrinos produced by the interaction of cosmic rays from space with molecules in the Earth’s atmosphere. The experiment detected muons coming from the direction just above the detector (close to the Earth’s surface), muons coming from the back side of Earth, and muons coming from other random directions. The number of neutrinos coming from the back side of Earth was smaller than that coming from close to the detector, suggesting that muon neutrinos passing through Earth turn into another Àavor of neutrino on the way. This was the ¿rst real evidence that at least muon neutrinos can change their Àavor; therefore, perhaps electron neutrinos from the Sun could change, as well. Recent experiments in Canada showed that two types of reactions can occur when electron neutrinos travel through a certain form of heavy water (that is, water containing atoms of deuterium instead of normal hydrogen). In one reaction, sensitive only to electron neutrinos, a very energetic electron is formed. It travels through the water with a speed higher than the local speed of light (which is slower than that in a vacuum, due to an interaction of light with water), producing electromagnetic radiation called Cerenkov radiation, or Cerenkov light. This accounts for one-third of the expected number of neutrinos, as in previous experiments. A second type of reaction, however, was able to detect all three known Àavors of neutrinos: electron, muon, and tau. Remarkably, the total rate at which neutrinos were detected matched theoretical expectations! This essentially proves the hypothesis that the Sun’s source of energy is nuclear fusion. Electron neutrinos are produced in the Sun, but about two-thirds of them turn into other neutrino “In fundamental Àavors during their journey to the Earth. particle physics, neutrinos are The three observed neutrino Àavors turn out to supposed to be be different combinations of more fundamental massless, and yet neutrinos, called type 1, type 2, and type 3. For example (simpli¿ed to illustrate the physical it turns out they principles), an electron neutrino might be cannot change a speci¿c combination of type 1 and type 2 Àavors if they’re neutrinos. The quantum mechanical waves of type massless.” 1 and 2 neutrinos can sometimes be in phase and sometimes out of phase, thus creating the different 251

Àavors of observed neutrinos—electron, muon, and tau. Such neutrino oscillations (from one observed Àavor to another) imply that neutrinos have nonzero (but very small) mass. Previously, scientists thought that neutrinos had no mass at all. In order to change their Àavor, neutrinos must move slower than the speed of light—but to move slower than the speed of light, they must have mass. Particles with no mass have to travel at the speed of light; otherwise, they wouldn’t exist. This great discovery challenges previous theories about particle physics, which had asserted that neutrinos are massless. It affects our understanding of the ways in which particles fundamentally behave at the microscopic and submicroscopic scales. Ŷ

Lecture 49: Solar Neutrinos—Probes of the Sun’s Core

Important Terms Cerenkov radiation: Electromagnetic radiation emitted by a charged particle traveling at greater than the speed of light in a transparent medium. The blue light emitted is the electromagnetic equivalent of a sonic boom heard when an aircraft exceeds the speed of sound. cosmic rays: High-energy protons and other charged particles, probably formed by supernovae and other violent processes. deuterium: An isotope of hydrogen that contains one proton and one neutron. particle physics: The study of the elementary constituents of nature. quantum mechanics: A 20th-century theory that successfully describes the behavior of matter on very small scales (such as atoms) and radiation.

Suggested Reading Golub and Pasachoff, Nearest Star: The Surprising Science of Our Sun. Institute for Advanced Study, School of Natural Sciences, John Bahcall, www.sns.ias.edu/~jnb/ (“popular articles” link). 252

Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Sudbury Neutrino Observatory (SNO), www.sno.phy.queensu.ca/. Sutton, Spaceship Neutrino.

Questions to Consider 1. Why do neutrinos give us different information about the Sun than light does?

2. Do you think astronomers were overly bold in predicting that the solar neutrino problem would be resolved by changes in our theories of fundamental particles, rather than by abandoning the standard model of solar energy production?

3. The solar neutrino experiments that preceded SNO were able to detect only electron neutrinos. Why was the ability to detect all Àavors of neutrinos so important in helping to resolve the solar neutrino problem?

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Brown Dwarfs and Free-Floating Planets Lecture 50

“As we’ve seen, true stars are de¿ned by the fact that they produce nuclear fusion in their cores.”

Lecture 50: Brown Dwarfs and Free-Floating Planets

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eep in the core of the Sun, temperatures are so high that protons can fuse together through the proton-proton chain, forming helium nuclei. This nuclear fusion provides a long-term source of energy for the Sun and, presumably, for other stars. Pre-main-sequence stars release energy through gravitational contraction, replenishing the energy supply that is lost to surrounding space and heating up the gas. As contraction continues and the center of the star gets hotter, nuclear fusion begins to take place, providing a stable new source of energy and halting contraction. Thus, a star is born, having reached hydrostatic and thermal equilibrium. Some astronomical bodies cannot reach suf¿ciently high temperatures (at least 3 million K for the least massive stars; higher for more massive ones) to allow fusion to begin. Thus, contraction remains the only source of energy (except deuterium fusion; see below). Such bodies are called brown dwarfs, which some astronomers think of as failed stars. Brown dwarfs are cool, dim, and small, and they continue contracting until a new form of pressure takes over—electron degeneracy pressure. Electron degeneracy pressure is a strange quantum-mechanical pressure arising from the fact that electrons repel one another (not electrical repulsion but, rather, quantum mechanical). Electrons are a type of fundamental particle called fermions, which cannot occupy the same quantum state. Another fundamental particle is a boson. Unlike fermions, two or more bosons (e.g., photons) can be in the same quantum state. Eventually, the density becomes so high in a brown dwarf that the electrons start overlapping spatially. To be in different quantum states, their momenta and, hence, their energies must be different. Some of the electrons must have very high energies and momenta because all of the lower-energy and lower-momentum quantum states are already fully occupied. These high-energy electrons exert an extra pressure— degeneracy pressure—which helps support the contracting brown dwarf. Before a brown dwarf becomes degenerate, temperatures are suf¿ciently 254

high and densities suf¿ciently low that electrons are spread more randomly and exert normal thermal pressure. Brown dwarfs are about the same size as Jupiter. Because they are cool and small, they are faint and dif¿cult to notice. What little light they do emit tends to be in the infrared wavelengths.

S. Kulkarni (Caltech), D.Golimowski (JHU) and NASA

Brown dwarfs were predicted many decades ago but weren’t found until the 1990s. Now, we know of at least 1000, the discoveries of which coincided with the explosive growth in studies of exoplanets. The spectrum of one of the ¿rst brown dwarfs showed absorption bands of methane, which is similar to the spectra taken of Jupiter. This con¿rmed that the object was a very cool brown dwarf; the presence of methane means that the atmosphere is much colder than that of the least massive stars. Brown dwarfs with methane in their atmospheres are called T dwarfs, while hotter ones are called L dwarfs (but some L dwarfs are genuine stars). After the ¿rst few discoveries, many more brown dwarfs were found. Sky surveys taken at infrared wavelengths reveal many brown dwarfs. Some of the brown dwarfs orbit nearby stars, but others appear to have formed in solitude. In order to truly know whether a star is a brown dwarf or an L-type main-sequence star, we need to know its mass. This tells us whether it’s capable of high enough temperatures for nuclear fusion to occur.

Brown dwarf Gliese 229B as observed by Palomar Observatory (left) and the Hubble Space Telescope (right). (Note: The spike at right is an artifact of the telescope.)

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Lecture 50: Brown Dwarfs and Free-Floating Planets

Some brown dwarfs are actually in binary systems, allowing us to measure their masses using Newton’s laws of motion and the law of universal gravitation. Just as there are exoplanets orbiting normal main-sequence stars, it is possible that exoplanets orbit some brown dwarfs. Debris discs have also been found around some brown dwarfs, which could potentially form small planets. Brown dwarfs do experience fusion, though not through the proton-proton chain, which requires temperatures over 3 million K. At lower temperatures, deuterium fusion can occur, essentially bypassing the dif¿cult ¿rst step in the proton-proton chain. Brown dwarfs begin fusion with deuterium (normally formed in the proton-proton chain), which collides with protons to fuse into light helium nuclei. This type of fusion is short-lived and occurs in brown dwarfs between 13 and 75 Jupiter masses. Above 75 Jupiter masses, the normal proton-proton chain occurs. Astronomers disagree about whether or not brown dwarfs should be called true stars or failed stars. One solution is to simply recognize that brown dwarfs and normal stars are “fusers.” Normal stars undergo nuclear fusion of protons, whereas brown dwarfs fuse deuterium. Below 13 Jupiter masses, even deuterium fusion doesn’t occur. Thus, we call these bodies planets. Suppose we plot the distribution of the number of bodies discovered through the Doppler wobble technique (Lecture 38) against their derived masses. As we discussed when considering exoplanets, the Doppler wobble technique actually leads us to infer M sin i—rather than the actual mass, M—where i is the inclination angle between the orbital plane and our line of sight and sin denotes “sine.” Only the radial component of the total velocity is measured with the Doppler effect. Thus, if sin i is less than 1, the true mass (M) must be greater than the measured quantity, M sin i. Objects that are 12 or 13 Jupiter masses, minimum, are almost certainly brown dwarfs. Some with a minimum mass below 12 Jupiter masses are probably also brown dwarfs. Even a few objects having a rather low minimum mass (say, 4 Jupiter masses) might actually be brown dwarfs if their true mass exceeds 13 Jupiter masses. Nevertheless, most objects with an inferred minimum mass below about 6 Jupiter masses are probably planets, not brown dwarfs; they don’t experience fusion of any kind, even deuterium fusion.

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What would we call an object of less than 13 Jupiter masses, not fusing deuterium, and not orbiting a star? Most astronomers would call it a freeÀoating planet because it has a planetary mass and it is not undergoing fusion. Some “All this is telling free-Àoating planets were ejected from their us is that, in the planetary systems, while others simply formed process of star and on their own through gravitational contraction out of a cloud of gas—like normal stars. Some planet formation, astronomers would like to call the result of the there’s a range of ¿rst scenario a planet and the second scenario masses that can a brown dwarf, regardless of whether the occur. It’s all part of object is massive enough for deuterium fusion one continuum, one to ever occur. Others don’t want to apply the term planet to objects that are not orbiting process that leaves another star. the same sorts of objects, but having Gibor Basri, of the University of California, a continuum Berkeley, has proposed that we call objects planemos (“planetary mass objects”) if they are of masses.” at least massive enough to be spherical but not massive enough to be deuterium-fusing brown dwarfs. If a planemo happens to orbit a star, we call it a planet. Because we are ¿nding more and more of these relatively low-mass objects through infrared studies of the skies, at some point, we will have to agree on the terminology and classi¿cation. Clearly, a range of masses can occur in the process of star and planet formation, from the most massive O-type stars to the least massive normal hydrogen-fusing stars, down to deuterium-fusing stars (brown dwarfs), and to planetary mass objects that don’t fuse at all. Ŷ

Important Terms brown dwarf: A gravitationally bound object that is insuf¿ciently massive to ever be a main-sequence star but too massive for a planet. Generally, the mass range is taken to be 1375 Jupiter masses.

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degenerate gas: A peculiar state of matter at high densities in which, according to the laws of quantum physics, the particles move very rapidly in well-de¿ned energy levels and exert tremendous pressure.

Suggested Reading California and Carnegie Planet Search, www.exoplanets.org. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. What are the problems associated with requiring knowledge of an

Lecture 50: Brown Dwarfs and Free-Floating Planets

object’s formation history to classify it as a brown dwarf, a planet, or something else?

2. Under what circumstances can the true mass of a brown-dwarf candidate identi¿ed through the Doppler wobble technique be determined?

3. Do you consider brown dwarfs to be failed or genuine stars?

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Our Sun’s Brilliant Future Lecture 51

“Through observational studies of stars at different stages of their lives and using the physics of gases held together by gravity, astronomers can predict with accuracy how stars are likely to evolve.”

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he laws of physics help us understand how stars will evolve based on the nuclear reactions that occur, pressures and temperatures in the core, and other factors. In this way, we can predict what will happen to our Sun as it evolves. For about 9 or 10 billion years, the Sun will remain on the main sequence—that is, it will fuse hydrogen into helium in its core through the proton-proton chain, releasing energy. At 4.6 billion years old, our Sun is about halfway through its normal main-sequence lifetime. As the Sun evolves, it will gradually brighten, because as it fuses hydrogen into helium, its core temperature necessarily has to rise, and the fusion rate will increase. For every four initial protons, only one helium nucleus will be produced. Therefore, the number of particles per unit volume in the middle of the Sun—that is, the number density—will gradually decrease. Pressure is proportional to the product of number density and temperature. If the number density decreases (because hydrogen is fusing to helium), the temperature has to rise to compensate and maintain the same pressure. In a few hundred million years, Earth will be substantially warmer because the Sun’s luminosity will have increased somewhat. In about half a billion to a billion years, the oceans will be gone, and the Earth will be like a scorching desert. It’s possible that some compensating effect will keep Earth’s temperatures lower than anticipated. We know that an inverse compensating effect must have occurred billions of years ago when the Sun’s luminosity was about 30% lower than it is now. Without such an effect, the Earth’s oceans would have been frozen, yet fossil evidence proves that certain life forms existed in relatively warm conditions. It’s possible that a more pronounced greenhouse effect was occurring on Earth at that time.

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Lecture 51: Our Sun’s Brilliant Future

What will happen in about 5 billion years when the Sun reaches the end of its main-sequence life? A similar future awaits other sun-like stars. Its helium core will increase to about 10% to 15% of the total mass. Remember, the core is the only part of the star where temperatures are high enough for nuclear fusion to be sustained. However, nuclear reactions in the core will stop because helium nuclei repel each other much more than protons do, and the temperature will not be high enough for helium nuclei to fuse into heavier elements. Heat will gradually diffuse out of the helium core, causing it to gravitationally contract in order to replenish the supply of energy lost to its surroundings. The energy released by the contracting helium core will heat the surrounding hydrogen-fusing shell. This will increase the fusion rate in that hydrogen shell, causing the star to become much more luminous than before. The energy liberated by the hydrogenburning shell causes the surrounding “Our Sun will probably form layers (all the way out to the surface) to a spherically symmetrical expand. Thus, contraction of the helium planetary nebula. We don’t core leads to an expansion of much of the rest of the star. know exactly what it’ll look like, but I’m hoping that it’ll be really pretty, so that future aliens, looking at our dying Sun, will say, ‘Wow, that’s a real beauty.’ ”

The expanding atmosphere of the star cools and its color shifts to more yellow, then orange (like that of a K-type star), and eventually, perhaps even somewhat red, because the peak of the spectrum shifts to longer and longer wavelengths. The Sun will become a red giant— perhaps 100 times more powerful than it is now—and much more luminous because of the vigorously burning hydrogen shell around the small helium core. The Sun will bloat to such a large size in its red-giant stage that it might extend to the orbit of Mercury. Contraction of the helium core will heat it up. Eventually, this slowly contracting helium core will reach temperatures of about 100 million K, suf¿cient for three helium nuclei to fuse, forming a carbon nucleus. The carbon nucleus can pick up another helium nucleus and turn into oxygen. Both of those reactions, the formation of carbon and the formation of oxygen, liberate still more energy. At that point, the Sun will have two sources of energy: the helium-fusing core surrounded by an inert helium shell and a hydrogen-burning shell around that. 260

The fusion of helium into carbon and oxygen lasts only about 1 million years because the individual fusion reactions don’t produce much energy compared to the original proton fusion reactions. Yet because the star is very luminous, it produces a prodigious amount of energy quickly; therefore, helium is used up rather quickly, and a carbon-oxygen core forms. The carbon-oxygen core does not have high enough temperatures for fusion; thus, it begins to contract, just as its predecessor helium core had done. That contraction heats the carbon-oxygen core and liberates energy to a helium-fusing shell, which burns even faster, making the star’s luminosity rise. The hydrogen-burning shell also fuses at a faster rate, releasing even more energy. This extra energy pushes out the outer envelope of the star even more, causing it to become a still larger red giant, which in the case of the Sun, might encompass Earth’s orbit (or at least Venus’s orbit). Different stars have different red giant time phases, ranging from about 100 million years to a few billion years. The Sun’s red-giant stage will last about half a billion years. During the red-giant stage, our Sun will become unstable, and its outer layers will be ejected in a series of relatively nonviolent outbursts. At such a huge size, a star’s outer atmosphere is barely bound to the star; gravity is weak there because the gases are so far from the core. The star begins losing its outer atmosphere through a steady stellar wind (analogous to the current solar wind) as radiation pushes out the gases. The star also becomes unstable, oscillating in size, and some of these pulsations actually eject the outer parts of the star—10% to 20% of its mass—in a relatively nonviolent way, like a cosmic burp. When such material is ejected, the star becomes an expanding, glowing shell of ionized gas. The ejected shell can appear in the shape of a disk or a ring, called a planetary nebula, though it has nothing to do with planets. The term was derived in the 19th century before scientists knew that these nebulae were actually dying stars. Over a few tens of thousands of years, the nebula’s light spreads so much that it fades. The gas in a planetary nebula is ionized because many ultraviolet photons are emitted from the hot central star, whose surface used to be the core of the star (prior to the ejection of the outer atmosphere). The gas glows as the electrons recombine with positive ions. Also, electrons Àying around in the gas hit other electrons bound in atoms, kicking them up to higher energy levels. These excited electrons subsequently jump back down to 261

lower energy levels, thereby emitting light. Many interesting photographs have been taken of such light emitted from planetary nebulae, showing not only brilliant colors but some fascinating structures. Deep photographs can capture layers ejected long ago. Dying stars can also produce bipolar ejections—that is, ejections that occur along an axis, forming planetary nebulae that are not spherically symmetric but, rather, shaped somewhat like an hourglass. We think that bipolar ejections are formed in a binary system in which one star expands into a red giant and begins transferring material to its companion. The transferred material envelops the companion and the red giant. As the common envelope contracts, a disk forms, forcing the ejecta of the expanding nebula to be expelled predominantly along the plane of the rotating disk. Ŷ

Important Term planetary nebula: A shell of gas, expelled by a red-giant star near the end of its life (but before the white-dwarf stage), that glows because it is ionized by ultraviolet radiation from the star’s remaining core.

Suggested Reading

Lecture 51: Our Sun’s Brilliant Future

Kippenhahn, 100 Billion Suns: The Birth, Life, and Death of Stars. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. Do planets form directly from a planetary nebula? 2. How can we be so con¿dent in our theory of the Sun’s future evolution? 3. It is often said that we on Earth have about 5 billion years before we need to worry about the Sun’s death. Why is this incorrect?

4. Why doesn’t the helium core of a red giant immediately start fusing to heavier elements? 262

White Dwarfs and Nova Eruptions Lecture 52

“By looking at more advanced stages of evolution of other Sun-like stars, and by using the laws of physics—in particular, the physics of hot gases—we have deduced that, in about 5 or 6 billion years, our Sun will expand greatly and then eject its outer envelope of gases, becoming a beautiful, glowing planetary nebula.”

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n this lecture, we will examine what happens when relatively low-mass solitary stars (such as the Sun) die at the end of their lives. Stars with initial sizes of between 0.08 and 8 solar masses and, perhaps, up to 10 solar masses eventually expel their outer atmosphere of gases during the planetary nebula stage and cease all nuclear fusion to become white dwarfs. The Sun is a representative star in this range. After the Sun becomes a red giant and then a planetary nebula, the remaining star (what used to be the core of the red giant) consists of carbon and oxygen. The nuclei repel each other so strongly that fusion cannot take place. Even in the helium shell around the carbon and oxygen core, temperatures are too low for fusion to be maintained. The core continues to contract as the star loses energy, increasing its density. Electron degeneracy pressure keeps the star from contracting inde¿nitely; it eventually reaches an equilibrium size. Heat is still liberated from the dying star by electrons moving to the lowest energy levels “At the ends of their and from positively charged atomic nuclei. lives, stars can do a Yet no new energy is created because nuclear variety of interesting reactions and gravitational contraction have stopped. White dwarfs are about the size things: from the surface of Earth. The radius of a white dwarf is explosions of white proportional to its mass raised to the 1/3 dwarfs, to instabilities in power: R v M–1/3. As mass increases, radius more-massive stars that decreases because of the high compression of electrons by gravity. A tablespoon cause them to brighten of white dwarf material would weigh and fade occasionally.” several tons.

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Lecture 52: White Dwarfs and Nova Eruptions

The atomic nuclei of a white dwarf are not degenerate; they can still lose energy, because although the electrons are all in their lowest energy states, the nuclei are not. Thus, white dwarfs can be thought of as “retired stars.” Their light comes from the supply of thermal energy built up in the nuclei over the star’s lifetime. A white dwarf gradually becomes dimmer and dimmer as the atomic nuclei cool down. After tens of billions of years, white dwarfs are no longer visible, and they become black dwarfs—though there is no sharp dividing line between white dwarfs and black dwarfs, and some astronomers avoid this term. Black dwarfs are still supported by electron degeneracy pressure, but the positive ions inside have cooled to low temperatures. If we could touch a very cold white dwarf (black dwarf), it wouldn’t burn you, despite the fact that many electrons are moving at very high speeds. All of the electrons are already in the lowest energy states possible. In other words, the electrons can’t transfer energy to a touching hand because they can’t move to lower energy levels and give off excess energy. Now let’s review what we have learned about the post-main sequence, or after-main sequence, evolution of a Sun-like star. We’ll also add some details and examine the physical properties of white dwarfs. The position of a star on the temperature-luminosity diagram is dependent on its mass. A main-sequence star remains nearly unchanged in luminosity and surface temperature for a long time. (It grows somewhat brighter with time, but to a ¿rst approximation, we can ignore this.) Once a star’s core hydrogen is used up, the helium core contracts and the star transforms into a red giant. The helium then fuses to carbon and oxygen. Contraction of the carbonoxygen core turns the star into an even larger red giant. The red giant’s outer atmosphere becomes unstable and is dispersed through winds and gentle ejections. The temperature of the central star’s surface increases as its outer layers are peeled away. This pattern of degeneration to a white dwarf is what happens in general to all stars between about 0.08 and 8 solar masses and, perhaps, up to 10 solar masses, following their long period of stability as main-sequence stars. It turns out that what happens in detail to a star as it dies depends on its mass at birth. Regardless of its initial mass (up to 8 solar masses), those stars that

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become white dwarfs will always be less than 1.1 solar masses in the white dwarf stage. Our Sun will end up as a roughly 0.6-solar-mass white dwarf. Stars with initial mass below 0.45 solar masses will consist of helium in the white dwarf stage; those stars never achieve a suf¿ciently high temperature for helium to undergo fusion into carbon and oxygen. A star with an initial mass between 8 and 10 solar masses fuses carbon and oxygen to form oxygen, neon, and magnesium in its core. Though we don’t know for sure, such a star could turn into an oxygen-neon-magnesium white dwarf having a mass perhaps somewhat larger than 1.1 solar masses. Other calculations say that such stars explode at the end of their lives. We are not yet certain what will happen. Stars initially greater than 10 solar masses eventually explode, which we’ll discuss in Lecture 53. White dwarfs have a theoretical maximum mass of 1.4 solar masses. This is known as the Chandrasekhar limit, named for a great Indian astrophysicist who derived it. The limit occurs because as a white dwarf accumulates material, its radius shrinks. Eventually, the radius is so small and the electrons are squeezed into such a tiny volume, that their speeds approach the speed of light, and their ability to exert more pressure diminishes. A star in a gravitationally bound binary system can change its mass by accreting material from its companion. Thus, stars whose initial masses were low can increase in mass—and, hence, core pressure—causing them to behave like more-massive stars, which in turn, speeds up their evolution. In a binary system in which one star is already a white dwarf and its companion star begins “feeding” it material through an accretion disk, a sudden brightening can occur, called a nova. The eruption is caused when accreting material forms clumps that fall onto the white dwarf’s surface, releasing gravitational energy. The white dwarf can brighten by a factor of 100, sometimes even more, for a few weeks. Or the material can accumulate on the surface and undergo an uncontrolled chain of nuclear reactions, releasing even larger amounts of energy and making the white dwarf up to a million times brighter for a short time.

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In addition to white dwarfs, other stars can undergo such rapid eruptions, though the physical mechanisms may differ. One example is Eta Carina, in the southern hemisphere, a massive star that sometimes brightens considerably. Clearly, at the end of their lives, stars exhibit a variety of interesting phenomena, from the surface explosions of white dwarfs to instabilities in more massive stars that cause them to occasionally brighten and fade. Ŷ

Name to Know Chandrasekhar, Subrahmanyan (19101995). Indian-born American astrophysicist. Awarded the Nobel Prize in Physics in 1983 for his work on the physical understanding of stars, especially the upper mass limit of white dwarfs.

Important Term

Lecture 52: White Dwarfs and Nova Eruptions

Chandrasekhar limit: The maximum stable mass of a white dwarf or the iron core of a massive star, above which degeneracy pressure is unable to provide suf¿cient support; about 1.4 solar masses.

Suggested Reading Kippenhahn, 100 Billion Suns: The Birth, Life, and Death of Stars. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. If you compare a photograph of a nearby planetary nebula taken 100 years ago with one taken now, how would you expect them to differ?

2. Why is the surface of a star hotter after the star sheds a planetary nebula?

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3. What forces balance to make a white dwarf? 4. If you wanted to prove that a nova must be a binary star system, what kinds of observations might you make?

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Exploding Stars—Celestial Fireworks! Lecture 53

In the last lecture, we saw that most stars die rather quietly, becoming red giants, planetary nebulae (gentle ejections of matter), and white dwarfs. A small minority of stars, however, ends their lives with catastrophic explosions: supernovae.

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Lecture 53: Exploding Stars—Celestial Fireworks!

supernova can increase a star’s luminosity to as much as 10 billion Suns. At its peak, a supernova can rival the brightness of an entire galaxy of stars. The star’s gases may be ejected at speeds greater than 10,000 kilometers per second, which we can determine by examining the spectra of supernovae, as we’ll see in the next lecture. Supernovae heat the interstellar medium—the gases between the stars—causing winds to blow out of entire galaxies. They also give rise to compact remnants in some cases, such as neutron stars and bizarre black holes. Supernovae accelerate charged particles to very high speeds, creating cosmic rays that cause at least some of the mutations that led to the evolution of life. From the human perspective, the most important aspect of supernovae is that they create and disperse into the cosmos the very elements of which life is made. Though the hot, dense, early Universe (the so-called Big Bang, to be studied in future lectures) produced hydrogen and helium, all the heavier elements were created inside stars. If some stars didn’t explode, those heavy elements would remain forever locked up inside white dwarfs, unavailable as the raw material from which new stars, new planets, and even life could form. Indeed, all of the elements in the upper part of the periodic table, such as silver and gold, were produced from such “stardust.” In addition, iron, calcium, carbon, and oxygen, ejected by exploding stars, are essential for life on Earth. We can look at the spectra of supernova remnants and see those elements, which weren’t present when the star ¿rst formed. After tens of thousands of years, nebulae expand even more, gradually merging with other existing clouds of gas and dust within galaxies to form new stars, new planets, and even life. DNA, the basis of life itself, owes its existence to previous 268

Let’s discuss some speci¿c supernovae. The most famous supernova remnant is the Crab Nebula, an expanding set of gases created by a supernova that occurred in A.D. 1054, ¿rst seen on July 4 by Chinese astronomers. The supernova was alleged to be visible during the day for 23 days. In A.D. 1006, another supernova left a bright remnant recently photographed with the Chandra X-ray Observatory and other telescopes. A clear supernova was last seen in 1604 in our own Milky Way Galaxy by Johannes Kepler, of which we can see the remnant. Kepler’s mentor, Tycho Brahe, also witnessed a supernova in 1572 that has produced an expanding remnant. Supernovae are rare; in a big galaxy like our Supernova remnant, Cassiopeia A. own, they might occur a few times per century. The reason we may not have seen a bright supernova since 1604 is that some may be hidden by the extensive gas and dust in the plane of our Galaxy. One supernova occurred in the 1670s in the constellation Cassiopeia, but only one person possibly noticed it. However, today, we clearly see its remnant and can even detect a neutron star in the middle. Ironically, supernovae are easier to ¿nd than other galaxies. Because they are so rare, we have a better chance of ¿nding one by looking at many galaxies over time to observe changes. The Lick Observatory’s Katzman Automatic Imaging Telescope (KAIT), owned and operated by my research group, is programmed to take pictures 269

NASA and The Hubble Heritage Team (STScI/AURA) using data collected by Principal Astronomer Rob Fesen (Dartmouth U.) and collaborators and the Hubble Heritage team (STScI/AURA)

generations of stars. The ejection of the heavy elements into the cosmos, and the production of the elements themselves, is the most centrally important aspect of supernovae. Is our Sun, then, a second-generation star? From what supernova did we come? In reality, our Solar System was formed from a mixture of exploding stars in which debris from many explosions coalesced. In other words, many different generations of stars gave rise to the cloud of gas from which our Solar System formed over a vast time scale.

Lecture 53: Exploding Stars—Celestial Fireworks!

(CCD images) of more than 1000 galaxies over the course of a single night in search of supernovae. Each week, new images of 7000 or 8000 galaxies can be compared with previous images to see if anything new appears. The computer software automatically makes the comparisons and identi¿es supernova candidates; then, undergraduate students examine them to determine which ones are likely to be genuine supernovae. My group has discovered more than 600 relatively nearby supernovae during the past decade, about half of all the bright supernovae that have occurred during this interval. We are the world’s leaders in ¿nding such objects. Supernovae are named in the order of discovery in any given calendar year. For example, the ¿rst supernova of 2000 is named SN 2000A, the second is named SN 2000B, and so on, up through SN 2000Z. The next two after that are SN 2000aa and SN 2000ab, and so on. “You want to spend Though this is not scienti¿cally important, my group even found both SN 2000A and your time with the SN 2001A— the ¿rst supernova of the new Keck telescopes millennium, regardless of one’s de¿nition and others studying of the new millennium (Jan. 1, 2000, or Jan. the supernovae, not 1, 2001). We now study nearby supernovae in great detail for a better understanding of searching for them. how stars explode. It’s really a great form of cooperation between professionals and amateurs.”

Amateur astronomers have discovered many supernovae by making similar observations. Rev. Robert Evans, who lives in Australia, was the ¿rst amateur astronomer to systematically ¿nd bright supernovae. He conducted visual observations of galaxies through his telescope and found about 40 supernovae over the course of a few decades. Inspired in part by the success of Evans and in part by our KAIT search at the Lick Observatory, several amateur astronomers have now found more than 100 supernovae each by repeatedly taking CCD images of galaxies and comparing them to look for new objects. For this reason, amateurs are important in our studies of the heavens. Amateur astronomers in general contribute to our study of the stars, helping to increase our chances of discovering interesting celestial phenomena. Ŷ

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Important Terms interstellar medium: The space between the stars, ¿lled to some extent with gas and dust. supernova remnant: The cloud of chemically enriched gases ejected into space by a supernova.

Suggested Reading Filippenko, “Stellar Explosions, Neutron Stars, and Black Holes,” in The Origin and Evolution of the Universe. Harvard-Smithsonian Center for Astrophysics, www-cfa.harvard.edu/oir/Research/supernova/SNlinks.html.

Supernova,

Kirshner, The Extravagant Universe: Exploding Stars, Dark Energy, and the Accelerating Cosmos. Marschall, The Supernova Story. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. Does the fact that you are made of stardust give you a sense of unity with the cosmos?

2. Why do we think that the Crab Nebula is a supernova remnant? 3. If one or two supernovae occur in a typical galaxy every century, how many galaxies would you need to monitor to ¿nd 20 supernovae each year?

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White Dwarf Supernovae—Stealing to Explode Lecture 54

In the previous lecture, we looked at supernovae, catastrophic explosions of a small minority of stars at the ends of their lives. We begin this lecture by discussing the two main kinds of exploding stars.

A Lecture 54: White Dwarf Supernovae—Stealing to Explode

s we have seen, spectra of stars provide us with information about the stars’ chemical compositions. Similarly, spectra of stellar explosions can tell us a tremendous amount about the stars from which the supernovae arise and about the explosions themselves. There are two main types of exploding stars. Those that show hydrogen in their spectra are called Type II; those that do not show hydrogen in their spectra are called Type I. The Type I class is further divided into subclasses Type Ia, Ib, and Ic, based on the details of the optical spectra. Type Ia supernovae were formerly known simply as Type I before the other two subclasses were recognized. Type Ia supernovae reach their peak brightness over the course of about 3 weeks, then decline for many months or years. Type II supernovae reach their peak brightness in just a day or two, then maintain that brightness for up to 3 months before quickly declining. Type Ia supernovae occur in all kinds of galaxies, including elliptical ones that consist only of old stars. Type II supernovae, as well as Types Ib and Ic, tend to occur in the arms of spiral galaxies and those galaxies where young stars are forming. This suggests that Types II, Ib, and Ic are somehow related to the deaths of massive stars. The spectra of supernovae show evidence for the rapid ejection of gases at speeds sometimes exceeding 10,000 kilometers per second. We can deduce this by plotting their brightness against wavelength and seeing how the absorption lines are blueshifted relative to the emission line. The invention of robotic technology and computer software allows us to examine supernovae in great detail. For example, we can obtain the spectra and compare the light curves of many such events, teaching us about the physics of explosions.

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We can also study the rates at which different kinds of supernovae occur (that is, how many per century per galaxy, on average) and in what types of galaxies. This information is important because different types of supernovae produce different kinds of chemical elements, and they infuse their galaxies with that material. If certain kinds of galaxies produce more Type Ia supernovae than Type II, the chemical evolution of those galaxies will be different from the galaxies that produce more Type II supernovae, for example. The data can also help us determine the rate of formation of neutron stars and pulsars, as well as how quickly the gas between the stars is heated by these explosions. What produces a Type Ia supernova? Traditional Type Ia supernovae don’t show hydrogen in their spectra, which means that there’s very little or no hydrogen present in their ejecta. This is signi¿cant because hydrogen is by far the most common element in the Universe. In addition, as we said earlier, Type Ia supernovae “An understanding tend to occur in galaxies that have only old stars. Further, all supernovae of this type have of Type Ia nearly the same observed properties—similar supernovae and light curves and similar peak power. These how they occur will characteristics suggest that Type Ia supernovae be very important arise from carbon-oxygen white dwarfs, perhaps surrounded by a thin helium layer, but possibly in our studies of with little or no hydrogen. cosmology, the overall structure Such a white dwarf in a binary system can and evolution of sometimes accrete hydrogen from a companion the Universe.” star that is on its way to becoming a red giant. The accreted material increases the white dwarf’s mass. If the accretion rate is just right, the star can avoid nova-like surface explosions that prevent the mass of the white dwarf from growing substantially. Instead, its mass increases. Once the white dwarf reaches its limiting mass, the Chandrasekhar limit of about 1.4 solar masses, it becomes unstable, setting off a runaway chain of nuclear reactions (starting with the fusion of carbon and oxygen) that releases tremendous energy and completely obliterates the star.

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Lecture 54: White Dwarf Supernovae—Stealing to Explode

About half of the white dwarf’s mass fuses to a radioactive isotope of nickel. This nickel-56 decays into radioactive cobalt-56, then into stable iron-56. The decay process emits gamma rays, which are extremely energetic photons. Those gamma rays bounce around inside the exploding star, gradually being converted into optical light. The optical radiation escapes from the expanding gases, giving rise to the optical display of light that we see for a few months or a few years. If radioactive nuclei had not been produced, the explosion would not be visible because all of the released energy would have been used up in the star’s expansion. We are not certain about the details of such explosions. For example, what happens if we incorporate rotation and magnetic ¿elds? How, exactly, is the thermonuclear runaway initiated, and how does it proceed? Although we think that only carbon-oxygen white dwarfs in binary systems can accrete enough material to reach the Chandrasekhar limit and explode in the observed manner, we don’t exactly know which kinds of binary systems are suitable and how the white dwarfs reach this limit. Main-sequence stars are generally much smaller than their Roche lobes—the region within which a star’s gravity dominates—and, therefore, are not capable of spilling material onto their companion white dwarfs. On the other hand, if a red giant is spilling material onto a white dwarf, we would expect the explosion to rip some of the gas away from the envelope of the red giant, causing the hydrogen to glow and show up in the spectrum. Yet it doesn’t. Some physicists have proposed the existence of sub-Chandrasekhar white dwarfs—with masses of less than 1.4 solar masses yet still explosive. For example, an explosion can be initiated at the boundary between the helium envelope and the carbon-oxygen core. The problem is that the spectra and light curves from such models don’t agree with what is observed. Some physicists have proposed that two white dwarfs in a binary system will gradually spiral together and merge, causing an explosion. However, we know of too few binary white dwarfs in our own Galaxy to account for the observed number of Type Ia supernovae in a typical galaxy. We don’t really know how a star reaches the Chandrasekhar limit, but this question offers a great opportunity for future astronomers to discover the fundamental mechanism by which white dwarfs reach their explosive stage. Ŷ

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Important Terms neutron star: The compact endpoint in stellar evolution in which typically 1.4 solar masses of material is compressed into a small (diameter = 2030 km) sphere supported by neutron degeneracy pressure. pulsar: An astronomical object detected through pulses of radiation (usually radio waves) having a short, extremely well-de¿ned period; thought to be a rotating neutron star with a very strong magnetic ¿eld.

Suggested Reading Filippenko, “Stellar Explosions, Neutron Stars, and Black Holes,” in The Origin and Evolution of the Universe. Harvard-Smithsonian Center for Astrophysics, www-cfa.harvard. edu/oir/Research/supernova/SNlinks.html.

Supernova,

Kirshner, The Extravagant Universe: Exploding Stars, Dark Energy, and the Accelerating Cosmos. Marschall, The Supernova Story. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. Distinguish between what goes on in novae and Type Ia supernovae. 2. Do you think the observed widths of emission and absorption lines in the spectra of supernovae give some indication of the speed of the ejected gas?

3. Most white dwarfs have a mass of about 0.5 to 0.6 times the mass of the Sun. Does this pose a problem for the hypothesis that most Type Ia supernovae arise from the explosion of a merged white dwarf binary whose mass reaches the Chandrasekhar limit? 275

4. Given that the nuclear reactions at the surface of a white dwarf

Lecture 54: White Dwarf Supernovae—Stealing to Explode

undergoing a nova explosion release enough energy to eject the material accreted from the companion star, why do you think it is important for a white dwarf to avoid the nova process if it is to eventually become a supernova?

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Core-Collapse Supernovae—Gravity Wins Lecture 55

In previous lectures, we’ve seen how some white dwarfs reach an unstable mass, the Chandrasekhar limit, causing them to explode. In this lecture, we will look at another kind of mechanism for stellar explosions in Type II supernovae and related subclasses.

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ype II supernovae appear in spiral galaxies, usually in or near spiral arms, where lots of massive stars are forming or have recently formed. Red supergiants are most likely to become supernovae, and these stars typically have masses initially at least 10 times that of our Sun. A crosssection of such a star would show an iron core with shells of progressively lighter elements surrounding it: silicon and sulfur; oxygen, neon, and magnesium; carbon and oxygen; helium; and ¿nally, hydrogen. Most of the volume, however, is hydrogen. Red supergiants have this onion-like layering because the ashes of one set of nuclear reactions become the fuel for the next set. Hydrogen fuses to helium; helium fuses to carbon and oxygen; and carbon and oxygen fuse to neon, magnesium, and so on, all the way up to iron. Each set of reactions liberates energy because the products are more and more tightly bound compared to the reactants; the binding energy is released during nuclear fusion. Iron and other elements of similar mass—nickel and cobalt, for example—are the most tightly bound elements. For this reason, their fusion does not produce energy; rather, it requires energy. Very heavy elements (such as uranium) can undergo ¿ssion, or break up, into lighter elements, releasing energy. Per nucleon (proton or neutron), the binding energy of the products is higher than the binding energy of the very heavy elements. However, this is not what occurs in a red supergiant. We mention ¿ssion of very heavy elements simply to stress that iron-group elements are the most tightly bound (that is, have the highest binding energy per nucleon). Thus, as a red supergiant undergoes successive stages of nuclear burning, iron eventually forms in the core, with a silicon-sulfurfusing shell surrounding it.

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Lecture 55: Core-Collapse Supernovae—Gravity Wins

As the iron core gains mass, it eventually reaches the Chandrasekhar limit of roughly 1.4 solar masses. At its mass limit, the iron core collapses due to gravity, to a radius of only about 10 kilometers, liberating a tremendous amount of gravitational energy. Microscopically, the electrons and protons combine to form neutrons and neutrinos. The pressure support, previously provided mostly by the electrons, disappears until the star is just a ball of neutrons—a neutron star. During the core’s collapse, it rebounds from itself because its constituent particles repel one another when they get too close together. Because material surrounding the core is no longer supported by pressure, it collapses, but then it collides with the rebounding core and is propelled outward at high speeds. But this prompt mechanism, or rebounding effect, is not enough to completely eject the material into space. The gravity of the central neutron star pulls it back; thus, a stronger force is needed to give the material an extra push and create the full visual effect that we see in an exploding star. When the star collapses, its protons and electrons combine to form neutrons and neutrinos. Far more neutrinos are produced simply because of the fact that the young neutron star has an extremely high temperature, about 100 billion K; neutrinos are ef¿ciently produced at such temperatures. Some of the released neutrinos can hit the surrounding layers of gas and eject them into space, creating a successful supernova explosion. During the explosion, elements even heavier than iron can form, generally through the sequential capture of many neutrons (followed by radioactive decay of some of them into protons). In this process, we get the rich periodic table of the elements, of which we and other Earth-like, rocky planets consist. It is dif¿cult to know precisely when a red supergiant will explode because we can’t tell what the core is doing, and there are different time scales associated with the various stages of nuclear burning. For example, because Betelgeuse is a red supergiant, we know that it’s at least in the helium-burning stage, which lasts 500,000 years. (For comparison, the main-sequence stage lasted perhaps 7 million years.) It might be in the carbon-burning stage, which lasts only 600 years, or it might even be in the silicon-burning stage, which lasts only a day. Most likely, it’ll explode sometime in the next half a million years. In the last few stages of a red supergiant’s life—oxygen fusing to silicon and sulfur, and silicon fusing to iron—the temperatures are so high 278

that many neutrinos are formed, which escape from the star immediately at speeds close to the speed of light. If we could develop a highly sensitive neutrino detector, we might be able to predict more accurately when a star is about to explode. Red supergiants are not the only stars that can explode in this way, as corecollapse supernovae. Several other subclasses of stars belong to this category. Most core-collapse supernovae have a hydrogen shell, formally making them Type II supernovae, but some massive stars lose this shell before exploding. Such a progenitor star has a helium envelope and other elements (carbon, oxygen, and so on) in its core, ending with iron at the center. These stars explode as Type Ib supernovae. The progenitor stars of Type Ic supernovae have lost both their hydrogen and helium outer layers, leaving an envelope of carbon and oxygen, with shells of successively heavier elements inside. These subclasses of stars are important because we now recognize that not all Type I supernovae obliterate themselves and produce a large amount of iron (¿rst in the form of radioactive nickel), as Type Ia supernovae do. Instead, Type Ib and Ic supernovae form compact neutron stars and eject large quantities “It looks like of intermediate-mass elements, such as oxygen, gravity is ultimately calcium, magnesium, and sulfur. Thus, Type Ib and Ic supernovae affect the chemical evolution victorious in all of galaxies in a way that differs from that of Type these stars, all Ia supernovae. these massive stars, regardless How does the envelope of hydrogen—and, in of how much of an some cases, helium—get stripped away from a star? Some massive stars experience winds and envelope they gentle ejections, where the pressure of photons still retain.” expels the envelope. Stars in a binary system can also transfer part of their gas atmospheres onto a companion star. In some cases, only partial stripping of the hydrogen envelope occurs, creating a low-mass shell of hydrogen. We call the subsequent explosion a Type IIb supernova. Thus, core-collapse supernovae come in a number of varieties: Type II, the hydrogen-rich and most common kind, and Types Ib and Ic, classi¿ed according to whether or not they have

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helium envelopes. Regardless of how much of a hydrogen envelope they have, their iron cores ultimately collapse to form neutron stars. Ŷ

Important Terms progenitor: In the case of a supernova, the star that will eventually explode. stripped massive stars: Stars that have lost their hydrogen and helium envelopes, either through stellar winds or through transfer of gas to a companion star; thought to be the progenitors for gamma-ray bursts.

Suggested Reading Kirshner, The Extravagant Universe: Exploding Stars, Dark Energy, and the Accelerating Cosmos.

Lecture 55: Core-Collapse Supernovae—Gravity Wins

Marschall, The Supernova Story. Filippenko, “Stellar Explosions, Neutron Stars, and Black Holes,” in The Origin and Evolution of the Universe. ———, “A Supernova with an Identity Crisis,” Sky & Telescope, Dec. 1993. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. What are the observational and physical differences between Type Ia and Type II supernovae? Which kinds of stars explode, and how do they explode?

2. In a supernova explosion of a 15-solar-mass star, about how much material is ejected (blown away)?

3. Do you expect Type Ib and Ic supernovae to produce a burst of neutrinos, just as a Type II supernova does?

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The Brightest Supernova in Nearly 400 Years Lecture 56

The brightest supernova in nearly 400 years was studied in great detail. It occurred in the Large Magellanic Cloud, a satellite galaxy of the Milky Way, only 170,000 light years away from Earth.

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hough astronomers have never directly witnessed the explosion of a visible white dwarf as a Type Ia supernova, we have seen some very massive stars explode as Type II supernovae. One in particular, SN 1987A, was observed in great detail, both before and after the explosion. Supernova 1987A, the ¿rst supernova to be witnessed in the year 1987, was the brightest supernova in nearly 400 years. It occurred in the Large Magellanic Cloud, a satellite galaxy of our Milky Way Galaxy. The Large Magellanic Cloud is about 170,000 light years away, which means that the explosion occurred about 170,000 years ago, just about the time of early hominids on Earth. The supernova was discovered by Ian Shelton, a student working at Las Campanas Observatory in Chile. Using a small telescope, he took numerous photographs of the Large Magellanic Cloud in his study of the variable brightnesses of stars. One of Shelton’s photographs indicated an extra point of light that hadn’t appeared in previous photographs. The supernova appeared near the Tarantula Nebula and was visible to the naked eye. Other astronomers, both amateur and professional, had also witnessed the same supernova from other parts of the world, though Shelton is credited with its discovery. SN 1987A was a Type II supernova; that is, it had an envelope of hydrogen. But it was a peculiar object. For example, SN 1987A faded much more rapidly than it should have at ultraviolet wavelengths. Moreover, it didn’t brighten as much as astronomers had expected. Being so bright and nearby, SN 1987A was studied with a broad range of telescopes, allowing us to test our theories of Type II supernovae. By examining pre-explosion photographic plates, we discovered that the progenitor star (the star that exploded) was a blue supergiant with an initial mass of about 20 solar masses. Blue supergiants have about the same luminosity 281

The discovery of SN 1987A taught us that under some conditions, blue supergiants can develop an iron core and explode. The mechanism is unclear, but it is possible that, because the Large Magellanic Cloud is de¿cient in heavy elements relative to our own Galaxy, stars de¿cient Supernova 1987A rings, taken by the Hubble in heavy elements have a Space Telescope. different structure in their envelopes (outer layers), allowing them to explode as hotter but smaller stars—blue supergiants. Some astronomers think that the star was a blue supergiant when it exploded because it could have been part of a binary system and perhaps swallowed its companion star prior to the explosion, changing its outer structure. Another theory tested was whether multitudes of neutrinos are emitted when a Type II supernova occurs. Indeed, neutrinos were detected by at least two underground tanks of water that had originally 282

Dr. Christopher Burrows, ESA/STScI and NASA

Lecture 56: The Brightest Supernova in Nearly 400 Years

as red ones, but blue supergiants have much higher surface temperatures. Previously, astronomers didn’t think blue supergiants could explode because we thought they were on their way to becoming red supergiants and would not yet have been able to build up their iron cores. The supernova showed peculiar characteristics, such as the rapid decline of ultraviolet light and a much dimmer than expected appearance. Its apparent magnitude began at about 4.5, then gradually grew to only 2.5 (remember, the lower the magnitude, the brighter the object). Thus, it was visible to the naked eye, but it should have been much brighter than what was actually seen. The de¿cit of light is consistent with the star being a blue supernova because such stars are smaller than red supergiants. The smaller size translates to less radiating area; thus, the star could not become as bright as a larger star would.

been designed to search for the decay of protons. Calculations showed us that the total energy emitted by SN 1987A, in roughly a few seconds, was comparable to the total amount of energy emitted by all the normal stars in the rest of the observable Universe during those few seconds. Aside from the Big Bang itself, this type of explosion is about the biggest we can get. More than 99% of the explosion energy was in the form of neutrinos. Most of the other 1% was the kinetic energy of the ejected gases. Only about 0.01% “I’m sure that in of the energy was emitted as optical radiation. Thus, even though SN 1987A was a bright, the next decade naked-eye supernova, the visible light constituted or two, Supernova only 1/10,000 of the true energy emitted by the 1987A will have explosion. additional secrets When neutrinos are emitted by a supernova and to tell us.” hit Earth, they generally don’t indicate from which direction they came. In other words, how did we know that the neutrinos detected around the time of SN 1987A came from that star? One obvious factor was that the neutrinos were detected at about the same time as the supernova was discovered. Two reactions can occur when neutrinos released from an exploding star interact with material on Earth. First, neutrinos can scatter off electrons, propelling the electrons forward in roughly the same direction from the supernova. These electrons produce Cerenkov light cones, which can then be detected by a light detector and tell us from which direction the neutrinos came. However, a second reaction—and far more common—is for antineutrinos to combine with protons, forming energetic positrons and neutrons. In such a case, positrons can go in any direction with nearly equal probability (described by the term isotropic); thus, they do not indicate where in the sky the supernova occurred. In general, if a supernova were to occur in our Galaxy (that is, close by), it would produce enough detectable neutrinos (scattering off electrons) to allow us to know in which direction the supernova was likely to become visible within a day. The neutrinos would reach Earth before the light of the exploding star, telling us where to look for the impending supernova 283

light. Although neutrinos don’t quite travel at the speed of light, they get a “head start” over the photons from the surface of the exploding star (which are formed only after the shock wave coming from the star’s central region reaches the surface, traveling at about 1/10 the speed of light).

Lecture 56: The Brightest Supernova in Nearly 400 Years

Another theory con¿rmed by SN 1987A was that heavy elements are synthesized by supernova explosions. Electromagnetic radiation from such elements was detected by gamma-ray telescopes and other instruments launched above the Earth’s atmosphere after SN 1987A was discovered. Gamma rays were detected arising from speci¿c radioactive elements. The explosion formed radioactive nickel, which quickly decays into cobalt, which—on a longer time scale—decays into iron. These radioactive elements could have been produced only by SN 1987A. Because they are short-lived, they would not have remained in the star at the time of its death had they been present in the material from which the star was ¿rst formed, millions of years earlier. Supernova 1987A is surrounded by rings of gas released before the actual explosion. These rings can be used to study the progenitor star’s behavior during the last few thousand years before its death. Ejected gases from the supernova explosion itself are now colliding with the external rings, which are consequently beginning to increase in brightness. During the next few years, the supernova will experience a renaissance, appearing substantially brighter than it is now. Ŷ

Important Term isotropic: The same in all directions (that is, no preferred alignment).

Suggested Reading Filippenko, “Stellar Explosions, Neutron Stars, and Black Holes,” in The Origin and Evolution of the Universe. Goldsmith, Supernova! The Exploding Star of 1987. Kirshner, The Extravagant Universe: Exploding Stars, Dark Energy, and the Accelerating Cosmos. Marschall, The Supernova Story. 284

Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. Is it surprising that SN 1987A occurred near a giant cloud of gas (called the Tarantula Nebula) where massive stars have been produced for the past few tens of millions of years?

2. If only 10 neutrinos from SN 1987A were detected by each of two underground tanks containing several thousand tons of water and if a typical human consists of 100 pounds of water, what are the odds that your body directly detected a neutrino from SN 1987A (assuming that you were alive in Feb. 1987)?

3. How compelling do you ¿nd the arguments that we are made of stardust?

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The Corpses of Massive Stars Lecture 57

In the previous lecture, we saw how supernova 1987A helped con¿rm our basic ideas about supernovae but showed that we also needed to re¿ne some of our ideas. Though the progenitor star of the peculiar SN 1987A was a blue supergiant, other, more typical Type II supernovae have been found to come from red supergiant stars.

Lecture 57: The Corpses of Massive Stars

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s recently as 2005, the Hubble Space Telescope observed a supernova in M51, the Whirlpool Galaxy. The progenitor of SN 2005cs was a red supergiant of about 12 solar masses, and the supernova had a more normal—or expected—spectrum than that exhibited by SN 1987A. The data for SN 2005cs strengthened the evidence that the cores of red supergiants implode and the outer parts get ejected. In most cases, an imploding core forms a neutron star, a very dense ball of neutrons maintained by neutron degeneracy pressure, similar to the electron degeneracy pressure experienced by white dwarfs. A neutron star 1.5 times the mass of the Sun can be only about 20 kilometers in diameter. A teaspoonful of material from such a star would weigh about 1 billion tons. A neutron star is similar to a white dwarf in that it is made of degenerate material crammed into a very small space. The pressure exerted by degenerate neutrons prevents the star from collapsing. Neutron stars were predicted by Fritz Zwicky and Walter Baade in 1933. They also predicted that neutron stars were produced during cataclysmic explosions of massive stars. Neutron stars weren’t actually discovered until 1967, when Jocelyn Bell detected one in the form of a pulsar; these objects generally can’t be seen clearly, but they emit regular pulses of radio radiation. The ¿rst pulsar Bell detected had a periodicity of 1.3373011 seconds. The spacing of the pulsar’s blips was regular, although the intensity, or brightness, varied considerably with time. At ¿rst, it was suggested that pulsars might be extraterrestrial communications. Shortly thereafter, however, several more regular series of pulses were found coming from other parts of the sky but with different periodicities. It was deemed unlikely that a network of intelligent species, all communicating in a similar manner, was present in our Galaxy. Moreover, there was no evidence of a periodically changing Doppler 286

shift, indicating that the pulsars were not coming from another planet or object that was orbiting a star. Through an interesting process of elimination, astrophysicists quickly determined that pulsars probably emanated from rapidly rotating, highly magnetized neutron stars. One clue was that most of the pulsars originated from the plane of the Milky Way Galaxy, where many of the more massive stars are concentrated. Pulsars can’t arise from oscillating (vibrating) normal stars or white dwarfs, whose periodicity is too slow. In contrast, the expected vibration period of neutron stars is too fast. Two normal stars or white dwarfs cannot orbit each other so quickly, either. Two neutron stars can have such a tight orbit, but they would rapidly lose energy, and the orbital period would decrease—yet pulsar periods were observed to be very stable. The surface of such a rapidly rotating normal star would exceed the speed of light. Similarly, a white dwarf is disrupted if its rotation period is less than about 0.3 seconds, too slow for the rapid pulsars. Neutron stars, on the other hand, are capable of rotating about their axes at speeds that are consistent with the observed pulsar rates. We now have additional, more direct evidence that pulsars are rapidly rotating neutron stars. Let’s look at some of the characteristics of pulsars and their causes. We don’t really know the details of why pulsars shine, but this characteristic is undoubtedly related to their magnetic ¿elds. Neutron stars have magnetic ¿elds within and surrounding them, the axes of which generally differ from the stars’ axes of rotation, forming conical patterns as they rotate. The magnetic axis ¿rst points in one direction, then in another direction. This rotation can create electric ¿elds that are strong enough to accelerate electrons to speeds close to that of light. Accelerating charged particles emit radiation along their direction of acceleration, creating (by methods still not fully understood) two oppositely directed beams of light that are visible from Earth—with their associated periodicity—as the star rotates. The effect is similar to that of a lighthouse: It is on all the time, but you see a Àash only when the rotating lamp is pointing at you. We think that the magnetic ¿eld is a trillion times as strong as Earth’s magnetic ¿eld. (The unit of magnetism is a gauss, and the Earth’s magnetic

287

¿eld is about 1 gauss.) It is possible that the strong magnetic ¿eld is a result of the star’s collapse, forcing the star’s magnetic ¿eld into such a small space that its strength increases dramatically. Why does a neutron star rotate so quickly? All stars rotate to some extent, and as they collapse, the spin rate must increase in order to conserve angular momentum.

Lecture 57: The Corpses of Massive Stars

Very young pulsars shine not only at radio wavelengths but at optical and x-ray wavelengths and at other wavelengths. As the stars get older, the highenergy forms of radiation subside; what remains are low-energy forms of radiation, such as radio waves. We have observed that one particular pulsar in the Crab Nebula, the remnant of the supernova of A.D. 1054, creates a wind, as well as jets of material, energizing the Crab Nebula and causing it to glow brightly. Over time, this neutron star has been losing energy through the production of its light beams and jets of material, slowing its pulsation rate. Quantitatively, the rate of energy gain in the Crab Nebula is equal to the rate of energy loss of the rotating neutron star, providing strong support for our basic model of pulsars. We expect pulsars to remain turned on for only about a few million years before their rotation rates (and, perhaps, the strength of their magnetic ¿elds) diminish so much so that light beams are no longer produced. Every pulsar is a neutron star, but not every neutron star will be visible as a pulsar. Some will have died, or some might have axes of rotation oriented in such a way that they don’t allow the beams of light to cross Earth’s line of sight. Typically, pulsars spin about once per second, or 10 times per second, or maybe once every 10 seconds. But some spin hundreds of times per second—these are called millisecond pulsars. Converting the frequencies at which these pulsars spin to audible signals will produce corresponding musical notes. Some astronomers have written musical pieces with the notes of known millisecond pulsars. We think these pulsars spin so fast because they previously accreted material from a companion star orbiting them. In 1991, one millisecond pulsar was discovered to have at least three planets orbiting it. The key to this discovery was that, sometimes, the pulses arrived sooner than expected and, other times, they arrived later than expected. This slight deviation from perfect periodicity is caused by orbiting planets; the

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planets and the neutron star orbit their common center of mass, so the neutron star is sometimes slightly closer to Earth, and sometimes slightly farther away. These “planets” are quite different from those in our Solar System, though they happen to be comparable in size to the terrestrial planets. In addition, these “planets” could not have existed before the supernova that gave rise to the pulsar because the planets would have been destroyed in the supernova explosion. Therefore, it’s likely that they formed from a disk of debris around the neutron star that remained after the explosion. In the last decade, astronomers have learned some interesting things about neutron stars. Some neutron stars have magnetic ¿elds up to 1015 gauss units; these are called magnetars, the strongest magnets in the Universe. Magnetars sometimes emit tremendous amounts of energy because, apparently, the structure of their crust changes such that it creates a kind of “starquake.” Furthermore, the magnetic ¿eld changes, also releasing a tremendous amount of energy. One such magnetar was observed on December 27, 2004, in the constellation Sagittarius, “Magnetars creating the brightest Àare ever seen from outside our Solar System. The eruption was so bright that are exciting, it ionized Earth’s atmosphere and activated the but don’t get sensors on several satellites. Satellites transmitted anywhere near the information to radio telescopes on the ground, one—especially which immediately moved to begin observing that location of the sky. These telescopes detected debris if you have a emanating from the magnetar and moving at speeds pacemaker, close to the speed of light. We believe this was a because it’ll restructuring of the surface layers of a neutron star. de¿nitely mess After the main burst of energy, alternating Àashes of light from the neutron star’s north and south it up.” poles became visible as the star rotated. We believe that this type of neutron star, which gives rise to a magnetar, has an interior of liquid neutrons and other particles with a generally solid crust. The crust essentially buckles or cracks, changing the magnetic ¿eld con¿guration, as well. We know that magnetars survive this basic burst because some of these events have been seen to repeat after a few years. Ŷ

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Name to Know Zwicky, Fritz (18981974). Swiss-American astronomer; proposed that supernovae result from the collapse of the cores of massive stars, producing neutron stars and energetic particles (cosmic rays). Compiled an extensive atlas of galaxy clusters and showed that many such clusters must contain dark matter in order to be gravitationally bound.

Important Terms lighthouse model: The explanation of a pulsar as a spinning neutron star whose beam we see as it comes around and points toward us. magnetar: Spinning neutron star with an extraordinarily powerful magnetic ¿eld that occasionally releases a burst of gamma rays when the crust of the star undergoes a sudden restructuring (a “star quake”).

Suggested Reading

Lecture 57: The Corpses of Massive Stars

Filippenko, “Stellar Explosions, Neutron Stars, and Black Holes,” in The Origin and Evolution of the Universe. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. Can you ¿nd any loopholes in the process-of-elimination argument used to conclude that pulsars are rotating neutron stars?

2. How did studies of the Crab Nebula pin down the explanation of pulsars? 3. Calculate the density (mass per unit volume) of a neutron star having a mass of 1.4 solar masses and a radius of 10 kilometers. Compare this with the density of a neutron or a proton (each of which has a radius of about 10–15 m and a mass of about 1.67u10–24 g). 290

Einstein’s General Theory of Relativity Lecture 58

Based on the idea that there is no difference between a uniform acceleration and a uniform gravitational ¿eld, Einstein’s theory postulates that gravity is a manifestation of the warping of space and time produced by matter and energy; objects follow their natural trajectory through curved space-time.

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n our understanding of the physical properties of neutron stars—in particular, their immense density—we need to consider Einstein’s general theory of relativity. Though Newton’s famous laws of motion and of universal gravitation were tremendous breakthroughs in science, the laws break down when we consider objects traveling at very high speeds or in strong gravitational ¿elds. Einstein’s special theory of relativity accounted for high speeds, as discussed in Lecture 42. Moreover, Newton never fully understood how gravity worked, and Einstein also knew that standard Newtonian gravity was inconsistent with his special theory of relativity. The fundamental problem with Newton’s theory of gravity is revealed in a thought experiment, in which Einstein tried to predict what would happen to the Earth if the Sun were to simply vanish, leaving no gravitational forces to affect Earth. Because Newtonian gravity invokes instantaneous “action at a distance,” the moment the Sun disappeared, the Earth would sail along the tangent to its trajectory, no longer in orbit. With no forces acting upon Earth, it would continue moving in a straight line at a constant speed, according to Newton’s ¿rst law of motion. Thus, Einstein knew that Newton’s law of gravitation violated his own special theory of relativity because relativity claims that no information can travel faster than the speed of light. How can the Earth instantaneously “know” that the Sun’s mass vanished? Einstein worked on this problem for more than a decade and came up with the general theory of relativity, which deals with accelerations and gravitational ¿elds. The theory is based on the idea that there’s no fundamental difference between a uniform acceleration and a uniform gravitational ¿eld. Recall that special relativity is based on the idea that there is no difference in the laws of 291

physics experienced in laboratories at rest and in uniform motion (constant speed and direction). This is a more restricted theory than general relativity.

Lecture 58: Einstein’s General Theory of Relativity

Let’s look at another thought experiment of Einstein’s for general relativity. A person standing in a windowless elevator that suddenly accelerates upward would momentarily feel heavier. From the person’s perspective, either the elevator accelerated up or a large mass was temporarily placed beneath the elevator, increasing the gravitational ¿eld and creating that momentary heavy feeling. Einstein theorized, then, that a person in an elevator moving with a constant speed would see light travel in a straight line, because that is what happens in elevators at rest. However, that person in an elevator accelerating upward would theoretically see light travel in a path that curved downward, because the light cannot “know” that the elevator is accelerating. Because accelerations and gravitational ¿elds are equivalent, according to the general theory, light must therefore also bend in a gravitational ¿eld. As Einstein further formulated general relativity, he found that the paths of light and particles in a gravitational ¿eld can be represented by their natural paths in curved space-time. Gravity is a manifestation of the warping of space and time; effectively, objects move along their natural paths in an intrinsically warped space. This space-time warping, or curvature, is caused by mass or energy. The warping occurs in some fourth spatial dimension, which we cannot see and to which we have no physical access. The denser and more massive the object, the more it bends the space-time around it. For example, the Sun produces a warping that causes Earth to go around it, but Earth has a little warp around it as well, so the Moon follows its natural path around Earth. Can we actually test Einstein’s theory? We know that the orbits of objects are not closed ellipses; rather, their long axis shifts, or precesses, with time. The rate of shift increases in stronger gravitational ¿elds, as was ¿rst seen with the orbit of Mercury (compared with that of Venus or Earth). Many perturbations of Mercury’s orbit can be explained by effects from the large planet Jupiter and other smaller inÀuences. However, Mercury’s orbit shifts by 43 arc seconds per century, which is not caused by Jupiter’s gravity. Einstein explained the shift using his general theory of relativity. We also know that light from stars moving past the Sun is shifted, proving that gravity can bend light. Quasars are central regions in distant galaxies where we think a giant 292

black hole is swallowing material. We can measure shifts in the quasars’ positions relative to the Sun’s position, indicating that their light bends through space.

“The global positioning system is a great practical application of relativity. If it didn’t work, it wouldn’t get you to the right place at the right time.”

Finally, we know that light emerging from a gravitational ¿eld is redshifted as the photons lose energy. This has been seen even in weak ¿elds, such as Earth’s, though the effect is very subtle. Einstein also predicted that time is warped by gravitational ¿elds. We can actually measure this on Earth by using global positioning system (GPS) units. GPS satellites must have atomic clocks that are slower by 38 microseconds per day compared to clocks on Earth’s surface in order for the system to work on Earth. Ŷ

Suggested Reading Hawking, The Universe in a Nutshell. Mook and Vargish, Inside Relativity. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Wolfson, Simply Einstein: Relativity Demysti¿ed.

Questions to Consider 1. If you were immersed in a gravitational ¿eld that is not uniform, how might you distinguish this from an acceleration?

2. According to the elevator thought experiment showing that light is bent by a gravitational ¿eld, does the amount of bending depend on the wavelength of light?

3. Why do the special relativistic and general relativistic corrections to GPS satellite clocks go in opposite directions?

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Warping of Space and Time Lecture 59

Another effect of general relativity is the bending of light through space, also a measurable phenomenon that can help us detect the presence of brown dwarfs and black holes.

Lecture 59: Warping of Space and Time

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n the previous lecture, we looked at Einstein’s general theory of relativity and mentioned how it applies to the global positioning system (GPS). Let’s consider this in more detail to see how relativity works quantitatively and, at least in this one case, affects our everyday lives. Timing is crucial; in order for a GPS device to work, we must know exactly how far away each of the GPS satellites is. We can ¿gure this out by measuring when a satellite’s signal was emitted and how long it takes to reach Earth. The speed of light is about 1 foot per nanosecond (1 billionth of a second). But the relativistic effect in time difference between the satellites and our unique position on Earth is 38 nanoseconds. Such a difference, though seemingly small, would accumulate to large errors over the course of a month. If GPS designers did not take relativity into account, then after a few days, a GPS unit would begin providing quite inaccurate information. Thus, a GPS satellite’s atomic clock is programmed to run at a rate that exactly compensates for both the special relativistic effect, a slowdown of 7 microseconds per day, and the general relativistic effect, an increase of 45 microseconds per day. The net effect is a compensation of 38 microseconds per day. Today, lasers, computers, and other electronic devices depend on our understanding of quantum mechanics. Thus, who knows in the future what other technological inventions will have to take into account the effects of general relativity? Let’s review Einstein’s thought experiment in which the Sun’s mass suddenly vanished. Then, we will consider other ways that we can test for Einstein’s general theory. As we saw in Lecture 58, according to Newton’s law of gravitation, at the moment the Sun disappeared, Earth would be thrown off its orbit along the tangent of its trajectory. However, Einstein claimed that Earth would not experience the Sun’s disappearance until 8.3 minutes later. Thus, information about the Sun’s disappearance would travel via gravitational waves at the speed of light, according to theory (the speed has never actually 294

been measured). Once this information reached Earth, 8.3 minutes later, our planet would then travel along the tangent to its trajectory. An analogy would be tossing a ball into a calm swimming pool. The ball sends out concentric waves, but someone at the pool’s edge wouldn’t experience those waves until they reached the edge. Likewise, the removal of the Sun would create a disturbance in the warping of space, a disturbance that travels at the speed of light through the Solar System. The warp that the Sun used to produce no longer exists; space would be Àat there instead, though it wouldn’t happen instantaneously. Recall that the ¿rst historical test of relativity was the con¿rmation that “We think that Mercury’s extra precession, 43 seconds of arc per century, could be quantitatively explained on large scales through general relativity. That was a great the theory of triumph, but 43 arc seconds per century is a relatively is correct small amount. quantitatively. But it’s always possible We now have much better evidence through our study of two neutron stars, discovered (in that it is false. Any 1974) to be orbiting each other in just 8 hours. new experimental One of the stars is a pulsar; thus, the system test is welcome with was dubbed a binary pulsar, even though only open arms.” one star is visible as a pulsar. The precession of the pulsar’s elliptical trajectory is 4 degrees per year, much greater than Mercury’s orbital precession of 43 arc seconds per century. Each star forms a warp in space, creating a ripple, or gravitational wave, that propagates through space at the speed of light. As these ripples travel and the stars continue to orbit around their common center of mass, energy is removed from their system. The removal of energy forces the stars to move closer to each other, due to gravity, which in turn, increases the stars’ orbital speed and decreases their orbital periods. As the stars’ orbital period decreased over time, the pulsar signal also changed. The cumulative measurement of the pulsar’s change over time exactly corresponded to what general relativity predicts. In 2003, an even more closely spaced binary pulsar was found, with an orbital period of just 2.5 hours, in which both of the neutron stars have visible pulsars. 295

Astronomers have determined that the stars’ orbits shrink by 7 millimeters per day. This system, as well, strongly con¿rms quantitatively the predictions of general relativity.

Lecture 59: Warping of Space and Time

A related effect of this warping of space occurs in a process called gravitational lensing. We’ve already encountered this in our discussion of the deÀection of starlight by the Sun and other massive objects. As we’ve seen in a previous lecture, if we observe the light of a distant star, our Sun deÀects—bends—the star’s light. If we look at an intrinsically point-like light, we might actually see what is called an Einstein ring. Such rings have been photographed at visible wavelengths by the Hubble Space Telescope. The ring appears in perfectly symmetrical situations, such as when a black hole passes between our line of sight and a distant galaxy. In this case, the galaxy’s light is actually bent such that it appears as a ring of light. If the focusing effect is caused by a foreground star, rather than by a galaxy, we call it gravitational microlensing. Usually, small deviations from symmetry cause a ring to break up into smaller units, such as partial arcs or even point-like images: We can see several images of the background object that is lensed by the foreground object. Each image is a mirage; for example, quasars often become imaged into several discrete mirages when a galaxy appears in the foreground and gravitationally lenses the light from the background quasar. If the clarity of the images is not enough to show distinct mirages, we would still see an apparent brightening of the object due to the focusing of light rays toward us. The cumulative brightness of the ring, or the mirages, is increased through the gravitational focusing of light. This brightening effect can be used to detect the presence of foreground gravitationally lensing objects, even if they aren’t directly noticeable. For example, if a brown dwarf or a black hole passes along our line of sight to a background star, the focusing effect still occurs, revealing the presence of an otherwise hard-to-see object. Some brown dwarfs and wandering black holes have been detected through this process. Even a few isolated, free-Àoating planets have been detected by their gravitational microlensing of a background star. In 2005, a small planet (about 5 Earth masses) was

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discovered through this effect, which also has the potential to reveal many more exoplanets having relatively small masses. Finally, using one more emerging test for general relativity, we are hoping to demonstrate that a rotating object drags space around it; that is, space itself rotates around a rotating object. Data gathered in 2006 from a satellite called Gravity Probe B are now being analyzed. The experiment involves a complex technique and the orientation of gyroscopes within the satellite. This dragging effect, which has never been measured, is believed to occur at a rotation of 0.042 arc seconds per year at the location of the satellite. By measuring the orientation of the satellite’s gyroscopes, we should be able to demonstrate the effect, if general relativity is correct. Ŷ

Important Terms binary pulsar: A pulsar in a binary system. Often, this term is used for systems in which the pulsar’s companion is another neutron star. gravitational lens: In the gravitational lens phenomenon, a massive body changes the path of light passing near it so as to make a distorted image of the object. gravitational waves: Waves thought to be a consequence of changing distributions of mass. relativistic: Having a speed that is such a large fraction of the speed of light that the special theory of relativity must be applied.

Suggested Reading Hawking, The Universe in a Nutshell. Mook and Vargish, Inside Relativity. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Thorne, Black Holes and Time Warps: Einstein’s Outrageous Legacy. 297

Will, Was Einstein Right? Putting General Relativity to the Test. Wolfson, Simply Einstein: Relativity Demysti¿ed.

Questions to Consider 1. Suppose you ¿nd several closely spaced quasars that you think are the gravitationally lensed images of a single quasar. How might you test your hypothesis?

2. Because of time dilation in the special theory of relativity, an observer on Earth sees a rapidly moving twin in a spaceship aging more slowly than he does. After returning to Earth, the traveling twin will be younger than the one who stayed on Earth. But consider this: The traveling twin thinks that he is at rest and the Earth twin is moving—in which case, the Earth twin would be younger than the spaceship twin. How do you think this famous twin paradox is resolved? (Hint: What does the traveling twin have to do in order to return to Earth? Does this allow the two frames of reference to be distinguished from one another? Is this similar to being placed in a gravitational ¿eld?)

3. If a speci¿c observer sees an apparent brightening of an object due to Lecture 59: Warping of Space and Time

the focusing of light rays during an episode of gravitational lensing, will this object appear fainter than expected from some other lines of sight at that same time?

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Black Holes—Abandon Hope, Ye Who Enter Lecture 60

Our discussion of general relativity is motivated in part by the existence of neutron stars, very dense stars that form when a massive star collapses. But there exists a phenomenon that is even stranger than a neutron star—a black hole.

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black hole is a region of space where material is compressed to such a high density and the local gravitational ¿eld is so strong that nothing—not even light—can escape. If we could shine a light on a black hole, nothing would be reÀected; also, no light is emitted from within a black hole. To understand how black holes form, we must recall that a neutron star, held up by neutron degeneracy pressure, can have only a certain maximum mass before it collapses. We don’t know the exact limiting mass for a neutron star because we don’t yet fully understand the structure of matter at nuclear densities. The limiting ¿gure could be 2 to 3 solar masses. If we consider rotation, a neutron star could be stable at up to about 5 solar masses. Beyond 5 solar masses, barring the existence of some yet unknown form of matter, a typical rotating neutron star would collapse to form a black hole. The most massive star whose mass has been reliably measured has about 60 solar masses. Some stars may be as large as 100 solar masses; beyond this point, the radiation pressure of a star itself would tear it apart and prevent its formation. Yet the most massive stars have strong winds, so their outer layers essentially evaporate away. These stars (and others) can also lose mass through transfer of matter to companion stars if they are in binary systems. Therefore, it is possible that the most massive stars do not give rise to black holes because much of their mass is easily lost and they end up with relatively small cores that become neutron stars instead. It is also possible that a massive star’s core could collapse to form a black hole. Some astronomers believe that stars having initial mass between 20 and 40 solar masses are the most likely to form black holes. Below 20 and above 40 solar masses, a neutron star is more likely to form at the end of a star’s life. There is some evidence to support this hypothesis. 299

NASA/Goddard Space Flight Center

Lecture 60: Black Holes—Abandon Hope, Ye Who Enter

Let’s look at why an object compressed at a high density would appear black, as well as some characteristics of a black hole. Newton’s law of gravity states that F = GM1M2/d2, in which F is force, G is Newton’s constant of universal gravitation, M1 and M2 are the masses of two objects, and d is the distance between them (more precisely, the distance between their centers of mass). From this, we can derive an object’s escape velocity—that is, the speed at (or above) which a projectile would have to travel in order to completely escape from the object. If the radius of the object is compressed but its mass remains the same, then the escape velocity increases. That is, the projectile would have to travel even faster to fully escape from the object.

Such an argument was proposed in the late 18th century independently by John Mitchell and Pierre-Simon de Laplace to suggest that there may An artist’s rendition of a black hole. be objects in the Universe that are so dense that not even light can escape—black holes. This is an example of a Newtonian plausibility argument. The Newtonian argument provides a formula for determining the radius to which an object would have to be compressed in order for its escape velocity to reach the speed of light: RS = 2GM/c2. The derivation is not rigorously correct, but fortuitously, it agrees with the result from the general theory of relativity. The relativistic calculation was done by the German physicist Karl Schwarzschild in 1916, and this radius is now known as the Schwarzschild radius in his honor. The Schwarzschild radius of the object is directly proportional to its mass. The more massive the object, the larger the minimum radius to which it would have to be compressed in order to become a black hole. For example, the Schwarzschild radius for a 10-solar-mass star is 30 kilometers; thus, if the star were compressed to a radius of 30 kilometers or less, it would form a black hole. What would the Earth’s radius have to be in order to form a black 300

hole? Of course, this isn’t possible, but for the sake of illustration, Earth would have to be compressed to a radius of about 1 centimeter. A 60-kilogram person would have to be compressed to a radius of 10–23 centimeters, 10 orders of magnitude smaller than a proton, in order to become a black hole! The event horizon of a non-rotating black hole is the imaginary spherical surface with a radius equal to the Schwarzschild radius. It is called an event horizon because we cannot see events that occur beyond it, and nothing can escape from within it. Once matter is inside a black hole, gravity still acts on it, and thus, that matter continues to collapse. Theoretically, the matter would reach a point of in¿nite density, called a singularity. However, quantum mechanical effects will surely modify this, which we will discuss later when we talk about string theory. Despite the correct equation for the Schwarzschild radius given by the Newtonian argument, the only way we can truly understand “It’s possible that black holes is through general relativity. The 2 Newtonian formula, F = GM1M2/d , obviously there are types breaks down where black holes are concerned of stars that because light doesn’t have mass. Thus, light is not are smaller and trapped by the “gravitational force” but, rather, denser than a by the extreme curvature of space-time around a dense object. classical neutron star, yet not truly Recall our example of a ball distorting a rubber a black hole, not sheet, making the sheet (or space) bulge. As the smaller than the ball (or celestial object) increases in density, the bulge increases in its depth, making it more event horizon.” dif¿cult for light to escape that depth. Indeed, light coming from a strong gravitational ¿eld is bent and redshifted. For example, light shining tangent to the surface of a collapsed star having a radius of 1.5 Schwarzschild radii, can be bent so much that it actually goes into orbit around the star, creating a photon sphere. If the star were to contract even more, most of the light would be bent so much that it would be absorbed back into the star. Only a small amount of light could escape in a narrow beam, called the exit cone, which has a certain opening angle. Once the star was suf¿ciently contracted (to a radius equal

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to the Schwarzschild radius), the exit cone’s opening angle would shrink to zero and no light could escape. Far from a black hole, the properties of space are basically normal; the idea that black holes are giant cosmic vacuum cleaners, sucking up everything around them, is a misconception. Once a black hole has reached equilibrium— after the star has fully collapsed—its properties are simple. According to the famous no hair theorem, a black hole is described completely by its mass, electric charge, and angular momentum (total spin). The nature of the objects thrown into the black hole is irrelevant. Some physicists have suggested the possible existence of material on a stellar scale even denser than that of neutron stars, yet that is not an actual black hole. There is some tentative observational evidence for this, but nothing conclusive. Ŷ

Lecture 60: Black Holes—Abandon Hope, Ye Who Enter

Important Terms event horizon: The boundary of a black hole from within which nothing can escape. photosphere: The visible surface of the Sun (or another star) from which light escapes into space. Schwarzschild radius: The radius to which a given mass must be compressed to form a nonrotating black hole. Also, the radius of the event horizon of a nonrotating black hole. singularity: A mathematical point of zero volume associated with in¿nite values for physical parameters, such as density.

Suggested Reading Begelman and Rees, Gravity’s Fatal Attraction: Black Holes in the Universe. Ferguson, Prisons of Light—Black Holes. 302

Kaufmann, Black Holes and Warped Spacetime. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Thorne, Black Holes and Time Warps: Einstein’s Outrageous Legacy. Will, Was Einstein Right? Putting General Relativity to the Test.

Questions to Consider 1. How would the gravitational force at the surface of a star change if the star contracted to 1/5 of its previous diameter without losing any of its mass?

2. Why doesn’t the pressure from electrons or neutrons prevent a suf¿ciently massive star from becoming a black hole?

3. If someone close to (but not inside) a black hole were shining a blue Àashlight beam outward, how would the color that you see be affected if you are far from the black hole?

4. The average density of an object is its mass per unit volume. If the volume of a non-rotating black hole is proportional to the cube of its Schwarzschild radius, show that its average density is inversely proportional to the square of its mass. (Of course, all of the mass in a black hole is actually concentrated at the singularity—either the classical or the quantum variety.)

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The Quest for Black Holes Lecture 61

A major prediction of general relativity is the physical possibility of a black hole, a region of space where there’s so much material in such a small volume that the space-time curvature is suf¿ciently strong to trap everything, even light. But if we can’t see black holes, how do we know they exist?

Lecture 61: The Quest for Black Holes

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e don’t see black holes directly, but we can detect them through their gravitational inÀuence on other objects. Recall a binary system, in which two stars orbit their common center of mass. If one star is more massive than the other, that star is closer to the common center of mass than the less-massive star. We can detect the stars’ orbits and deduce their masses. If the larger object isn’t visible, we can still detect its mass by measuring the wobble in the smaller star’s spectrum. Recall that this method is used to detect the presence of extrasolar planets orbiting suns. If we have a wobbling star and the cause of that wobble (the other object) is not visible, we might conclude that the other object is a black hole if its mass exceeds a certain amount. For example, if the object shows no absorption lines in the spectrum, is not visible, and is 10 solar masses (a star this size would be visible), we might conclude that it is a black hole. Other observations would verify whether the object really is a black hole. The best place to look for black holes is in a spectroscopic binary system. Owing to the number of such systems, how can we narrow down our search to those that might yield black holes? Observations at x-ray wavelengths can provide such a clue. If a black hole or a neutron star is orbiting around another star, it can steal material from the other star. This material would glow as it settled into an accretion disk; the accretion disk’s gases come so close to the compact object—either a neutron star or black hole—that they heat up in the strong gravitational ¿eld. One such object found with x-ray telescopes is Cygnus X-1, the brightest x-ray source in the constellation Cygnus the Swan. This object appears to be a star orbiting a black hole, creating an accretion disk that glows at x-ray wavelengths. The black hole is at least 7 solar masses, but it could be as large as 16 solar masses. If it 304

were a star, it would be easily visible, but it’s not. The problem that arises in this case is that the visible star is giant, possibly as large as 33 solar masses. Using Newton’s version of Kepler’s third law, 33 solar masses makes the black hole’s mass small and uncertain by comparison. In addition, the mass of the giant star itself is uncertain, making the companion’s mass even more uncertain. Thus, the evidence for a black hole is less conclusive than one would like. The best case for determining whether or not an invisible object is a black hole is to ¿nd a low-mass star, say a K or an M main-sequence star, orbiting the candidate black hole. In this case, the mass of the orbiting star would be irrelevant. If a low-mass star is orbiting a black hole, then a measurement of the orbital speed (V) and period (P) yields the mass of the black hole. Mass = V3P/2SG, and we can measure V and P from spectra. Thus, we can deduce M, the minimum possible mass of the invisible object. This is only a minimum possible mass because we don’t know the inclination of the system—that is, whether or not we’re observing it edge on or face on. If this minimum mass exceeds 5 solar masses (the maximum for a rapidly rotating neutron star) or even 3 solar masses (the maximum for a non-rotating neutron star), there is a good chance the object is a black hole. Let’s take a closer look at low-mass stars orbiting black holes and see what information our observations can reveal about black holes. Sometimes, the accretion disks that form around the compact object (the black hole or neutron star) develop “blobs” that rapidly fall inward and release tremendous energy. At x-ray wavelengths, this energy appears as a Àare, a giant burst similar to a nova. The Àaring accretion disk also emits ultraviolet radiation and optical radiation in its cooler regions. The whole disk is hot, but not all parts are equally hot; thus, different parts emit different forms of radiation. X-ray satellites ¿nd these x-ray novae and alert optical astronomers. We then wait for the radiation to fade, and eventually, we might see the faint normal star in the system. We can then take spectra of the star. A sophisticated analysis of the spectra over time would show the wobbling of absorption lines, indicating that the star is orbiting around something that is gravitationally tugging on it. From this, we can deduce the minimum mass of the invisible object.

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Lecture 61: The Quest for Black Holes

How do we get an idea of the system’s inclination—whether we are viewing it edge on, face on, or somewhere in between? We look at the brightness of the visible star over time, its light curve. If the brightness varies over time (as a result of how we observe the tidally distorted star), then we are viewing the system inclined to our line of sight. If the light curve is Àat—that is, no change in brightness—then we are viewing the star system face on. In the past decade, about 20 such binary systems—wherein a star orbits a probable black hole—have been found and accurately measured. Some black holes spin (rotate), and gas particles in an accretion disk from the orbiting star can get closer to a spinning black hole (closer than 3 Schwarzschild radii) than they could to a non-rotating black hole. We know this by looking at the shape of the x-ray spectrum. A rotating black hole with a spinning accretion disk can also show high-speed jets of particles emitted along the rotation axis of the black hole and the disk. These jets can reach speeds of more than 90% of the speed of light. For a black hole with an orbiting star, we notice that the accretion disk isn’t bright in the central region during times of quiescence—that is, prior to an outburst, when it is faint. If the star were orbiting a neutron star instead of a black hole, the accreting material would glow in the center, where it hits the surface of the neutron star and releases its energy of motion. If the center is actually a black hole, it is likely that the accretion material is being swallowed by the black hole; hence, there is no hard surface to hit, and the material doesn’t glow as much. Though still somewhat tentative, this observation suggests that we really have seen evidence for material going beyond the event horizon and being swallowed by a black hole. Ŷ

Suggested Reading Begelman and Rees, Gravity’s Fatal Attraction: Black Holes in the Universe. Ferguson, Prisons of Light—Black Holes. Kaufmann, Black Holes and Warped Spacetime. ———, The Cosmic Frontiers of General Relativity.

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Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Thorne, Black Holes and Time Warps: Einstein’s Outrageous Legacy.

Questions to Consider 1. Under what circumstances does the presence of an x-ray source associated with a spectroscopic binary suggest to astronomers the presence of a black hole?

2. If a visible star orbits an object at least ¿ve times the mass of the Sun in a period of only 8 hours, can you think of anything the object could be besides a black hole?

3. Based on what you’ve learned previously in this course, is it possible to detect a black hole that is not part of a binary system or is not surrounded by stars and gas in a galaxy? If so, how?

4. Given that objects can fall into a black hole, what do we mean when we say that the interior of a black hole is cut off from the Universe?

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Imagining the Journey to a Black Hole Lecture 62

“What you, yourself, would see and experience if you were to go into a black hole, and what an outside observer would see as you are going toward the black hole and into it … the two perspectives yield very, very different results.”

Lecture 62: Imagining the Journey to a Black Hole

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hat’s a black hole really like, and how could we simulate the experience of going toward and into one? Recall that a nonrotating black hole has a spherical event horizon with a radius known as the Schwarzschild radius (2GM/c2). Within the event horizon, the black hole has a tight grip on everything, including light. An outside observer can’t see any events that occur at or inside the event horizon. If an object is outside this radius, on the other hand, it can, in principle, escape from the vicinity of the black hole. A massive black hole has a stronger gravitational ¿eld over a larger area than a small black hole. The event horizon has a radius that is directly proportional to the mass; thus, a massive black hole has a bigger event horizon than a low-mass black hole. Intuitively, larger black holes seem more dangerous to approach than smaller ones. However, we could theoretically get closer to a supermassive black hole than a smaller one before being torn apart. What would happen to us if we got close to a black hole? If we fell feet ¿rst, we would be stretched along the length of our bodies and squeezed along the width by the hole’s tidal forces. The stretching (informally known as spaghetti¿cation) occurs because the gravitational pull on our feet (closest to the black hole) signi¿cantly exceeds that on our heads. The tidal effects on a human body (say, 2 meters in height) would be smaller for a supermassive black hole than for a stellar-mass black hole because the length of a human is smaller relative to the hole’s Schwarzschild radius. Outside a stellarmass black hole, the tidal spaghetti¿cation is so extreme that it would tear a human apart. What would we see if we could safely approach a black hole? We would see a highly distorted sky because of the strong curvature of space-time around 308

us. Starlight traveling in one direction is bent toward us and enters our eyes such that the star appears to be in a completely different direction. The degree to which this would happen depends on the exact path of the light. Light that passes closer to the black hole is bent more than light that passes farther away. Indeed, we might see multiple images of the same stars. Assuming that we were traveling at a certain speed toward a black hole, the stars would begin to appear to move away from the black hole. They would also get brighter, and eventually, we would see secondary images of the stars. If we circled the black hole from a distance of 10 Schwarzschild radii, we would see a distorted view of stars whirling around the hole, reminiscent of the Einstein rings we talked about in a previous lecture. From the photon sphere at 1.5 Schwarzschild radii, the sky would be behind us, and we would see nothing but black “You can get as we peered inside the hole. If we looked up closer to a from the photon sphere itself, while stationary, we would see the stars, but they wouldn’t be supermassive big circling. If we circled while at the photon sphere, black hole without we would see a wild view of millions of stars being torn apart whizzing past and all around, with dramatic than you can to a distortions of space. Continuing farther down, all we would see as we looked up would be a small black hole.” point of light representing the whole sky of stars squashed into one tiny spot. As we got closer and closer to the event horizon, that circular patch would get smaller and smaller. Beyond the event horizon, no one really knows what we would see. But we might see much of the future of the Universe squeezed into a tiny amount of time, before we hit the singularity. What would we experience while falling into the black hole? The closer we came to the event horizon, the more time would slow down as seen by an outside observer. In a strong gravitational ¿eld, clocks run more slowly than in a weak gravitational ¿eld. The closer we get to the event horizon, the greater is this apparent slowing down of time, called time dilation. At the event horizon, time would stop as seen from an outside perspective. Nothing appears to actually reach the event horizon, because it would take in¿nite time to do so. In fact, anything that has ever fallen into a black hole, from the 309

Lecture 62: Imagining the Journey to a Black Hole

outside perspective, is actually hovering in¿nitesimally above this imaginary surface we call the event horizon. Indeed, there’s a paradigm for studying black holes, called the membrane paradigm, in which nothing ever falls in. But from the perspective of the person falling in, he or she really would cross the event horizon and crash into the singularity in a ¿nite amount of time. From the outside perspective, a collapsing star would reach some minimum size—essentially the size of the event horizon—at which point, it would not get any smaller. If we could get close to a black hole, then escape, our clocks would have registered a much shorter time period than those clocks outside the black hole. In this way, we could theoretically travel to the future without having aged much. From the outside perspective, the light emitted from a Àashlight outside the event horizon would experience gravitational redshifting. As the photons escape the gravitational ¿eld, they lose energy and exhibit progressively longer wavelengths. The emitted light would also fade because photons appear to be emitted at slower and slower rates as gravity increases (time dilation). Similarly, a star collapsing to form a black hole fades because of gravitational redshifting, time dilation, and another effect in which less and less of the star’s light is visible as the exit cone shrinks. Finally, someone falling into a black hole would quickly be torn apart by gravity, but not before this traveler noticed the surrounding stars as being blue—the opposite effect of redshifting caused by light coming into a black hole rather than trying to escape from it. The previous effects all apply to non-rotating black holes, and most of them apply to rotating black holes as well, with some modi¿cations. Let’s now look at rotating black holes, whose structures are more complex. For a given mass, the event horizon of a rotating black hole is smaller than that of a nonrotating black hole, but it remains spherical. A region called the ergosphere surrounds the event horizon, where space is inexorably dragged around the black hole. It is impossible to remain stationary relative to the outside world if one is in the ergosphere. As the rotation of a black hole increases, its event horizon shrinks until the black hole reaches a maximum rotation speed; at this point, the event horizon has a radius equal to 0.5 of the normal Schwarzschild radius.

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In fact, we will see in the next lecture that two event horizons form, one inside the other. At the maximum rotation rate, the two horizons meet and vanish, giving rise to a naked singularity, or a singularity that is not cloaked by an event horizon. Because there is no indication of the event horizon, we wouldn’t know we were approaching a naked singularity until we hit it. Some theorists think that naked singularities cannot occur because they believe that a black hole can never reach its maximum rotation rate. This has never been completely theoretically proven. Ŷ

Important Term gravitational redshift: A redshift of light caused by the presence of mass.

Suggested Reading Begelman and Rees, Gravity’s Fatal Attraction: Black Holes in the Universe. Ferguson, Prisons of Light—Black Holes. Kaufmann, Black Holes and Warped Spacetime. Nemiroff, Virtual Trips to Black Holes and Neutron Stars, antwrp.gsfc.nasa. gov/ htmltest/rjn_bht.html. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Pickover, Black Holes: A Traveler’s Guide. Thorne, Black Holes and Time Warps: Einstein’s Outrageous Legacy.

Questions to Consider 1. As measured by distant observers, nothing ever enters a black hole because time slows down near the event horizon. Where does the material go?

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2. If you were an astronaut in space, could you escape (a) from within the photon sphere of a non-rotating black hole, (b) from within the ergosphere of a rotating black hole, or (c) from within the event horizon of any black hole? Explain each of these cases.

3. Explain why the tidal stretching (spaghetti¿cation) is smaller near a

Lecture 62: Imagining the Journey to a Black Hole

supermassive black hole than near a stellar-mass black hole.

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Wormholes—Gateways to Other Universes? Lecture 63

“There are some mathematical studies that suggest that it might, in principle, be possible to traverse a black hole—in particular a rotating black hole, or possibly a charged black hole—and end up either in a very distant part of our Universe through a shortcut, or possibly even in another universe altogether.”

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e’ve seen what can happen, theoretically, if a person were to fall into a black hole. Let’s now take a look at the structure of black holes. First, recall how space curves from our diagram of a rubber sheet distorted by a paperweight in the middle. The two-dimensional sheet was initially Àat, but the presence of mass or energy causes it to warp, curving the space around a third mathematical dimension (but retaining the two-dimensional character of the sheet). In Àat space, traveling from point A to point B while always keeping an arrow pointing in the same direction, parallel to itself, leads to a ¿nal arrow orientation that is independent of the path we take. In curved space, on the other hand, the ¿nal arrow orientation depends on the adopted path. It is fairly obvious that the surface of a sphere is a curved space, not a Àat space, but what about the surface of a cylinder? A cylinder is actually Àat space, which is perhaps counterintuitive. A cylinder is not distorted in the same way as a sphere; it still retains the mathematical properties of Àat space. There is always some distortion when we try to project a sphere onto a Àat two-dimensional map. Thus, as we look at Àat diagrams of curved space or warped space-time, keep in mind that the maps do not reliably portray all aspects of the curvature. This is evident in Mercator projections of Earth onto a Àat map, for example, but these maps still have important uses. Warped-space diagrams, or maps, show the geometrical structure of space—a two-dimensional slice of space—outside of a massive body that is causing this distortion. If we make the massive body denser, the local curvature of space and time becomes more severe (more warped), resulting in what appears to be a stronger gravitational ¿eld. When the object becomes suf¿ciently dense, space around it is curved so much that it becomes vertical, 313

Lecture 63: Wormholes—Gateways to Other Universes?

marking the presence of a black hole. But space is so curved that, as seen from the outside, it appears as if the black hole joins up with another part of space through a passage formally named the Einstein-Rosen bridge, or more often called a wormhole. Such maps make it appear as if we could travel the long way around from point A to point B or simply go through the wormhole and make the journey far shorter. They also suggest that different universes are connected by wormholes, providing a way to enter other universes. Though these maps nicely illustrate the geometry of space outside a black hole, they don’t actually tell us what’s going on inside. To see this, we need another kind of map, and it, too, will have certain distortions. As shown using the Kruskal-Szekeres diagram of a non-rotating black hole, we could not traverse a wormhole because to do so, we would have to travel faster than the speed of light. The horizontal axis of the diagram denotes one dimension of space (for example, the x, or left-right, direction). The vertical axis of the diagram denotes time. This is an example of a spacetime diagram. The diagram is set up in such a way that light travels along 45° lines. We would have to travel along lines less than 45° to the vertical because our speed must not exceed that of light. The diagram also shows that after passing through the event horizon, there is no way to escape from a black hole—inevitably, we reach the singularity at some point in the future. The diagram also proposes the possibility of white holes—theoretical regions of space from which matter could emerge into our Universe, although such matter would not be able to return to its origin. (In contrast, matter could not escape from a black hole.) We don’t believe white holes exist “It looks like because we’ve never seen any evidence for you could go them. The singularity in the Kruskal-Szekeres through the ring, diagram is basically a horizontal structure rather than a particular point. This implies that, as or, in a sense, seen by us within the black hole, the singularity between these two covers much of space instead of being a speci¿c event horizons, point, and we would hit it at some time in the and end up in future. In essence, we can’t avoid the singularity another universe.” because it’s everywhere around us. The time at which we hit the singularity would depend on

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exactly what trajectory we took into the black hole. That time is always ¿nite and, indeed, is quite short. The structure of rotating black holes is very different. The Kruskal-Szekeres diagram of a rotating black hole shows an in¿nitely repeating pattern of additional universes. Thus, in principle, we could cross a series of event horizons as we moved forward in time and emerge into another universe. The structure of such rotating black holes allows for travel across universes without having to move faster than the speed of light. The singularity of a rotating black hole is vertical, running parallel with the direction of time; therefore, we could avoid hitting it, depending on our trajectory. Recall that we said a cylinder represents Àat space. If we take a piece of paper (Àat space) and roll it into a cylinder, we’ve changed its overall topology but not its local geometry. Now imagine the Àat Kruskal-Szekeres diagram of rotating black holes rolled into a cylinder. We could take all kinds of interesting journeys through space into and out of other universes. Mathematically, then, it is possible to take such a journey and arrive back at Earth at a time before our initial departure! What if we decided to alter history in our travels to prevent certain events from happening? Physicists call this a violation of causality, a disturbing prospect. We can’t go back in time, physicists think, and change the history of the Universe in such a way as to prevent our existence—for example, by preventing our parents from ever having met and, thus, precluding our own birth. How could we do so if we weren’t born? It is possible that the geometry implied by the diagram is valid only for an idealized black hole into which no material is falling or has previously fallen. In other words, as soon as an object actually tries to traverse the wormhole, it closes. If a wormhole results from a black hole that was formed by the collapse of a rotating star, there is enough matter in the central regions to crunch up the wormhole and squeeze it shut. Thus, for the case of idealized black holes and wormholes, the Universe would need to be born with these objects already present. But even if we traveled into an idealized black hole, we would gain so much energy that it would cause the wormhole to squeeze shut. Thus, a wormhole in an idealized black hole may present a passage to another universe (or to a distant part of our Universe) as long as we don’t actually attempt to travel

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through it. If we do so, our own mass—and the energy associated with our motion—would curve space enough to close the wormhole. Some physicists have wondered what would happen if we could travel in a spaceship made of antigravitating material that would prevent the wormhole from closing. In this case, we still have the problem of the violation of causality. Perhaps we can take solace in the fact that no such antigravitating substance has been found, though we will see later that dark energy, perhaps a property of space, has properties reminiscent of antigravity. Ŷ

Important Term wormhole: A hypothetical connection between two universes or different parts of our Universe. Also: Einstein-Rosen bridge.

Lecture 63: Wormholes—Gateways to Other Universes?

Suggested Reading Begelman and Rees, Gravity’s Fatal Attraction: Black Holes in the Universe. Hawking, The Universe in a Nutshell. Kaufmann, Black Holes and Warped Spacetime. ———, The Cosmic Frontiers of General Relativity. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Pickover, Black Holes: A Traveler’s Guide. Thorne, Black Holes and Time Warps: Einstein’s Outrageous Legacy.

Questions to Consider 1. Given that in a non-rotating black hole, the singularity takes up much space at a particular time, rather than a point in space over a long period of time, does it make sense to think that space and time have, to a certain extent, reversed roles inside a black hole?

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2. What sorts of problems could be produced by the violation of causality— that is, if you could travel through a wormhole and return before your departure?

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Quantum Physics and Black-Hole Evaporation Lecture 64

“Though each of them works well in its own realm of applicability, when you try to put them together, and you try to describe the properties of very small particles, or even of space itself, over very small spatial scales, the results from quantum physics and general relativity are completely at odds with one another.”

Lecture 64: Quantum Physics and Black-Hole Evaporation

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or many decades, physicists thought that black holes were truly black. But now, in attempts to unify general relativity and quantum mechanics, we have found that perhaps black holes may exhibit characteristics never before imagined. Even though the two theories (general relativity and quantum mechanics) work well in their own applicable realms, when we try to describe the properties of small particles or even of space itself over tiny spatial scales, quantum physics and general relativity are at odds. We don’t yet have a consistent uni¿ed theory for general relativity and quantum physics, but it is thought that a generic property is the peculiar evaporation of black holes. Why might we expect a black hole to evaporate? We will answer this question in general terms, initially ignoring quantum effects in favor of classical physics. Recall that the mass of a non-rotating black hole cannot decrease; it can only stay the same or increase by accumulating material falling into it. As its mass increases, so does its Schwarzschild radius, increasing its surface area. Because the mass cannot decrease, the surface area cannot decrease. It can only remain the same or increase. For a rotating black hole, again, the surface area of the event horizon can only increase or remain constant. However, the mass can actually decrease under certain circumstances because its rotational energy is tapped when matter enters it in a certain way through the ergosphere. The second law of black-hole dynamics states, “In any natural process, the surface area of the event horizon of a black hole always increases or, at best, remains constant; it never decreases.” This resembles the second law of thermodynamics—the study of the relationship among heat, work, and other

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forms of energy—which plays a signi¿cant role in governing the physical Universe. This law states, “In any natural process, the entropy of a closed system always increases or, at best, remains constant; it never decreases.” A closed system is one from which nothing escapes; entropy is a measure of the amount of disorder in the system. Black holes behave in ways that can be described similarly by the other laws of thermodynamics, not just the second law. The correspondence between the laws led the physicist Jacob Bekenstein to propose that a black hole’s surface area is proportional to its entropy. The entropy of a black hole is related to the no hair theorem (Lecture 60), in which black holes in equilibrium can simply be described by their mass, spin (more precisely, angular momentum), and charge (if any). “The Schwarzschild Because matter devoured by a black hole radius is proportional to is no longer identi¿able, we don’t know the mass of a black hole, what the black hole consists of. This loss so the surface area of a of information corresponds to a gain in entropy. Therefore, black holes must non-rotating black hole have a tremendous amount of entropy. is proportional to the square of the mass of the black hole.”

The analogy with the laws of thermodynamics suggests that a black hole is physically a thermal body. Indeed, it closely resembles what we called a black body (in Lecture 43). Recall that a black body doesn’t transmit or reÀect any radiation; it only absorbs it, being a perfect absorber. It also emits radiation through thermal motions of its constituent particles in a manner dependent only on its temperature. Similarly, a black hole doesn’t transmit or reÀect any radiation; it only absorbs photons. If a black hole can be thought of as a thermal body, then it must have a temperature. If there’s a temperature, then it must radiate, or shine. The idea that a black hole shines is paradoxical if we ignore quantum effects. In classical physics, nothing can escape from within a black hole. Yet the whole shining process of a thermal body is really a quantum-mechanical property. Classically, nothing can escape a black hole. For this reason, Bekenstein didn’t pursue his idea any further. But Stephen Hawking realized that the 319

conclusion that nothing can escape a black hole might be false if we consider quantum-mechanical processes.

Lecture 64: Quantum Physics and Black-Hole Evaporation

Hawking’s theory that black holes can evaporate via quantum-mechanical processes, regardless of the details of any unifying theories, is related to the creation of particles and antiparticles. The basic idea for black-hole evaporation is also related to Heisenberg’s uncertainty principle (Lecture 20), according to which there is uncertainty in any measurement. We cannot know with arbitrary precision the energy of a system or the time at which we made that measurement; the product of their uncertainties cannot be equal to zero, or less than the quantity h/2ʌ, de¿nitely not 0. Similarly, there is a relationship between the product of the uncertainties in the position of a particle and its momentum, its mass times its velocity. Thus, we can know the position of any real object but not its momentum with certainty. Or we can know its energy (momentum) but not its position with certainty. It is possible for pairs of virtual particles to form spontaneously out of nothing. They now have some energy and they exist for a nonzero amount of time, but the product of the uncertainties in energy and time is less than h/2ʌ. Quantum mechanics allows for (and even demands) such violations of classical laws in which something (the pair of virtual particles) appears out of nothing. This is called a quantum Àuctuation. One way of thinking about this process (though not the only way) is that the positive energy created by the pair of particles creates a negative-energy hole, so that the particles and the hole cancel each other out; the net energy is still zero. However, one could also say that there is no negative-energy hole. Quantum mechanics is consistent with a small violation of the classical law of conservation of energy. Thus, we begin with nothing, have something for a short time, and then the particles annihilate each other, leaving a net energy of zero. These quantum Àuctuations are virtual in that we can’t directly measure them because they don’t last long enough. But they occur everywhere, and they do affect the Universe, as we will see. Near the event horizon of a black hole, a particle (or antiparticle) can sometimes escape, while the other particle enters the black hole with negative energy (from our outside perspective). The escaping particle takes positive energy with it. This decreases the mass of the black hole. One can also think of this as a quantum tunneling effect, with 320

particles emerging outside from inside the black hole. As particles escape, they accelerate past each other, emitting photons, and annihilate each other, creating even more photons. The result is a thermal distribution of energies called Hawking radiation—the evaporation of black holes. In summary, outside the event horizon, particles and photons are emitted, the black hole loses energy, and the temperature is proportional to the inverse of the black hole’s mass. As the black hole evaporates, its mass decreases, its temperature rises, and the rate of evaporation consequently also increases. As the mass nears zero, the evaporation rate approaches in¿nity, and the black hole explodes. The rate at which stellar-mass and supermassive black holes evaporate is utterly negligible because they accrete material from their surroundings much more quickly. A high rate of evaporation occurs only for miniature black holes, maybe a billionth of the mass of the Earth or less. Hawking has suggested that such tiny black holes formed shortly after the birth of the Universe. If that’s the case, then all of the ones born with less than 1015 grams have already evaporated. Those with initial masses of 1015 grams, having an event horizon roughly the size of a proton, are now evaporating. Because the rate of evaporation approaches in¿nity as the mass approaches zero, we end up with explosions. Most of the released photons from the explosions should be emitted as gamma rays. Have we ever detected gamma-ray bursts that might be indicative of the evaporation of miniature black holes? We’ll see in the next lecture. Ŷ

Name to Know Hawking, Stephen (1942 ). English physicist, best known for his remarkable theoretical work while physically incapacitated by Lou Gehrig’s disease (ALS). His prediction that black holes can evaporate through quantum tunneling is an important step in attempts to unify quantum physics and gravity (general relativity). He is Lucasian Professor of Mathematics at Cambridge University, as was Newton.

Important Terms Hawking radiation: According to Stephen Hawking, the thermal radiation emitted by black holes because of quantum effects. 321

quantum Àuctuations: The spontaneous (but short-lived) quantum creation of particles out of nothing. second law of thermodynamics: In any closed system, entropy (the amount of disorder) never decreases; it always increases or remains constant. virtual particle: A particle that Àits into existence out of nothing and, shortly thereafter, disappears again.

Suggested Reading Ferguson, Prisons of Light—Black Holes. Hawking, A Briefer History of Time.

Lecture 64: Quantum Physics and Black-Hole Evaporation

Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Pickover, Black Holes: A Traveler’s Guide. Shu, The Physical Universe: An Introduction to Astronomy. Thorne, Black Holes and Time Warps: Einstein’s Outrageous Legacy.

Questions to Consider 1. Are you surprised to learn that black holes aren’t completely black after all?

2. If an evaporating black hole behaves like a black body (speci¿cally, the Stefan-Boltzmann law), and if the temperature of a black hole is proportional to the inverse of its mass while the Schwarzschild radius is proportional to its mass, to what power of the mass is the black hole’s luminosity proportional?

3. Given that an outside observer has no knowledge of the composition of a black hole (that is, what kinds of materials or objects were thrown in it), can you argue that a black hole has enormous entropy (disorder)?

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Enigmatic Gamma-Ray Bursts Lecture 65

“We do think that gamma-ray bursts are linked with the formation of black holes—not miniature ones, but stellar-mass black holes. … These gamma-ray bursts, or GRBs, are among the hottest topics of modern astrophysics.”

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elestial gamma-ray bursts (GRBs) have been seen, and their presence is one of the most exciting and intriguing areas of study in the ¿eld of astrophysics. GRBs were ¿rst detected in the late 1960s when the U.S. Air Force launched the Vela spy satellites to monitor Soviet compliance with the Nuclear Test Ban Treaty. They did not ¿nd any violations of the treaty, but they did ¿nd peculiar celestial bursts of gamma-ray light. The bursts appeared in random parts of the sky, and when we look at curves of the brightness of the gamma rays versus time, we ¿nd that no two of them are alike. Some of the curves are spiky, while others have a smoother distribution; some have only two spikes, and some have many. Nevertheless, there are two main types of GRBs: long-duration and short-duration. The long-duration GRBs can last as long as several hundred seconds (average: about 20 seconds) and tend to emit fewer very-high-energy gamma rays. The short-duration GRBs last for less than 23 seconds (average: a few tenths of a second) and tend to emit more very-high-energy gamma rays. For many decades, we didn’t know what produced GRBs, though there was a plethora of hypotheses. Between 1973 and 1992, theoretical astrophysicists published about 120 distinct hypotheses in an attempt to explain the physical nature of GRBs. Could they be explosions on neutron stars or comets hitting such stars? Could they be annihilations of large quantities of matter and antimatter? Unfortunately for Stephen Hawking, the hypothesis that they are exploding miniature black holes was not viable. If it were, then GRBs would not show spikes in brightening and fading (and there were other problems, as well). A major impediment to the understanding of the physical nature of GRBs was the fact that we didn’t know their distance. Are they close to Earth or billions of light years away? Are they halo objects bound to our Galaxy? Between 1991 and 2000, NASA’s orbiting Compton Gamma 323

Lecture 65: Enigmatic Gamma-Ray Bursts

However, even with the Compton Gamma Ray Observatory, we still could not precisely pinpoint the locations of GRBs in the sky. In 1996, a huge breakthrough occurred with the launch of BeppoSAX, an x-ray satellite capable of taking images of the sky where bursts occurred at lower photon energies—x-ray energies rather than the high-energy gamma rays. The satellite could use the x-ray image to pinpoint where a GRB occurred. With these precise positions, optical astronomers could then search the sky for fading optical afterglows The Compton Gamma Ray Observatory. corresponding to GRBs. It was found that long-duration GRBs appear to be associated with galaxies, indicating that they really are far away and that, undeniably, their luminosity must be incredibly great. Further satellite launches, as well as ground-based telescopes, have been able to gather still more information about GRBs. Thus far, we have found de¿nitive optical counterparts primarily for long-duration GRBs. There are only a few known counterparts for short-duration bursts because our satellites generally don’t have enough time to determine an accurate position for the short-duration bursts. Studies of the radiation from GRBs show that the bursts must be ejected in jets in a highly beamed fashion, like the narrow beams of lasers. Some kind of driving force creates a burst of relativistic particles—those traveling near the speed of light—which are ejected along two oppositely directed axes. The particles hit each other, causing internal 324

NASA

Ray Observatory detected and mapped the approximate positions of 2700 GRBs. The most signi¿cant ¿nding was that GRBs occur with a completely uniform distribution. No area of the sky has a concentration of GRBs that is statistically greater than any other area. This fact strongly suggested that GRBs occur at cosmological distances—very, very far away.

shocks. The collisions produce gamma rays; then, sometime later, those energetic clumps of particles hit clouds of external gas to produce radio waves, optical radiation, and x-rays. The external shocks produce the afterglow at other wavelengths, and internal shocks produce gamma rays. Long-duration bursts occur in galaxies forming enormous numbers of massive stars; thus, the jet mechanism should be associated with massive stars. The collapsar model describes this process. A collapsing massive star can form a jet along its axis of rotation. This jet of radiation and particles pummels its way through the star, bursting through the surface and creating two oppositely directed beams, or jets. If one of the jets happens to be pointing toward our line of sight, it appears very bright. If neither of them “In the 20 years between points our way, we don’t see the GRB, 1973 and 1992, 118 distinct but we may see a relatively normal supernova. Such bursts probably hypotheses had been work best in stripped, core-collapse published by theoretical supernovae—for example, those that astrophysicists trying to don’t have much or any hydrogen explain the physical nature or helium envelopes. Massive stars of gamma-ray bursts.” with an iron core and an outside layer of helium (which produce Type Ib supernovae) and those with an iron core and an outside layer of carbon and oxygen (which produce Type Ic supernovae) don’t have as much material in their envelopes, so the jets can pummel through much more easily than in the case of hydrogen-rich massive stars. So far, the model suggests that at least some long-duration GRBs arise from core-collapse supernovae. Further studies are needed to verify this theory. Ŷ

Important Term collapsar model: Model proposed for some types of gamma-ray bursts, wherein a rotating, massive star collapses and forms two highly focused beams (jets) of particles and light.

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Suggested Reading Katz, The Biggest Bangs: The Mystery of Gamma-Ray Bursts, the Most Violent Explosions in the Universe. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Schilling, Flash! The Hunt for the Biggest Explosions in the Universe. Wheeler, Cosmic Catastrophes: Supernovae, Gamma-Ray Bursts, and Adventures in Hyperspace.

Questions to Consider 1. What would we expect the gamma-ray light curve of a GRB to look like if GRBs were the evaporation of miniature black holes according to Stephen Hawking’s hypothesis?

2. Why did the essentially uniform (isotropic) distribution of GRBs in

Lecture 65: Enigmatic Gamma-Ray Bursts

the sky found by the Compton Gamma Ray Observatory support the hypothesis that GRBs are at cosmological distances?

3. Assume that the Andromeda Galaxy (M31, 2.4 million light years away) is very similar to our Milky Way Galaxy. If GRBs were associated with a very extended, spherical halo of our Galaxy, do you think there should be a non-uniformity across the sky in the observed distribution of GRBs, given enough data points?

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Birth Cries of Black Holes Lecture 66

“Why do we prefer a stripped star for the massive progenitor of a GRB? It’s simply because the more material that has been lost prior to the implosion and explosion, the easier it is for this jet of particles to pummel its way through the remaining material and actually get out.”

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e continue our discussion of long-duration GRBs, beginning with a recap from the previous lecture. The leading hypothesis—the collapsar model—for long-duration GRBs is that they arise from massive, stripped, core-collapse supernovae that implode, forming a jet of high-energy particles along the axis of the star’s rotation. We think that GRBs are more likely emitted from stars whose hydrogen and helium envelopes have been stripped away by stellar winds or through transfer of material to a companion star. In addition, these collapsing stars are likely to rotate rapidly, and rotation creates a natural axis along which to funnel jet-like ejecta. Moreover, rotation creates an accumulation of material in the equatorial plane, forcing the jets to shoot along the path of least resistance, the rotation axis. Why would some massive stars produce jets—which we detect as GRBs— when they implode while others don’t? One leading hypothesis states that this is the same mechanism as the core collapse previously described for Types II, Ib, and Ic supernovae. In this case, however, the star collapses not just to a smaller neutron star but, instead, to a black hole. Thus, it’s possible that GRBs signal the birth of black holes. If the material collapses to a radius smaller than 10 kilometers (the average size of a neutron star), a greater release of gravitational energy will occur. As the material collides, it emits radiation in the form of photons, as well as high-speed charged particles. If there is more rapid rotation than normal, a high-speed jet can sometimes form. Material that isn’t ejected could collapse into the emerging black hole to form an even bigger black hole, or it could explode. On the other hand, if a neutron star formed during the collapse, a Àood of neutrinos could push out the remaining material in the normal way of a supernova, or some other effect might push out the remaining material. Thus, the prediction is that at 327

Lecture 66: Birth Cries of Black Holes

In 1998, a peculiar, low-luminosity GRB (GRB 980425, found on April 25) was detected that happened to be spatially consistent with the position of an optical supernova (SN 1998bw); the two observations were also consistent in time. The supernova occurred about a week after the GRB, consistent with the time it takes for supernova light to brighten. In this particular case, there was no GRB optical afterglow associated with the burst of gamma rays. The absence of the GRB optical afterglow made the supernova especially obvious in this case. Despite misgivings about the general connection between normal GRBs and stripped-envelope supernovae, the properties of the low-luminosity GRB An artist’s depiction of a supernova. 980425 and its associated SN 1998bw supported the collapsar model. The supernova was not just a highly stripped Type Ic but perhaps an even more highly stripped variety in which even part of the carbon-oxygen layer was absent. In 2003, another GRB and an associated supernova occurred, and a comparison of its spectrum with that of SN 1998bw showed great similarity between the two events. The supernova was again clearly of the strippedenvelope, core-collapse variety. Because this GRB was more typical, more luminous, than GRB 980425—including a normal optical afterglow—this sealed the case in support of the collapsar model. But whether such events really do signal the birth of a black hole, rather than a neutron star, we still are not certain. Further satellite explorations have observed many GRBs. In particular, the Swift satellite, launched in 2004, has detectors that scan the sky in search of GRBs. It also has x-ray and UV optical telescopes that quickly 328

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least some long-duration GRBs are also associated with visible supernovae. A GRB afterglow fades with time, but perhaps a week later, supernova light becomes visible, dominating the declining afterglow of the GRB itself.

take pictures of the part of the sky in which GRBs occur and ¿nd x-ray and optical afterglows possibly associated with GRBs. Swift has con¿rmed that some low-luminosity GRBs emit much of their energy at x-ray wavelengths rather than in gamma rays. At least a subset of these might be associated with the formation of a neutron star rather than a black hole. So far, we’ve discussed properties of long-duration GRBs, but what about short-duration bursts, which are only about one-¿fth or one-sixth as frequent as long bursts? Swift has discovered several short-duration GRBs, for which it also detected an optical counterpart. We have veri¿ed that these shortduration GRBs often come from distant galaxies having only old stars. The data also reveal that there is no supernova light associated with those particular afterglows, suggesting that rather than a massive star undergoing core collapse and exploding, the event may be two neutron stars “In December of 2005, there was merging to form a black hole. a magnetar burst that produced If true, this would indicate that enough gamma rays to actually short-duration GRBs are also the birth cries of black holes. Some affect Earth’s atmosphere.” short-duration GRBs might arise from the merger of a neutron star with a black hole, as opposed to the merger of two neutron stars. This would indicate a growth spurt of the black hole because it accretes a neutron star. At least some short-duration GRBs could arise from magnetars, or starquakes, during which the surfaces of neutron stars with exceptionally high magnetic ¿elds (1000 times stronger than those of normal pulsars) redistribute their crusts and magnetic ¿elds. In December 2005, a magnetar burst produced enough gamma rays to ionize part of Earth’s atmosphere. This magnetar was atypical in that it occurred in our own Galaxy, yet it was as bright as a GRB. Should we worry about GRBs? Could gamma rays affect Earth’s atmosphere so much that life on Earth would be greatly endangered? We think that GRBs are rare enough that they don’t produce mass extinctions more than once every billion years or so. It’s unlikely that there have been more than one or two mass extinctions on Earth from GRBs. In particular, new evidence suggests that at least long-duration GRBs tend to occur in galaxies with low

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abundances of heavy elements compared to our own Galaxy. The fact that our Galaxy is abundant with heavy elements decreases the chances that a GRB will extinguish us.

Lecture 66: Birth Cries of Black Holes

How can we be sure that GRBs are produced by the collapse of a star to form a black hole, or the merging of two neutron stars forming a black hole, or some other energetic process? One way to verify the claim, and to test general relativity, would be to detect gravitational waves, ripples in the fabric of space-time created during the formation of a black hole. When a massive star collapses, gravitational waves are emitted. Likewise, when two neutron stars orbit each other and merge, gravitational waves are emitted. But these waves are extremely dif¿cult to detect because they’re very weak. Such waves have interesting signatures: They ¿rst stretch an object along one axis, while squeezing it along the other axis. Then, they stretch the object along the second axis and squeeze it along the ¿rst. Gravitational waves are so weak, however, that they would cause a 1-meter-long rod to change size by an amount only equal to 106 of the diameter of a proton! Joseph Weber ¿rst tried to detect this movement, and though he wasn’t successful, his methods paved the way for future attempts. The basic idea for detecting tiny movements is based on the concept of oscillating an object at its natural resonant frequency, thus amplifying the effect, similar to pushing someone on a swing at just the right time to increase his or her amplitude (the height reached). Hence, to attempt the detection of gravitational waves from merging neutron stars, physicists have built large, L-shaped vacuum tubes through which laser beams pass. The two such gravity-wave detection facilities in the United States (in Washington and Louisiana) are called, collectively, LIGO, the Laser Interferometer Gravitational-Wave Observatory. The laser beams measure the distance between mirrors mounted on hanging masses at the ends of the tubes and at their intersection point. If a gravitational wave passes through, the space in one tube contracts, while in the other, it expands. LIGO has not yet detected any gravitational waves; however, it is an important step in the development of better instruments for the future. Ŷ

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Important Term interferometer: Two or more telescopes used together to produce highresolution images.

Suggested Reading Katz, The Biggest Bangs: The Mystery of Gamma-Ray Bursts, the Most Violent Explosions in the Universe. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Schilling, Flash! The Hunt for the Biggest Explosions in the Universe. Thorne, Black Holes and Time Warps: Einstein’s Outrageous Legacy.

Questions to Consider 1. If GRBs are beamed, are the energy requirements per GRB smaller than if isotropic emission (i.e., uniform across the sky) is assumed? Is the number of GRBs that we detect per galaxy affected by the beaming?

2. Why was identi¿cation of the optical afterglows of short-duration GRBs of critical importance to the interpretation of such GRBs?

3. Given that we feel the effects of gravity every day (it is a very familiar force), why do you think gravitational waves are so dif¿cult to detect?

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Our Home—The Milky Way Galaxy Lecture 67

“We’ll start with our own home, the Milky Way Galaxy, a grand structure—a spiral galaxy about 100,000 light years in diameter, and only a couple of thousand light years thick—containing several hundred billions of stars.”

Lecture 67: Our Home—The Milky Way Galaxy

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n this ¿fth and ¿nal unit of the second major part of the course, we will examine the contents of the Universe on large scales, beginning with a look at our own Milky Way Galaxy. The Milky Way Galaxy is spiral, about 80,000 (though perhaps 100,000) light years in diameter, and a few thousand light years thick. It contains several hundred billion stars, all gravitationally bound together and orbiting the central part of the Galaxy. Our Sun is one-half to two-thirds of the way out from the center of the Galaxy, orbiting in a near-circular fashion at about 200 kilometers per second. Being about 24,000 light years from the center of the Galaxy, our Sun takes about 250 million years to complete one full orbit around the center. Given that the Sun is roughly 4.5 billion years old, it has thus far made about 18 orbits around the center of the Galaxy. The Milky Way has a nucleus and a central bulge of stars from which a bar-like structure emerges. The bar’s ends have two major arms that break into two or more other arms. The four main arms of our Galaxy are Norma, Sagittarius, Orion, and Perseus. The Sun is on the inside edge of the Orion arm. Star clusters and nebulae tend to congregate in the arms, with many nebulae and clusters in the Sagittarius arm toward the center of the Galaxy. Star clusters arise from giant clouds of gas and dust, like the Orion Nebula. They are gravitationally unstable and, thus, begin to contract, fragmenting into smaller sub-units and eventually forming stars, as we discussed in a previous lecture. From Earth’s position near the outskirts of the Galaxy, we can look toward the center and see the bulge. If we look to the sides, we see a disk of stars growing fainter farther away from the bulge. When we look along the plane of the Galaxy, we can see a multitude of stars. When we look at other angles through the disk of the Galaxy, we don’t see as many stars. This effect is what produces the “Milky Way” in the sky, as discussed 332

in Lecture 5. The ecliptic plane of our Solar System is tilted by about 60 degrees relative to the Galactic plane. In addition, Earth’s axis is tilted 23.5 degrees relative to the rotation axis of the Solar System. During the northernhemisphere summer, we can see views toward the center of our Galaxy. During the northern-hemisphere winter, we look in a direction opposite the center. Because of the combined tilting effects, the center of our Galaxy is nearly overhead from the southern hemisphere during its winter, enhancing our view from that vantage point. Now we look at nebulae, clouds of gas and dust. The Orion Nebula, about 1500 light years away in the sword of the constellation Orion, is a region where stars have been forming for the past few million years. Peering into its depths, we can witness the process of star formation as it occurs. Some nebulae, in particular spiral nebulae, are actually distant galaxies. We will consider them further in Lecture 69. The spiral arms of our Galaxy and other spiral galaxies contain most of the nebulae, which glow from massive young stars forming within them. These are called emission nebulae. The gas is ionized by ultraviolet radiation from the newly forming, hot, massive stars, making the surrounding clouds of gas glow. When atoms are ionized, such as hydrogen, an electron is liberated from the hydrogen atom. If the electron recombines with a free proton, it can emit a photon of light and, subsequently, jump to still lower energy levels, continuing to emit light. An electron can also collide with another electron already bound in an atom, bumping it up to a higher energy level. When that electron subsequently jumps to a lower level, it emits light. Previously, in Lecture 51, we considered both processes when discussing the glowing cloud of gas ejected by dying stars (planetary nebulae), but here, we concentrate on nebulae from which new stars are forming. Photons can ionize the atoms in their vicinity, but beyond some distance, there are not enough photons to ionize atoms, so they remain neutral. Ionized hydrogen is called HII, while neutral hydrogen is called HI. If suf¿ciently energetic ultraviolet photons are present, they can produce ionized helium, though this happens only around very hot stars. We can produce wonderful photos of nebulae and their various colors by using special ¿lters that capture the different emission lines produced by a glowing nebula. ReÀection nebulae shine because visible photons from nearby stars reÀect off small particles 333

Lecture 67: Our Home—The Milky Way Galaxy

of matter, or space dust, which is usually mixed in with gas. Because the reÀection process works best for blue light, reÀection nebulae tend to glow blue. ReÀection nebulae don’t glow from ionization but, rather, from light bouncing off particles. Their color is blue for essentially the same reason our sky appears blue; as the light ¿lters through our atmosphere, the blue, green, and violet photons are reÀected more easily than the red and orange ones. Absorption (or dark) nebulae are dense and dusty, with so much material that “The Milky Way is what you Earth’s view of their light is blocked. get when you look along These are the regions in which stars are currently forming. All three types the plane of our galaxy.” of nebulae can occur together. Not only can we view visible wavelengths of the light they emit, but using infrared and radio telescopes, we can also see new stars forming in these nebulae, especially the dark nebulae. Diffuse clouds of gas and dust between the stars form part of the interstellar medium (ISM), much of which is low in density. However, some regions have dense clouds of gas, which can become gravitationally unstable and collapse to form new stars. The densities of particles in these clouds can be so high, up to 1 million particles/cm3, that molecules begin to form. These dense clouds span regions up to a few hundred light years across and are where giant clusters of thousands of stars are formed. We know that our Sun and planets formed from this ISM, whose composition is gradually changing as a result of the heavy elements ejected into the cosmos by supernovae. The realization that we formed from such structures, chemically enriched by previous generations of massive stars, was a monumental step in our understanding of our place in the cosmos and our origins in this vast Universe. Ŷ

Suggested Reading Croswell, The Alchemy of the Heavens: Searching for Meaning in the Milky Way. Ferris, Coming of Age in the Milky Way. Henbest and Couper, The Guide to the Galaxy.

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Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Verschuur, The Invisible Universe Revealed: The Story of Radio Astronomy.

Questions to Consider 1. How would the Milky Way appear if the Sun were closer to the edge of our Galaxy?

2. If the Sun is 8 kiloparsecs (about 24,000 light years) from the center of our Galaxy and it orbits with a speed of 200 kilometers per second, show that the Sun’s orbital period is about 250 million years. (Assume that the orbit is circular.)

3. Compare (a) absorption (dark) nebulae, (b) reÀection nebulae, and (c) emission nebulae.

4. Describe the relation of hot stars to H I (neutral hydrogen) and H II (ionized hydrogen) regions.

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Structure of the Milky Way Galaxy Lecture 68

“The astronomers in the late 19th century who looked at the sky and counted stars in different parts of the sky saw about the same number of stars in all directions of the band of the Milky Way, and they concluded that our Sun is in the center of the Milky Way. … Harlow Shapley, in 1917, realized that [it is] not.”

Lecture 68: Structure of the Milky Way Galaxy

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ased on observations that the naked-eye stars within the band of light called the Milky Way appeared to be roughly evenly distributed in all directions, astronomers once believed that our Solar System is at the center of the Milky Way Galaxy. They also concluded that the Galaxy is relatively small because they couldn’t see stars more than a few thousand light years away. Further studies showed these conclusions to be false. Many stars are hard to see, and others appear dim, because dense clouds of gas and especially dust block their light, causing an extinction, or obscuration, of light similar to the effects of smog. In 1917, Harlow Shapley realized that our Solar System is not in the center of the Galaxy. His conclusion was based on the observed distribution of globular star clusters, which are more highly concentrated in one region of the celestial sphere than in the opposite region. Globular clusters contain hundreds of thousands of stars bound to each other, as discussed in a previous lecture. Shapley correctly assumed that these clusters form a roughly spherical distribution around the Galaxy’s center. Because of the observed concentration of globular clusters in one region of the celestial sphere, Shapley realized that our Sun is near the edge of the Galaxy. From his measured distances to the globular clusters, he was able to determine the Sun’s distance to the center of the Galaxy. It was much larger than previously thought, thus implying that the entire Galaxy was very large. However, he overestimated the size of the Galaxy because he wasn’t aware of the obscuration (extinction) by dust. Obscuration also prevents us from seeing, in detail, the Milky Way’s spiral arms. Other galaxies have spiral arms that are readily visible from the outside, such as those of the Whirlpool Galaxy (M51). We can map the spiral arms in our own Galaxy by looking at the distribution of types O and B 336

main-sequence stars, young and massive stars that don’t wander far from their nebular birthplaces in spiral arms. Recall that open star clusters also form from nebulae; thus, we can map spiral arms by looking at the distribution of open clusters. We can better map spirals by measuring radio waves emitted by clouds of atomic hydrogen because such waves easily penetrate clouds of gas and dust. In its ground state, hydrogen has one electron in its lowest energy level. However, that level can be split by a hyper¿ne transition into two closely spaced energy levels, which are de¿ned by the energy of the electron and proton when both spin in the same direction versus opposite directions. Because spinning protons and electrons behave like magnets, they naturally want to Àip over so that they spin in opposite directions. This is a lower energy state than when both point in the same direction. During this Àip, a photon of radio radiation is emitted. “How do we get the motions of stars relative to the Sun? The radial motion, toward us or away from us, is easy to obtain from the Doppler shift.”

A hydrogen atom with its electron in the lowest energy level can be kicked up to the higher level by a collision with another electron. That upper level is not perfectly stable, though typically, it takes about 11 million years before the electron decides to Àip its spin back down to the lower level. But because clouds of gas can be hundreds of light years across, there are enough hydrogen atoms constantly producing radiation that we can map the spiral arms of our Galaxy with this technique. Our Galaxy doesn’t appear to have a very orderly structure, as some other spiral galaxies do. Instead, it has clumps and spurs, making its spiral arms look stubby. How do the stars and clouds of gas and dust move in our Galaxy? Because we know the Sun orbits the center of our Galaxy in roughly a circle, with a speed of 200 kilometers per second (km/s), we can determine the absolute motions of the stars and gas-dust clouds. The radial motion, or velocity, of stars (toward us or away from us) is easy to obtain from the Doppler shift; we look at starlight spectra and measure how much the pattern of lines is shifted to redder or bluer wavelengths. The amount of shift gives us the radial velocity. Transverse velocity—the physical speed in the plane of the sky—is 337

© iStockphoto/Thinkstock

Lecture 68: Structure of the Milky Way Galaxy

harder to obtain. We know that stars move relative to one another with time in what are called proper motions, an angular motion across the sky (measured in seconds of arc per year). Some stars have a greater proper motion than others. If star A is the same distance from us as star B but physically moving faster than star B, star A will have a greater angular motion across the sky than star B. Alternatively, stars A and B could be moving at the same rate, but if star A is much closer to us, it would appear to move more quickly than star B. Thus, distance affects how we perceive stars to move. In addition, our view of a star affects how it appears to move. For example, if the star’s motion is largely perpendicular to our line of sight, it appears to move faster. If the star is moving mostly toward or away from us (radial motion), it will appear to move more slowly across the sky.

Our Sun moves around the Milky Way Galaxy at about 200 km/s.

If we know a star’s angular motion and its distance, we can determine its transverse velocity, which together with radial velocity, produces what we call space motion, or space velocity. If we measure the space velocity of stars in the vicinity of the Sun, we see much random motion; some stars move away from us and others move toward us. However, if we measure the

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space velocity for many stars, we observe an average, or mean, motion. Stars that are the same distance as our Sun from the center of our Galaxy appear to move with us at about 200 km/s, so their relative speed is essentially zero. Stars closer to the center of our Galaxy than the Sun appear to overtake us. Though they move at about the same physical speed, they have a smaller circumference to travel. Stars that are farther from the center than the Sun (but not too far) move at about the same physical speed as the Sun. But because they have a larger circumference to travel, they appear to lag behind the Sun. Thus, the stars appear to move at different speeds relative to us; this is called differential motion. We can map this relative motion at even larger distances in our Galaxy by looking at the radio radiation emitted by clouds of hydrogen gas. What happens when we plot the speed of the stars and clouds of gas in our Galaxy as a function of distance from the center? This gives us the rotation curve of our Galaxy. Our Sun (and Solar System) moves with a speed of about 200 km/s, as does most of the rest of the Galaxy, on average. In the inner 1000 parsecs or so, the speed gradually rises from roughly zero near the center to about 200 km/s. Here, we temporarily ignore the very central parsec, where speeds turn out to be much higher because of the presence of a supermassive black hole. At distances of about 1000 pc to more than 20,000 pc, the speed is roughly constant, 200 km/s. We say that the rotation curve is “Àat.” Other spiral galaxies show a similarly Àat rotation curve in general. But if the closer-in stars have a smaller orbital distance to traverse than the farther-out stars, why don’t the spiral arms of galaxies eventually become tightly wound up? It turns out that the arms are actually density waves, a compression of gas where new stars form and then gradually move away. The regions of compressed gas rotate around the center of our Galaxy at a different speed than that of typical stars. Therefore, at any given time, the spiral arms consist of different material than at some other time. Further, the orbits of stars are often elliptical because of perturbations from other galaxies. The ellipses rotate—or precess—at different rates, causing an apparent clumping, which forms the spiral structure. As we said, these clumps contain massive clouds of gas and dust from which new stars form.

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If we look at the rotation curve of the Milky Way Galaxy, it appears as if the stars at the very center have a speed of zero. However, on closer inspection, we see that the actual speed here is enormously high because of a black hole in the center of our Galaxy. The Milky Way’s central black hole is no ordinary one. From the movement of stars around it, we have deduced that its mass is 3.6 million solar masses con¿ned within a region smaller than 45 AU. So far, the center of our Galaxy provides the most compelling evidence for the existence of supermassive black holes, which we will see are a common characteristic of the centers of galaxies. Ŷ

Name to Know Shapley, Harlow (18851972). American astronomer; correctly deduced that the Sun is not at the center of the Milky Way Galaxy and that the Galaxy is larger than previously believed. Incorrectly concluded that the “spiral nebulae” are within the Milky Way, but most of his reasoning was logically sound.

Lecture 68: Structure of the Milky Way Galaxy

Important Terms rotation curve: A graph of the speed of rotation versus distance from the center of a rotating object, such as a galaxy. transverse velocity: The speed of an object across the plane of the sky (perpendicular to the line of sight).

Suggested Reading Croswell, The Alchemy of the Heavens: Searching for Meaning in the Milky Way. Ferris, Coming of Age in the Milky Way. Henbest and Couper, The Guide to the Galaxy. Melia, The Black Hole at the Center of Our Galaxy.

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Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Verschuur, The Invisible Universe Revealed: The Story of Radio Astronomy.

Questions to Consider 1. If the band of light called the Milky Way stretched only halfway around the sky, forming a semicircle rather than a circle, what would you conclude about the Sun’s location in our Galaxy?

2. Can Shapley’s conclusion regarding the Sun’s location in our Galaxy be considered an extension of the Copernican revolution?

3. While driving at night, you almost instinctively judge the distance of an approaching car by looking at the apparent brightness of its headlights and using the inverse-square law of light. Is your answer correct if you don’t account for fog along the way?

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Other Galaxies—“Island Universes” Lecture 69

For a long time, astronomers thought that our Milky Way Galaxy was the only galaxy in existence—essentially, the entire Universe. But by the early 20th century, there were good reasons to believe that other galaxies, or “island universes,” existed.

S Lecture 69: Other Galaxies—“Island Universes”

ome nebulae are clearly members of our own Galaxy because of their distance from us. The Orion Nebula, for example, is only 1500 light years away, and we can easily see the individual stars that light it up. But the nature of other so-called spiral nebulae was much more controversial because individual stars could not be seen within them and their overall structure differed from that of gaseous nebulae, such as the Orion Nebula.

In 1920, a famous debate took place between Heber Curtis and Harlow Shapley, two major astronomers of the time, on the subject of the “Scale of the Universe.” If our Galaxy is all that exists, then the Universe is pretty big but not gargantuan. On the other hand, if spiral nebulae are actually galaxies in their own right, then the Universe is far more vast. Curtis correctly believed that spiral nebulae were separate entities, far beyond the outskirts of our Milky Way, but part of his reasoning was Àawed. Shapley incorrectly believed that spiral nebulae were clouds of gas within our Galaxy, but his reasoning was sound. His conclusion was partly based on an erroneous measurement of the apparent rotation of one spiral nebula and the false assumption that the Andromeda Nebula was closer to Earth than it really is. In the mid-1920s, the famous astronomer Edwin Hubble resolved this controversy through his recognition of a certain type of star—a Cepheid variable (Lecture 45)—in spiral nebulae. Recall that Cepheid variables are evolved supergiant stars that grow bigger and smaller with time and, hence, brighter and fainter; these oscillation periods can last from 1 to 100 days. More luminous Cepheid variables have longer periods than less luminous ones. From this period-luminosity relationship, we can compare the average apparent brightness of a Cepheid variable of unknown distance with the known average luminosity of a Cepheid variable having the same period to 342

determine the distance of the ¿rst Cepheid variable and, hence, the distance of its associated galaxy or nebula. Hubble noticed that Cepheid variables in the Andromeda Nebula looked faint and correctly concluded that they must be incredibly distant. Furthermore, given the apparent angular size of the Andromeda Nebula (it spans several degrees in the sky), Hubble deduced that it was a huge system containing billions of stars—a galaxy. Today, we can see anywhere from 50 to 100 billion galaxies with our most powerful telescopes. Hubble classi¿ed two main types of galaxies: spiral galaxies, like our own Milky Way, and elliptical galaxies. There were also several additional types of galaxies. Spiral galaxies differ from one another in shape. Some have fairly open arms and fairly small central regions (bulges); others have larger bulges and more tightly wound arms. Some have bars through their centers with arms protruding from the ends. Generic spiral galaxies have a disk containing arms. New stars form continuously out of nebulae located primarily within those arms, then migrate away. The disks have a mixture of old and young stars, but in particular, the arms contain young stars. Old stars are present almost exclusively in the halo and in the bulge, the central part of the galaxy. The vast halo around a spiral galaxy tends to contain almost entirely old stars. Elliptical galaxies appear roughly spherical or elliptical (elongated). They have no disk or arms, and there is very little gas and dust. Further, they have no nebulae and, hence, very little active star formation. Presumably, large stars in these galaxies existed long ago and died as supernovae or GRBs. The largest elliptical galaxies (300,000 light years across) are more than three times the size of the Milky Way and contain up to 10 trillion stars. The Milky Way, on the other hand, has only a few hundred billion stars. Most elliptical galaxies are relatively small (5000 to 10,000 light years across), with perhaps only 1 million to 10 million stars. A third class of galaxies, irregular galaxies, is relatively rare in the local parts of today’s Universe. But as we look far away and back in time, we see more of these irregular galaxies. Nearby examples are the Large Magellanic Cloud and the Small Magellanic Cloud, satellite galaxies of the Milky Way Galaxy. There are also peculiar galaxies, which differ from irregular ones in that they 343

have fairly distinct spirals or elliptical shapes but also an unusual feature. Some spiral galaxies have rings or tails, both of which may be caused by gravitational interactions with neighboring galaxies. Some elliptical galaxies have lots of gas and dust, unlike the typical ones.

NASA, ESA, and The Hubble Heritage Team (STScI/AURA)-ESA/Hubble Collaboration

Lecture 69: Other Galaxies—“Island Universes”

One ¿nal class is a cross between spiral and elliptical galaxies, called S0 galaxies (pronounced “ess-zero”), or lenticular galaxies. They have a bulge and a disk like a spiral galaxy, but the disk doesn’t have much gas and dust. There are no arms, and there’s very little evidence for the formation of new, massive stars, either in the recent past or in the present.

The barred spiral galaxy NGC 1672, imaged with the Hubble Space Telescope.

Edwin Hubble tried to arrange the different types of galaxies in a “tuning fork” diagram: Ellipticals were arranged on the handle of the tuning fork, while normal spirals and barred spirals were arranged on one tine each. Hubble thought that there might even be an evolutionary progression from ellipticals to spirals or vice versa. We now think, in general, that no such 344

evolutionary progression exists, although some spirals do merge to eventually form ellipticals. A single lone spiral will not later turn into an elliptical, nor will an elliptical, on its own, turn into a spiral. In this sense, then, galaxies don’t undergo an evolutionary sequence. Gravity binds galaxies together. Indeed, they are formed out of primordial clouds of gas that collapse, creating many galaxies in about the same place. Orbiting our Milky Way Galaxy are the two Magellanic Clouds and six or seven smaller companions, dwarf galaxies that are harder to see. Our nearest big neighbor, the Andromeda Galaxy, also has two main companions and half a dozen smaller ones. We live not just in a binary system with the Andromeda Galaxy but with several dozen smaller galaxies in a loose cluster known as the Local Group, which has a diameter of a few million light years. Galaxies also occur in large clusters. The Virgo cluster spans about 15 degrees in the sky, contains more than 1000 galaxies, and is 60 million light years away. The Coma cluster is about 300 million light years away and contains more than 10,000 galaxies. Clusters appear to form even larger superclusters, spanning 50 to 100 million light years and separated from each other by vast empty regions called voids. Astronomers have come a long way since the days when they thought that ours was the only galaxy. We now know that there are up to 100 billion galaxies out to 14 billion light years from us—a giant leap in our understanding of our cosmic origins and our place in the Universe. Ŷ

Important Term Local Group: The roughly three dozen galaxies, including the Milky Way, that form a small cluster.

Suggested Reading Christianson, Edwin Hubble: Mariner of the Nebulae. Dressler, Voyage to the Great Attractor: Exploring Intergalactic Space. Hirshfeld, Parallax: The Race to Measure the Cosmos.

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Lightman and Brawer, Modern Cosmologists.

Origins:

The

Lives

and

Worlds

of

Malin, View of the Universe. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Petersen and Brandt, Visions of the Cosmos. Waller and Hodge, Galaxies and the Cosmic Frontier.

Questions to Consider 1. Explain why Cepheid variable stars are so useful for determining the distances of galaxies.

2. Why can’t we determine the distances to galaxies using the geometric method of trigonometric parallax (triangulation), as we do for stars?

3. How is the discovery of other galaxies an extension of the Lecture 69: Other Galaxies—“Island Universes”

Copernican revolution?

4. The sense of rotation of galaxies is determined spectroscopically. How might this be done, in practice?

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The Dark Side of Matter Lecture 70

“There’s now strong evidence that most of the mass in galaxies and clusters of galaxies may be dark matter—material that gravitationally binds the galaxies and clusters of galaxies together, but does not emit any signi¿cant amount of electromagnetic radiation, and so it can’t be seen.”

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ntil a few decades ago, astronomers thought that galaxies were composed primarily of stars. There is now strong evidence that most of the mass of galaxies may be dark matter. Dark matter is material that gravitationally binds galaxies and clusters of galaxies, yet it does not emit any signi¿cant amount of electromagnetic radiation, so it can’t be seen. The ¿rst evidence for this came in the 1930s when Fritz Zwicky saw that galaxies within clusters move incredibly quickly. Given that these clusters are unlikely to be chance, Àeeting groupings, there must be some additional material (beyond that of visible stars) gravitationally binding them together; otherwise, the galaxies would Ày apart. Though Zwicky’s theory was largely ignored, additional evidence came later through studies of the rotation curves (orbital speed versus distance from the center) for spiral galaxies. Let’s take a closer look at rotation curves. The rotation curve of our Solar System shows that distant planets move more slowly than nearby planets. Plotting these speeds (v) on a graph against their distance from the Sun (R) produces a curve that can be described as speed proportional to 1 divided by the square root of distance: v f 1/ R . This inverse-square-root law occurs when a single central mass dominates the gravity of a structure, as our Sun does in our Solar System. Because the Sun’s mass is so great, our planets’ masses are negligible in comparison. Recall from Lecture 68 that most of the stars in the Milky Way Galaxy orbit at about 200 km/s. In the central regions of the Galaxy, the stars orbit more slowly, but in the very center—near the supermassive black hole—stars orbit very quickly. The rotation curve of our Galaxy, as we’ve seen, levels off at a distance of about 1000 parsecs. However, the rotation curve for the Solar System is much different—it declines with distance from the Sun according to an inverse-square-root law. 347

Lecture 70: The Dark Side of Matter

The Sun’s mass accounts for the rotation curve of our Solar System, but in the Milky Way Galaxy as a whole, there is no single dominant mass; the supermassive black hole in the center (roughly 4 million solar masses) dominates only within the central few light years and isn’t big enough to dominate the cumulative mass of all the stars in our Galaxy. Most of the mass in our Galaxy is distributed throughout. There is enough mass in the bulge and inner disk to account for the observed speeds of the stars, but farther out into the disk, there are too few stars to account for the observed rotation curve. When we calculate the mass of the Milky Way Galaxy out to a certain distance, we get M = v2R/G, in which M is mass within an enclosed circle of radius R, v is orbital speed, and G is Newton’s gravitational constant. Only stars within the orbit of the Sun (or whatever other star we’re considering) count; stars outside that orbit don’t affect the orbital speed as long as they are uniformly distributed. This calculation is derived using Newton’s version of Kepler’s third law: (M + m)P2 = (4S2/G)R3. The equation M = v2R/G implies that the mass enclosed within progressively larger orbits grows in direct proportion to the radius of the orbit. Twice as far out encloses twice as much mass; four times “Where is most as far out encloses four times as much mass. But farther from the Galaxy’s center, we notice that the of the mass in observed speeds are as much as twice that of the our Galaxy? It’s expected speeds based on visible matter only. distributed over the Galaxy.” Clearly, there are not enough stars at large distances from the Galaxy’s center to account for differences between the observed and expected rotation curves. Therefore, there must be other matter inÀuencing the stars that orbit in the outer parts of our Galaxy. This material must be dark matter, gravitationally inÀuencing the stars. Most dark matter occurs in the halo surrounding our Galaxy, not in the disk or the bulge. We think that the galactic halo extends far out, even beyond the globular clusters. This is because we see very distant stars moving quickly, far beyond the region where there is much visible matter. Dark matter increasingly dominates farther away from our Galaxy’s center. Vera Rubin was the ¿rst to recognize that the rotation curves of most other spiral galaxies show this same general trend. If we plot the observed rotation 348

speed against distance from the center of a spiral galaxy, we notice that one side rotates away from us and the other side rotates toward us, with a roughly Àat rotation curve. Rubin concluded that there is extra, invisible mass in the galaxies, though few other astronomers took her seriously at the time. Historically, dark matter was called the “missing mass,” though this term is not favored anymore because the mass is not missing; rather, it is faint or invisible. Elliptical galaxies also show evidence of dark matter, as do pairs of galaxies that interact with speeds too great to have been produced by only the visible stars alone. If it weren’t for dark matter, the hot gases in galaxy clusters would quickly evaporate away from the clusters. Gravitational lensing also provides evidence for dark matter. Recall that a foreground object can bend, or lens, the light of a background object. Likewise, dark matter lenses the light of distant galaxies and clusters. A galaxy lensed by a foreground cluster of galaxies tends to produce arcs. The more galaxies being lensed, the more arcs are produced. Studying the brightness and distribution of the arcs can tell us more about dark matter. Clusters of galaxies are 90% dark matter, some of which may be visible because it emits x-rays, being quite hot. Indeed, recently, we’ve discovered that perhaps 10% of dark matter actually glows at x-ray wavelengths. If 10% of dark matter is visible at x-ray wavelengths, but the other 90% cannot be detected in any form of electromagnetic radiation, what could it be? One theory is that this invisible dark matter consists of massive compact halo objects (MACHOs), astrophysical objects in the halos of galaxies. MACHOs include stellar-mass black holes—not supermassive black holes— as well as old and dim white dwarfs or neutron stars, brown dwarfs, and free-Àoating planets. We can ¿nd MACHOs by studying their gravitational inÀuence on light. For example, if one were to move between Earth and our line of sight to a star in the Magellanic Clouds, it would bend the star’s light, causing the star to brighten and fade for a time. The amount by which the star brightens at blue wavelengths should be the same as the amount by which it brightens at red wavelengths, because the warping of space is not dependent on the wavelength of electromagnetic radiation. Through observations of this effect, we’ve found brown dwarfs, free-Àoating planets, and even some solitary black holes, especially toward the bulge of our Galaxy.

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Unfortunately, astronomers have determined that most of the lensing objects were not in the halo of our Galaxy. In fact, at most, 20% of the dark matter in the halo of our Galaxy consists of MACHOs. What could the other 80% of dark matter be? It could be golf-ball-sized rocks, but it is dif¿cult to see how such objects could form. Moreover, other studies show that very little dark matter could consist of objects containing normal neutrons and protons— that is, normal matter. Dark matter must be predominantly in the form of odd little particles known as weakly interacting massive particles (WIMPs), predicted to have been produced shortly after the Big Bang. If these particles still exist in great abundance, they could account for most of the dark matter in our Universe. Ŷ

Name to Know Rubin, Vera (1928 ). American astronomer; was the ¿rst to observationally show that the rotation curves of most spiral galaxies imply the presence of considerable amounts of dark matter. She also obtained early evidence for large-scale peculiar motions of galaxies relative to the smooth expansion of the Universe.

Important Terms

Lecture 70: The Dark Side of Matter

dark matter: Invisible matter that dominates the mass of the Universe. halo (galactic): The region that extends far above and below the plane of the galaxy. massive compact halo objects (MACHOs): Brown dwarfs, white dwarfs, and similar objects that could account for some of the dark matter of the Universe. weakly interacting massive particles (WIMPs): Theorized to make up the dark matter of the Universe.

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Suggested Reading Dressler, Voyage to the Great Attractor: Exploring Intergalactic Space. Lightman and Brawer, Origins: The Lives and Worlds of Modern Cosmologists. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Rees and Gribbin, The Stuff of the Universe: Dark Matter, Mankind and the Coincidences of Cosmology. Rubin, Bright Galaxies, Dark Matters. Waller and Hodge, Galaxies and the Cosmic Frontier.

Questions to Consider 1. Show that the mass of the Milky Way Galaxy within a radius of 10,000 light years from the center is about 3u1010 solar masses. (Assume a rotation speed of 200 km/s at that radius.)

2. To explain the Àat rotation curves of spiral galaxies, one might argue that gravity does not behave according to the inverse-square law at large distances. For this to work, would gravity have to be stronger or weaker than in the standard description? (It turns out that there is evidence against this hypothesis, but it is nevertheless useful to consider.)

3. Can the discovery that most of the matter in the Universe might be dark be considered an extension of the Copernican revolution?

4. Are you bothered by the notion that most of the matter in the Universe might be dark, detectable only through its gravitational inÀuence? Can you think of any alternative explanations for the data?

351

Cosmology—The Really Big Picture Lecture 71

“What’s going to happen to the Universe? What does it consist of? These are among the deepest and most profound questions that humans have ever asked.”

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Lecture 71: Cosmology—The Really Big Picture

e now enter the third major part of this course, the study of the Universe as a whole. In this lecture, we’ll talk about cosmic expansion as a tool for determining the distances of faraway galaxies, allowing us to study their evolution. Cosmology is the study of our Universe as a whole—its shape, size, structure, composition, age, and future. A fundamental question of our origins is: When did the Universe begin? We now know the answer: about 14 billion years ago. Perhaps a bolder question is: When will the Universe end? Although current data suggest that the Universe will expand forever, we don’t yet know whether this will really happen. Because galaxies are the building blocks of the Universe, it behooves us to understand where they came from and how they evolve. A typical small patch of the sky, roughly the apparent size of a grain of sand held at arm’s length, has about 1000 galaxies. If we extrapolate over the whole sky, we conclude that—within the realm of great telescopes, such as the Hubble Space Telescope—there are perhaps 50 to 100 billion galaxies, and that’s just in the parts of the Universe that we can see! We now have good reason to believe that the Universe extends far, far beyond the parts that are visible to us. There may even be an in¿nite number of galaxies. How did they form, and how do they evolve with time? Given the ¿nite speed of light, when we study distant galaxies, we see them as they were in the past. Thus, we can compare them with the galaxies of today, determining how, at least statistically, they evolve. In seeking and ¿nding answers to these profound cosmological questions, scientists are not trying to dispel the existence of God. Rather, they are attempting to discover the fundamental laws of physics and use them to understand how the Universe works. The goal is to have comprehensive models for the physical properties and behavior of the Universe and its 352

constituent objects. In general, there is no conÀict between science and religion, despite popular belief. They have different goals and different operational rules. Scientists don’t claim to determine the purpose of the Universe or of humans; those topics belong to theologians and philosophers. Further, scientists do not address questions of moral values or other non-scienti¿c issues. “Because redshift However, as we will see, some conclusions made through the scienti¿c process are not increases with testable (at least, not yet) and, hence, to some distance, you would extent, remove themselves from the realm of conclude that speed science. This blurs the distinction between of recession increases religion and science in some cases. with distance as well.” Our study of cosmology begins in the 1920s with Vesto Slipher, who noticed that, with a few exceptions, the spectra of galaxies (then known as spiral nebulae) are redshifted to longer wavelengths. Another galaxy might have the same absorption lines as ours, for example, but Slipher noticed that all of them are shifted toward redder hues of the spectrum. If we denote redshift by z, the de¿nition is z = 'O/O0 = (O – O0)/O0, where O0 is the rest wavelength of a given absorption line and O is its measured wavelength in the galaxy spectrum. Taking this a step further, in 1929, Edwin Hubble used the newly derived distances of some of the spiral nebulae to show that the observed redshifts were proportional to the galaxies’ distances. More distant galaxies have greater redshifts than nearby galaxies. If we interpret this redshift (z) as being due to radial velocity, as in the Doppler effect described in previous lectures, then we conclude that the speed of recession of galaxies increases with distance. The Doppler formula is z = 'O/O0 = (O – O0)/O0 § v/c, or simply 'O/O0 § v/c, or z § v/c. At the present time, the more distant galaxies have greater redshifts and, hence, greater speeds of recession than the nearby galaxies. Thus, in general, it appears that more distant galaxies are moving away from us faster than nearby galaxies. The Hubble diagram, a plot of distance against recession speed, reveals a straight line; thus, speed (v) is proportional to distance (d), and the constant of proportionality is Hubble’s constant: v = H0d, in which H0 is the current value of Hubble’s constant (a constant in space, not time). The value of 353

Lecture 71: Cosmology—The Really Big Picture

Hubble’s constant (H) actually changes with time. In the past few years, we have found that H0 = 71 r 4 kilometers per second per megaparsec (71 r 4 km/s/Mpc). Just recently, the measured value of H0 has been revised to 73 km/s/Mpc, but with a comparable uncertainty of ± 4 km/s/Mpc. This is not a physical change from 71 to 73 but, rather, a re¿nement of the determination of the present value of Hubble’s constant. However, we will assume for the rest of this course that the Hubble constant is 71 km/s/Mpc, because we have derived various quantities and diagrams based on this value, and in any case, it does not differ statistically from 73 r 4. The units of Hubble’s constant may initially seem strange: km/s/Mpc. However, the meaning is clear, when one considers Hubble’s law, v = H0d. A galaxy’s distance in megaparsecs cancels out the 1/Mpc in Hubble’s constant. If a galaxy is 10 megaparsecs away, then it is observed to be moving away from us at 710 km/s. A galaxy 20 megaparsecs away is moving away from us at 1420 km/s. According to the equation v = H0d, we might naively expect that as the distance of a given galaxy grows with time, its speed of recession increases. Yet this is not true; the speed doesn’t increase with time, because Hubble’s constant actually decreases with time in most reasonable universes, and the product H0d does not increase. The speed of any given galaxy, at best, remains constant. Or it should slow down with time (in the absence of repulsive effects, such as “antigravity”) because galaxies are gravitationally pulling on one another. In any case, Hubble’s law alone doesn’t imply that the speed of a galaxy should increase or decrease with time. It just says that right now, given a certain Hubble constant, galaxies that are farther away are moving away from us more quickly than galaxies that are nearby. Historically, there were several competing interpretations for the redshift. Some astronomers wondered if the redshift was gravitational. The problem with that hypothesis is that all parts of a galaxy have essentially the same observed redshift, aside from that caused by spin of the galaxy. If this effect were gravitational, different parts of the galaxy would show different redshifts because of different gravitational ¿eld strengths within the galaxy. Moreover, different galaxies in a cluster of galaxies have the same redshift, except for the slightly different radial velocities induced by gravitational interactions among the galaxies. An alternative is that light somehow loses energy on its way toward us, becoming redshifted; this is known as the tired 354

light hypothesis. However, the observed brightening and fading of distant supernovae compared with the much quicker time it takes nearby supernovae to brighten and fade is a major strike against this hypothesis. In other words, the observed light curves of distant and nearby supernovae should appear the same if light loses energy as it travels. If the redshift is caused by expansion of the Universe, however, those distant galaxies and the supernovae within them are moving away from us. From our perspective, their “clocks” should run more slowly than the clocks nearby. In an expanding Universe, time will be dilated for distant supernovae at a signi¿cant redshift and not dilated for nearby ones. Because we have observed dilation of the time scale of brightening and fading for the distant supernovae versus the nearby ones, we conclude that the redshift is caused by expansion. Further evidence that the Universe is expanding can be seen in what’s called the surface brightness—the brightness per unit area—of galaxies as a function of redshift. In an expanding Universe, at a progressively greater redshift, the surface brightness declines quite dramatically, which is what we observe. The surface brightness measurements speci¿cally imply that the correct interpretation of Hubble’s law is that space itself expands, rather than galaxies moving away from each other through a preexisting, non-expanding space. This view is also consistent with the underlying general theory of relativity, which is used to theoretically study the expanding universe. Thus, it turns out that the redshifts of galaxies are technically not Doppler shifts, which are produced when objects move through a preexisting space. Nevertheless, the Doppler formula works correctly, at least at low redshifts. When we say that the Universe is expanding, we mean that the space in between the very distant galaxies is getting larger. We don’t mean that the galaxies themselves are getting larger, nor do we mean that planets, planetary systems, stars, star clusters, and clusters of galaxies are expanding. All of these objects are held together by gravitational forces suf¿ciently strong to overcome the tendency of space to expand. Humans, as well, are not expanding, being held together by electromagnetic forces. The expansion of the Universe is one of the fundamental observations of cosmology. It will play a central role in the remaining lectures of this course. Ŷ 355

Important Terms electromagnetic force: One of the four fundamental forces of nature; it holds electrons in atoms. Hubble’s law: The linear relation between the current distance and recession speed of a distant object: v = H0d. The constant of proportionality, H0, is called Hubble’s constant.

Suggested Reading Ferguson, Measuring the Universe: Our Historic Quest to Chart the Horizons of Space and Time. Ferris, The Whole Shebang: A State-of-the-Universe(s) Report. Hogan, The Little Book of the Big Bang: A Cosmic Primer. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Lecture 71: Cosmology—The Really Big Picture

Waller and Hodge, Galaxies and the Cosmic Frontier.

Questions to Consider 1. Can you think of possible explanations for the redshifts of galaxies that do not involve the expansion of the Universe? How could you test these hypotheses?

2. What is the distance of a galaxy having a recession velocity of 3000 km/s if the Hubble constant is 71 km/s/Mpc?

3. At what speed is a galaxy 100 million light years away receding from us if Hubble’s constant is 71 km/s/Mpc? (Be careful with units!)

4. Do you think there is any fundamental conÀict between religion and science (speci¿cally, cosmology)?

356

Expansion of the Universe and the Big Bang Lecture 72

“Galaxies in our Local Group are gravitationally bound together. … Some might be moving away from us, and some might be moving toward us. … If Edwin Hubble had only looked at the Andromeda Galaxy, he might have concluded that the Universe is collapsing rather than expanding.”

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n the previous lecture, we learned that the Universe is expanding, one of the most monumental discoveries in astrophysics and an essential theme of cosmology. We continue our discussion of expansion, a tough concept, to help us understand it better. No matter which galaxy we look at, we see that it is moving away from us. At the present time, the nearby galaxies are moving away more slowly than more distant galaxies. There are some exceptions. For the closest galaxies, those in the Local Group, gravity is so strong that it overcomes any tendency for space to expand; instead, the galaxies are gravitationally bound together. Gravity is like a tight spring in this case; it is so tight that it can’t be budged by the expansion of space. Some galaxies in the Local Group are moving away from us and others toward us because of gravitationally induced motions. The Andromeda Galaxy, for example, is the nearest big galaxy (about 2.4 million light years away) and a member of the Local Group. It is moving toward the Milky Way Galaxy with a speed of roughly 100 km/s. Galaxies not strongly bound together but still reasonably close can affect the speed at which each moves. The Virgo cluster, about 60 million light years away and not a member of the Local Group, is receding from us at about 1200 km/s—yet if it weren’t for the gravitational effects of the Local Group, the Virgo cluster would recede even faster, by about 150 to 200 km/s. The Virgo cluster is, in a sense, connected to us by a weak spring that is able to stretch by the expansion of space. The Hubble Àow is the uniform expansion of the Universe. If galaxies were massless and had no reason to attract each other, then all motions other than those caused by universal expansion would be zero. Gravitational attraction produces a deviation from the uniform expansion of the Universe, a deviation from the Hubble Àow. 357

Lecture 72: Expansion of the Universe and the Big Bang

These gravitationally induced motions are signi¿cant only over relatively short distances, not over distances exceeding a few hundred million light years. Let’s consider uniform expansion of the Universe. Hubble’s law is suggestive of an explosion having a well-de¿ned center from which shrapnel is scattered. However, it turns out that the expansion of the Universe is not like a conventional explosion with a unique center. The distribution of galaxies, the number per unit volume as a function of distance from us, implies that there is no unique center to the Universe—at least not in any physically accessible dimension. If our Galaxy were at the center, other galaxies would appear to spread out more the farther away they are from us. Per unit volume, then, there would be fewer galaxies at greater distances, but this is observed not to be the case. A three-dimensional analogy is an expanding loaf of raisin bread. Let the loaf be in¿nite, or ignore the edges, which are irrelevant to our discussion. Because the yeast is uniformly spread throughout the dough, the dough expands uniformly. The raisins are the galaxies that do not spread themselves. From any one raisin’s perspective, the other raisins move away as the bread rises, or expands; that raisin thinks it is at the center of expansion. However, every other raisin also thinks it is at the center of expansion. Thus, there is no unique center. For any given raisin, the more distant raisins recede faster than nearby ones, simply because there is more expanding dough between raisins that were farther apart to begin with. Thus, Hubble’s law is satis¿ed. In the real Universe, Hubble’s law is also satis¿ed: More distant galaxies move away faster than nearby ones. Just as every bit of dough expanded, in the real Universe the more space (“dough”) there is between two galaxies to begin with, the more expansion there is and the greater is the apparent recession speed. Is it possible that the Universe has a unique center that we just can’t see? Using an inÀated balloon as an analogy of curved space, we have a twodimensional space; that is, we assume that the laws of physics are constrained to operate only on the surface of the balloon, which curves around itself. In this hypothetical universe, we can move only along the surface of the balloon; we cannot go into the balloon’s interior, nor upward out of its surface. This space, though curved, is two-dimensional because we can move forward/ backward and left/right and any combination of these two motions, but we 358

cannot move up/down. The center is actually inside the balloon itself, but that dimension is not physically accessible (not being part of the surface), though it is a mathematically real and distinct dimension. The surface curves around this additional mathematical dimension. To demonstrate the mathematically distinct dimensions, we can look at a one-dimensional circle, de¿ned by the equation x2 + y2 = r2, and a twodimensional sphere, de¿ned by the equation x2 + y2 + z2 = r2, each of which represents a hypothetical universe. Two variables, x and y, are needed to de¿ne the circle, or a one-dimensional curved path, which means that the path must wrap around a second mathematical dimension. Similarly, three variables are needed to represent the surface of a two-dimensional sphere, x, y, and z. The center of the sphere itself is not in the surface, yet clearly, it exists mathematically because there must be three dimensions—x, y, and z—describing this surface. In both the circle and the sphere, the origin—the center—is not part of the circle or sphere. We cannot physically “The number density of access this point. galaxies, the number of galaxies per unit volume, remains about If we live in a three-dimensional analog of a sphere, where a the same no matter where you volume bends around some look in the Universe.” fourth spatial dimension, the equation for our sphere would be x2 + y2 + z2 + w2 = r2, w now being this fourth dimension around which we curve. This is called a hypersphere, and it’s dif¿cult to imagine or describe because we live in a world with three spatial dimensions, not four. To help us visualize hyperspace (four-dimensional space as a general class), we can consider the shadow (projection) of a four-dimensional cube, or hypercube, onto three-dimensional space. Imagine displacing two cubes along a diagonal and connecting the corners. By analogy, the shadow (projection) of a three-dimensional cube onto two-dimensional space (a sheet of paper, for example) can be drawn by displacing two squares along a diagonal and connecting the corners. Even if the Universe is in¿nite (and we don’t know whether it actually is), it can still expand; it simply becomes less dense. For example, the counting 359

numbers reach from 1 to in¿nity. Even if we removed all the odd numbers and just counted with the even numbers, the numbers still keep going in¿nitely—they are just less dense, in a sense, because the odd numbers have been removed.

Lecture 72: Expansion of the Universe and the Big Bang

Could there be a universe denser than ours? Mathematically, the answer is yes, just as the counting numbers from 1 to in¿nity can be made denser by adding all the in¿nite fractions, or rationals, that fall in between them. Between 0 and 1, there is an in¿nite number of fractions, or rationals; this set of rationals, though denser than the counting numbers, can be placed in one-to-one correspondence with the counting numbers. Thus, there are no more rational numbers than there are counting numbers, yet there’s clearly a greater density of the fractions. We can demonstrate this mathematical effect by putting all the rational numbers in a table. Though each row and each column has an in¿nite amount of numbers, all of them can be put in one-toone correspondence with the counting numbers by tracing along diagonals. We are convinced that the Universe is expanding. If we extrapolate this observed expansion back in time, we could conclude that the Universe had a de¿nite beginning. If the Universe had a beginning, its matter must have been very dense. For whatever reason, it started expanding from a point called the singularity, a point at which everything was possibly in¿nitely dense (if we temporarily ignore quantum mechanics). We think of the Universe as an expanding gas. When gases expand, they cool, suggesting that the Universe began in a very hot and dense state at time = 0, when the singularity existed. We must determine how far away a distant galaxy is in order to know how far back in time we are looking (our lookback time), to understand the origins of the Universe. Recall that the light we see from distant galaxies reveals those galaxies as they were back in time because the light took so long to reach us. We return to Hubble’s law to determine the distance of galaxies that are so far away we can’t even detect Cepheid variables or any other discrete objects in them. Recall that we can derive the distance of a galaxy by measuring the redshift of its spectrum. If we adopt a certain cosmological model (or history) of the Universe, then for a given redshift, we can calculate the corresponding lookback time given in billions of years. At progressively greater redshifts, the lookback time is a progressively greater number of years, up to about 14 billion years, the age of the Universe. 360

When we read (in newspapers or magazines) about the distance of a newly discovered galaxy, for example, that quoted “distance” is actually the lookback time—how long it has taken for the light to reach us—not the current distance of the galaxy from Earth. When the galaxy emitted the light we now see, the galaxy was actually closer to Earth than the distance implied by the lookback time; space expanded during the light’s journey to Earth. Now, when the galaxy’s light ¿nally reaches us, the galaxy is farther away than the distance implied by the lookback time. Thus, the lookback time corresponds to some average, or representative, distance of the galaxy from Earth. Most precisely, it is the amount of time light took to reach us from the galaxy. By observing galaxies at progressively greater distances, we’re seeing progressively farther back in time. Thus, we essentially view a movie of the history of the Universe, from which we can learn something about how it and the galaxies within it evolved. Ŷ

Important Term lookback time: The duration over which light from an object has been traveling to reach us.

Suggested Reading Dressler, Voyage to the Great Attractor: Exploring Intergalactic Space. Ferris, The Whole Shebang: A Stat- of-the-Universe(s) Report. Hawking, The Universe in a Nutshell. Hogan, The Little Book of the Big Bang: A Cosmic Primer. Kaku, Hyperspace: A Scienti¿c Odyssey through Parallel Universes, Time Warps, and the 10th Dimension. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Smith, The Expanding Universe: Astronomy’s “Great Debate,” 1900–1931.

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Questions to Consider 1. Can Hubble’s law be used to determine the distance of (a) D Centauri and other stars relatively near the Sun, (b) the center of our Galaxy, (c) the Large Magellanic Cloud, a satellite of our Galaxy, and (d) a cluster of galaxies very far from the Local Group?

2. Why does the recession of galaxies not necessarily imply that the Milky Way Galaxy is at the center of the Universe?

3. Explain how the effective center of expansion can be in an unobservable spatial dimension. Also, what is the Universe expanding into?

4. Can you visualize what our Universe might look like if it’s the three-

Lecture 72: Expansion of the Universe and the Big Bang

dimensional analogue of the two-dimensional surface of a balloon?

362

Searching for Distant Galaxies Lecture 73

“Some astronomers have taken deep pictures of the sky and found faint, little, fuzzy objects, and then gotten spectra of them in the hopes that these are distant galaxies, and some of them are.”

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f light traveled at an in¿nite speed, we would see the entire Universe as it is right now. However, because light travels at a ¿nite speed, we can look at regions of space as they were in the past and begin to understand how typical regions of the Universe evolve with time. Recall that lookback time is de¿ned as the amount of time into the past we are looking in order to see light emitted from objects with a given redshift. Fairly large redshifts—such as 1—provide a lookback time of nearly 8 billion years; at redshift 7, we are looking back nearly 13 billion years. Thus, the greater the redshift, the farther back in time we are seeing. If we say that an object is 4 billion light years away, what we really mean is that its light has been traveling for 4 billion years before it reached us. Because the Universe expands with time, that object was closer to us than 4 billion light years when the light was emitted, and now it is farther from us than 4 billion light years. By looking at representative groups of galaxies at different redshifts, we can begin to visualize how those galaxies evolved and continue to evolve in the same way that we can study the different age groups of humans to get an idea of how we grow and change with age. Let’s review what galaxies look like today and see how technology has helped us ¿nd more distant ones. Recall that galaxies come in two main classes: spiral and elliptical. Spiral galaxies typically have old stars in the halo and bulge regions, while new stars form in the arms, and a mixture of old and new stars occupy the disks. The youngest stars are in the spiral arms, because that is where they formed. Elliptical galaxies have a roughly spherical, or elliptical, distribution of mostly old stars. They have very little gas and dust and don’t rotate as much as spiral galaxies do. To get some idea of how galaxies might evolve, we need to compare nearby ones with distant ones. But ¿nding distant galaxies isn’t easy because they’re faint and blurry. Catalogues of astronomical objects compiled over more than a century have 363

“During the time that the light has been traveling from that galaxy to us, the Universe has expanded.”

helped astronomers locate distant galaxies. Some astronomers used catalogued objects that had emitted radio waves, taking deep photographs of their positions, only to discover optical counterparts, which allowed them to get spectra. Some of this work has turned up galaxies with redshifts as high as 5.34.

Lecture 73: Searching for Distant Galaxies

The Hubble Space Telescope has provided amazing views of some of the distant galaxies that astronomers are ¿nding through more detailed research of these catalogued objects. In particular, Hubble has taken some very deep images, the ¿rst of which was the Hubble Deep Field (HDF), capturing dramatic pictures of galaxies extremely far away. A picture of a small but representative part of the sky revealed about 1000 galaxies in one image! To make sure that this northern HDF was representative of small patches of the sky, Hubble took a similar image in the southern hemisphere’s celestial sphere and found that it, too, had similar properties to those observed in the northern hemisphere. Extrapolated over the entire sky, we estimate that 50 to 100 billion galaxies are (in principle) within the grasp of the Hubble Space Telescope. After Hubble ¿nds these objects, larger-diameter, ground-based telescopes are used to take spectra of the galaxies and obtain their redshifts. More recently, the Hubble Space Telescope was used to take an even deeper picture of the sky, the Hubble Ultra Deep Field (HUDF), in the southern hemisphere constellation Fornax. In the full HUDF, with a diameter of only about 0.01 the diameter of the full Moon, we could see about 10,000 galaxies! Even with the greatest telescopes, many galaxies are hard to view, though we can map their distribution and begin to measure their redshifts. With so many galaxies, how do we know which ones to concentrate on? We can’t measure the spectra of all the galaxies because there are too many. Instead, we try to choose the most likely very distant candidates, those with the highest redshifts. Because of their high redshift, the most distant galaxies will appear red to us. They look redder because of the signi¿cant stretching of light caused by the expansion of the Universe during the time that the photons were on their way toward us. Intergalactic hydrogen also makes these 364

One way to look for these red galaxies is to take pictures of the same part of space using differentcolored ¿lters. Because each ¿lter will allow only light of certain wavelengths A spiral galaxy in the Hubble Ultra Deep Field. through, we can look for those galaxies with high redshifts—that is, those that “drop out” of photos taken with ultraviolet ¿lters (¿lters that let ultraviolet light through). Using this technique, we’ve identi¿ed many candidates for distant galaxies. The next step is to take spectra of these objects to be sure of what we’re looking at. Like the Hubble Space Telescope, the Spitzer Space Telescope is good for looking at distant galaxies; high-redshift galaxies are especially visible at infrared wavelengths. Spitzer can take images of candidate high-redshift galaxies and transmit the information via radio waves to Earth. We can also ¿nd distant galaxies by gravitational lensing, which can magnify, or amplify, the light of distant background galaxies. By carefully examining telescope images of clusters of galaxies, which act as a gravitational lens, we can see arcs (distorted background galaxies) formed from the lensing. Indeed, the only reason we can even see such distant galaxies is because their light has been ampli¿ed through this gravitational lensing effect. Using this technique and others, astronomers have seen some very faint galaxies, up to redshift 6 and beyond. The current record is redshift 6.6 as of mid-2006. When comparing galaxies, we have to use images of comparable rest wavelengths. In other words, we can’t compare an image of visible light 365

NASA, ESA, S. Beckwith (STScI) and the HUDF Team

galaxies appear particularly red because the hydrogen absorbs much of the light. In particular, an electron in the ground state of hydrogen can jump up to the second energy level and absorb an ultraviolet photon.

with one of ultraviolet light. The visible radiation from a highly redshifted galaxy corresponds to intrinsically ultraviolet radiation as emitted by that galaxy because that radiation has been stretched, or redshifted, as a result of the expansion of the Universe as the light traveled to us. We can compare visible-wavelength pictures of distant galaxies with ultraviolet pictures of nearby galaxies, because the visible light of distant galaxies is actually restframe ultraviolet light redshifted to visible wavelengths. We can also compare visible-light images of nearby galaxies with infrared images of distant, highly redshifted galaxies, because the visible light of distant galaxies has been redshifted to infrared wavelengths. The recent development of supercomputers and linked computers—small computers linked together and performing parallel processing—has allowed astronomers to make calculations involving tens of millions of “particles” (stars, galaxies, or galaxy clusters). We can watch how these objects evolve through their mutual gravitational interactions and compare the results of numerical simulations with the observed properties of the Universe. The calculations from supercomputers, combined with the fantastic images and spectra from our great arsenal of telescopes, allow us to study in detail the evolution of structure in the Universe. Ŷ

Lecture 73: Searching for Distant Galaxies

Suggested Reading Dressler, “The Origin and Evolution of Galaxies,” in The Origin and Evolution of the Universe. Hogan, The Little Book of the Big Bang: A Cosmic Primer. HubbleSite News Center, hubblesite.org/newscenter/. The Once and Future Cosmos (special edition of Scienti¿c American, 2002). Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

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Questions to Consider 1. What if the speed of light were in¿nite? Would there still be a way for astronomers to look back at galaxies as they appeared long ago?

2. Of what importance are spectra and clear, sharp images of distant galaxies in studies of galactic evolution?

3. Discuss how the phenomenon of gravitational lensing can be thought of as “nature’s telescope,” allowing us to detect distant, very faint objects.

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The Evolution of Galaxies Lecture 74

“Just like a ballet dancer spins faster as she brings her arms in—because of the conservation of angular momentum—for a given amount of mass, if that mass is concentrated into a smaller volume, it must spin faster, so the spin rate increases.”

Lecture 74: The Evolution of Galaxies

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e’ve explored how astronomers ¿nd distant galaxies and how they compare them with nearby galaxies. Now, we turn to some discoveries about the evolution of galaxies, clusters, and the Universe. First, let’s consider our basic expectations of galaxy formation. We believe that the disk of a spiral galaxy initially forms from a collapsing, slowly spinning cloud of gas. As it collapses, it spins faster as a result of the principle of conservation of angular momentum. As any given mass is concentrated into a smaller volume, it must increase its spin rate. Collisions between atoms in this cloud of collapsing, spinning gas radiate energy; hence, the cloud loses energy and Àattens. The disk of our Solar System, for example, has Àattened due to collisions among all its minute particles. After the disk of a spiral galaxy forms, stars coalesce from gas and dust, creating a mixture of young and old stars. Because this mixture isn’t prevalent in elliptical galaxies, we think that “Elliptical galaxies the initial collapsing cloud of gas spins much that formed clearly slower than that of a forming spiral galaxy. more recently … Stars appear to coalesce much earlier during the we think that they formation of an elliptical galaxy than in a spiral formed as a result of galaxy. If stars coalesce when the cloud of gas the interaction and is still roughly spherical and large, then energy cannot further dissipate because the stars are gradual merging of spaced far apart and rarely collide. The cloud’s spiral galaxies.” volume cannot Àatten because there is no way to dissipate the energy, resulting in a large distribution of stars in a roughly spherical or elliptical shape. Indeed, elliptical galaxies consist of old stars, as though they formed long ago when the gas clouds were still spherical or elliptical (somewhat Àattened). How can a spiral 368

galaxy form a halo and bulge (which are roughly spherical in shape) and a disk (which is Àat)? The gas cloud collapses and spins, with some initial star formation that creates the halo and somewhat later star formation that creates the bulge. Most of the star formation, however, occurs much later—after the gas settles into the disk—which is created by colliding gas particles and dissipating energy.

© StockTrek/Digital Vision/Getty Images

We’ve just discussed the basic expectations of galaxy formation, but what really happens? What have comparisons of galaxies actually demonstrated? Some of our expectations have been proved through observations and simulations, but unanticipated complexities arise. One complexity is that, though most elliptical galaxies formed a long time ago—especially those found in clusters—somewhat solitary ellipticals seem to have formed relatively recently. It’s possible that more recently formed elliptical galaxies resulted from the gravitational interaction and gradual merging of two spiral galaxies. Computer simulations show that such mergers produce elliptical galaxies similar to those we observe. The simulations can demonstrate what the galaxies might look like as their development progresses through time. The Andromeda Galaxy, our nearest neighbor at 2.4 million light years away, is moving toward the Milky Way at about 100 km/s. We can calculate that the two galaxies will begin to merge in 5 or 6 billion years and will gradually (over the course of a few billion years) form an elliptical galaxy.

These two interacting spiral galaxies are in the process of merging together. 369

Lecture 74: The Evolution of Galaxies

When two galaxies merge, their stars don’t actually collide because the spaces between stars are so vast; rather, the interaction is gravitational. A newly formed elliptical galaxy may have much gas and dust, suggesting that it is a remnant of two spiral galaxies that merged to form the elliptical. In this case, star formation still occurs, unlike in older ellipticals, where star formation has virtually ceased, and there is very little gas and dust. Spiral galaxies can form from smaller pieces—galactic building blocks—that gradually coalesce. We see many such galaxy pieces at high redshifts, indicating that they are very old, but we don’t see many recently formed ones. When these various bits and pieces of galaxies merge, their clouds of gas collide, leading to the formation of new stars. In interacting galaxies, where the stars themselves almost never collide but the nebulae (clouds of gas) do, we observe many clusters of stars. Their formation was presumably induced by collisions between the nebulae, leading to compression of the gas and, thus, to gravitational collapse. If a supernova occurs near a nebula, it sends shock waves through the cloud, which can induce new star formation. Those stars can explode, further compressing nearby clouds of gas and setting off a chain reaction of new star formation. Galaxies can also interact without colliding. One galaxy can gravitationally perturb the gas in a neighboring galaxy, inducing star formation. Often, star formation creates huge stellar winds, chemically enriching galaxies and the surrounding space. Gravitational interactions between two galaxies can also cause star formation in rings surrounding the bulk of one galaxy, where gas and dust are compressed and perturbed. Galaxy groups merge as well—not just binaries interacting with each other and merging to form other galaxies, but whole collections of galaxies. Our own Milky Way Galaxy has been merging with smaller galaxies for billions of years. Our two big remaining satellite galaxies, the Large Magellanic Cloud and the Small Magellanic Cloud, will almost certainly be fully consumed by the Milky Way in the next 5 or 6 billion years. We already have evidence that our Galaxy has consumed other dwarf galaxies that originally orbited it. We know this from some groups of stars that have a certain distance, set of motions, and other telltale properties. At the moment, the Milky Way isn’t consuming the Magellanic Clouds, but we are gravitationally interacting with them. Indeed, the Magellanic Clouds appear to have produced a warp 370

in the plane of the distribution of neutral hydrogen in our Galaxy. Extending far beyond the Sun is a plane of neutral hydrogen. One-half of that plane is warped upward, and the other half is warped downward. This warp changes over time. The only way the warp can exist is if the Large Magellanic Cloud interacts with a vast halo of dark matter in our Milky Way Galaxy. The interaction creates a wake behind the Cloud, causing neutral hydrogen to warp. This is also evidence that dark matter really does exist in the halo of our Galaxy. The warp would not be as large if there were no dark matter in the halo. Large clusters of galaxies form over time, as well as so-called cD galaxies that devour smaller galaxies (“galactic cannibalism”) through gravitational interactions. Thus, what began as thousands of galaxies might end up as only one or two. Observed giant clusters of galaxies do show one or two such dominant galaxies in their centers. Using computer simulations, we can see the formation of superclusters and voids in space. These models demonstrate that stars form at peaks in the density of a vast underlying distribution of dark matter. If we vary the simulations by altering the initial conditions, the details of the Universe’s formation also change. For example, we can change the amount and type of dark matter—neutrinos, WIMPs, black holes, and so on—as well as input different types of gases. In particular, the models show us that most of the dark matter can’t be made up of neutrinos, because they would wipe out the formation of the large-scale structure (vast superclusters and voids) that is created by simulations. Through observations and theoretical calculations, we can understand the way in which the structure of the Universe formed. In addition, these models have taught us that the appearance of our Universe on a large scale is actually dependent on the amount and properties of fundamental tiny particles, such as neutrinos. Ŷ

Important Terms elliptical galaxy: One of the two major classes of galaxies de¿ned by Edwin Hubble; has a roughly spherical or elliptical distribution of generally older stars, less gas and dust, and less rotation than its spiral counterpart. galactic cannibalism: The swallowing of one galaxy by another.

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merging: The interaction of two galaxies in space, with a single galaxy as a result.

Suggested Reading Dressler, “The Origin and Evolution of Galaxies,” in The Origin and Evolution of the Universe. Hogan, The Little Book of the Big Bang: A Cosmic Primer. HubbleSite News Center, hubblesite.org/newscenter/. The Once and Future Cosmos (special edition of Scienti¿c American, 2002). Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. Why must we be careful when comparing visible-light images of nearby and high-redshift galaxies?

Lecture 74: The Evolution of Galaxies

2. How do you think our view of the night sky will differ when our Galaxy has merged with the Andromeda Galaxy and formed an elliptical galaxy? (Assume we still exist at that time—which actually won’t be the case.)

3. Summarize the tentative conclusions drawn about the evolution of galaxies.

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Active Galaxies and Quasars Lecture 75

“An especially massive—supermassive—black hole, accreting, or swallowing, or devouring an especially large amount of gas in its vicinity … can shine profusely at optical and other wavelengths, causing the central region of the galaxy, the quasar, to far outshine the rest of the stars. It makes the rest of the galaxy actually quite hard to see.”

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stronomers now have a much better understanding of how the largescale properties of galaxies, galaxy clusters, and superclusters form and evolve. But there is a distinct group we call active galaxies that demonstrate unusual characteristics. The central regions of a minority of galaxies can experience a very active, luminous, and powerful phase. We call these active galaxies. We can use the redshifts of galaxies and Hubble’s law to derive the distances of these galaxies, then combine their apparent brightness with the distance to get their power, or luminosity. From the distance (d) and apparent optical brightness (b) of the galaxy nucleus—its center—we get its optical luminosity, L = 4Sd2b, using the inverse-square law of light. In some cases, the luminosity of the central part is enormous. Such nuclei are often very powerful at other wavelengths, such “Sometimes these as x-ray, ultraviolet (UV), and radio. jets can extend over a million light years, Some active galaxies have two lobes, or and they’re really regions of radio emission, far from the nucleus. These lobes contain a vast quantity of energetic highly collimated.” particles. Closer scrutiny sometimes reveals two long, narrow, oppositely directed jets joining the nucleus and the lobes of such radio galaxies. The jets are thought to consist of charged particles moving nearly at the speed of light (that is, relativistic particles) and emitting radio waves. Each jet can be more than a million light years long. Don’t confuse these active radio galaxies with pulsars. Pulsars are rapidly rotating neutron stars from which relativistic jets emerge, while it turns out that jets from active galaxies come from the vicinity of the galaxy’s central, supermassive black hole. In both cases, 373

Lecture 75: Active Galaxies and Quasars

there is a ¿nely collimated beam of particles and radiation. The radiation doesn’t come from the random motion of hot gas particles but, rather, from charged particles spiraling in magnetic ¿elds. These spiraling particles emit light called synchrotron radiation. Using a technique called interferometry, which we discussed in an earlier lecture, we can take detailed images of radio galaxies with radio telescopes that are separated from one another by a considerable distance. The interference pattern of the radio waves can show us what the galaxy looks like. The Seyfert galaxies are a subclass of active galaxies, discovered by Carl Seyfert, an astronomer in the mid-1940s. Before the development of radio telescopes, Seyfert discovered that some galaxies at optical wavelengths have bright, star-like (that is, point-like) nuclei, and their spectra have very broad emission lines, indicative of rapid motions. Moreover, the spectra showed narrow emission lines spanning a wide range of ionization stages, which were not characteristic of nebulae ionized by hot O-type stars. The Seyferts come in two types: those with very broad lines, the Seyfert 1 galaxies, and those without very broad lines, Seyfert 2 galaxies, but still spanning a wide range of gas ionization stages. From the breadth (width) of the emission lines in the spectra, we can see that the gases move faster than 10,000 km/s, a far greater speed than in normal galactic nuclei. The only stars that show such speeds in their gases are supernovae. We will see that accretion of matter by a central, supermassive black hole is responsible for the unusual characteristics of Seyfert galaxies, radio galaxies, and other active galaxies. After World War II, astronomers increased their use of radio telescopes and began searching the skies, discovering even more intriguing objects. During the early days of radio telescopes, astronomers began noticing many places in the sky that emitted radio waves, and at optical wavelengths, there were obvious counterparts, such as peculiar-looking galaxies and supernova remnants. But in some cases, at the nominal position of the radio source, there appeared to be nothing unusual happening at optical wavelengths. Radio astronomers couldn’t pinpoint exactly where much of the radiation was coming from because of the low resolution, or clarity, of a single radio telescope. In the general region from which the radio waves were coming, there was no obvious object that could be the source of radio waves—only a bunch of random stars. 374

The origin of these radio emissions was revealed when the Moon passed between Earth and one of these strong radio sources: 3C 273 in the third radio catalogue of the Cambridge Survey. Because we know accurately the Moon’s position, when it brieÀy occulted 3C 273 and its radio emissions, astronomers could pinpoint the location of the source. They found that 3C 273 optically corresponded to a blue, bright star—13th magnitude—that presentday amateur astronomers can easily see with moderate-sized telescopes. Further examination revealed a jet-like structure of radiation coming from the star. Soon, other blue stars were found at the nominal positions of the radio-emitting objects. These were called quasi-stellar radio sources, or quasars. The quasi-stellar refers to the fact that the objects looked like stars, yet normal stars don’t emit large quantities of radio radiation. Plotting the quasars’ spectra showed broad, rollercoaster-like undulations. The broad lines had peaks at wavelengths where normal elements in the laboratory don’t produce emission lines. In 1963, Maarten Schmidt realized that the spectrum of quasar 3C 273 is basically the spectrum of hot hydrogen gas—about 10,000 K—redshifted by 16% (z = 'O/O0 = 0.16)! Only a few galaxies were known at that time with a comparable redshift, and they were very faint and fuzzy (not point-like). If the redshifts of quasars were due to the expansion of the Universe, then they are very distant and incredibly luminous, an amazing conclusion. Earlier, an object (3C 48) had been discovered with a redshift of 0.37, but at the time, its spectrum had not been properly interpreted. In fact, 3C 48 is 16th magnitude and was the ¿rst quasar to be discovered. Why weren’t the spectra of quasars recognized to resemble the spectra of Seyfert galaxies, whose spectra had been obtained back in 1944? Even in the 1960s, few galaxies had been found with such high redshifts, and all of them appeared very faint and fuzzy, unlike the bright, star-like quasars. Moreover, because quasars appeared point-like, astronomers simply assumed that they were unusual stars, not galaxies; there was little reason to consider substantial redshifts. We believe that a quasar is the result of a supermassive black hole, millions or billions of times as massive as the Sun, accreting (devouring) a large amount of gas in the vicinity of its host-galaxy’s nucleus. Prior to entering the black hole, this material can shine profusely at optical and other wavelengths, causing the central region of the galaxy (the quasar) to far outshine the rest 375

of the stars. We also think that such galaxies are billions of light years away. Recall that large redshifts are due to expansion of the Universe and that the larger the redshift, the farther away the object must be. Redshift z = ǻȜ/Ȝ0, which is roughly equal to the speed of recession divided by the speed of light, v/c (for redshifts less than about 0.2). Therefore, the recession speed of quasar 3C 273, where z = 0.16—or 16% of the speed of light—is 48,000 km/s. Plugging this speed into Hubble’s constant, with an assumed value of 71 or 73 km/s/Mpc, we derive its distance as nearly 700 Mpc, or more than 2 billion light years. Ŷ

Important Term active galaxy: A galaxy whose nucleus emits large quantities of electromagnetic radiation that does not appear to be produced by stars. (Radio galaxies are one example of active galaxies.)

Suggested Reading Pasachoff, Astronomy: From the Earth to the Universe, 6th ed.

Lecture 75: Active Galaxies and Quasars

Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Preston, First Light: The Search for the Edge of the Universe. Vershuur, The Invisible Universe Revealed: The Story of Radio Astronomy.

Questions to Consider 1. Why is it useful to ¿nd the optical objects that correspond in position with radio sources?

2. Why did the optical spectra of quasars initially seem so mysterious before the correct interpretation was made?

3. What was the key breakthrough in the interpretation of quasar spectra? What was its signi¿cance?

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Cosmic Powerhouses of the Distant Past Lecture 76

“Soon after the discovery of quasars, some were found with redshifts comparable to, or even exceeding, 1. … If you were to use the formula … you would ¿nd that the speed of recession exceeds the speed of light. … It turns out that you get this incorrect interpretation that something’s moving away faster than the speed of light because you’re not using the correct relativistic formula.”

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he discovery of quasars caused a ¿restorm of activity among astronomers. How could objects with high redshifts appear star-like and bright compared with faint, fuzzy galaxies at similar redshifts? Astronomers began to study this phenomenon in search of answers. In the mid-1960s, no galaxies had yet been found with redshifts as high as those of the highest-redshift quasars. And once we started looking for them, more and more quasars were discovered. Because all known quasars appeared to be associated with blue star-like objects, astronomers began studying such blue objects in search of quasars. Some quasars didn’t emit radio waves yet still had quasar-like spectra and other quasar-like properties. These were called radio-quiet quasars, or quasi-stellar objects (QSOs). We will use QSO and quasar interchangeably in this course. Some quasars were found with redshifts exceeding 1 (z > 1). But in the formula z = v/c (where v is the speed of recession), v exceeds the speed of light, c. v > 1 does not imply speeds faster than light because the approximation z = v/c is reasonably accurate only when v/c d 0.2. Instead, we use the relativistic Doppler formula, z [(1  v / c) / (1  v / c)]  1 , to calculate the nominal speed. However, even this formula is not exactly correct; the redshift is produced by the expansion of space, not by motion through space, and hence, is technically not the Doppler effect. Astronomers quickly realized that quasars provided an incredible look back in time—10 billion years or more—so they began searching for quasars with

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Lecture 76: Cosmic Powerhouses of the Distant Past

large redshifts. New techniques identi¿ed quasars with redshifts exceeding 3 and 4. One technique was to look for objects that appeared to have broad emission lines in a certain type of photographic plate. This technique was used to ¿nd a record holder (Q 1208+1011, with z = 3.8) through the mid1980s. Later, astronomers discovered that at even higher redshifts, quasars appear red instead of blue. Thus, a more advanced technique is to look for objects with peculiar red colors that differ in detail from star colors. The Sloan Digital Sky Survey produces digitized versions of much of the sky and measures the colors of objects. In the southern hemisphere, the Two-Degree Field Galaxy Redshift Survey allows astronomers to ¿nd objects with high redshifts. Today, we have found millions of quasars, and as of mid-2006, the highest redshift for a known quasar was 6.4. Incidentally, astronomers may have recently found galaxies with redshifts greater than 7, giving us a glimpse into the Universe as it was at only 7% of its current age. Quasars appear star-like and smaller than galaxies, yet they emit a very large amount of energy. Just how physically small quasars are became apparent after their apparent brightness was monitored. Quasars vary dramatically in brightness—by factors of up to 100—over both long and short periods of time. This means that they have a small physical size. To illustrate, if an object is 1 light month in radius and intrinsically brightens everywhere instantaneously, we observe the light emitted from its near side one month before we observe the light emitted from its edge (or two months before we observe light emitted from its far side, assuming it is transparent to light). Similarly, an object that is 1 light year in radius will appear to brighten for at least one year. The observed brightening will last even longer if different parts of the object don’t intrinsically brighten simultaneously but, rather, at different times. Thus, the observed-variability time scale sets a minimum physical size for the light-emitting object. Because quasars vary over weeks, months, or years, we know that— physically—they are no larger than light weeks, light months, or light years in size. Yet remember, galaxies are typically more than 10,000 light years in diameter. Thus quasars, which emit 10 to 100 times as much energy per

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second as an entire galaxy, produce this energy in a far, far smaller volume than entire galaxies. Because it seemed unlikely for such small objects to produce so much energy (the so-called energy problem), astronomers wondered if their initial interpretations about quasars were incorrect. Perhaps quasars weren’t as distant as their redshifts seemed to indicate. For example, perhaps quasars were simply blobs of light-emitting material being ejected from the center of our Galaxy. But if that were the case, we would see quasars moving in an angular motion across the sky, which we don’t. Moreover, quasars can’t be ejected from other galaxies because none of them appears to be coming toward us. As we will see below, galaxies in which we ¿nd quasars have the same redshifts as the quasars themselves, proving that the quasars are as distant as their redshifts indicate. “If galaxies are at Barring any new observations to the contrary, the distance that there is overwhelming evidence that quasars their redshifts are very distant and powerful objects. But what indicate, then the can produce such luminosity? Chemical energy quasars in the could not possibly produce such energy in so middle of galaxies small a volume, nor could nuclear energy, nor even supernovae. By the process of elimination, are as well.” astronomers concluded that the central regions of galaxies have supermassive black holes—from a million to several billion solar masses. These black holes swallow, or accrete, gas from their vicinity at a rate of roughly 1 to 10 solar masses per year. This process leads to a tremendous amount of emitted radiation. As gases swirl toward the black hole, an accretion disk forms in which the gas particles collide with each other, transforming their kinetic energy (energy of motion) into radiated light—much as in the x-ray binary stars that we’ve already discussed. More luminous quasars are associated with bigger black holes that accrete faster than smaller ones. This accretion process can turn roughly 10% of the rest mass of material into emitted energy. A spinning black hole and a spinning accretion disk create a natural axis of rotation. By some asyet-unknown process, charged particles are ejected at relativistic speeds

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Lecture 76: Cosmic Powerhouses of the Distant Past

(close to the speed of light) along two oppositely directed jets. In many cases, magnetic ¿elds probably have something to do with the production of relativistic jets. Because the accretion rate is variable—clumps can form in the accretion disk and get eaten by the black hole—different amounts of energy are released at different times, which can lead to the observed variability in brightness. Recent images from the Hubble Space Telescope show that quasars are surrounded by light, generally called fuzz. Spectra of the fuzz surrounding quasars clearly show absorption lines produced by relatively cool atoms in the atmospheres of stars, indicating that the fuzzy light is actually starlight. Thus, quasars are the central regions of galaxies. Quasar activity can be rejuvenated through interactions with other galaxies. Some relatively nearby quasars have other galaxies next to them. Likely, these galaxies gravitationally interact with the quasar galaxies, sending more gas toward the central black hole. This process fuels the black hole, thereby causing the central region to glow brightly again as a quasar. Distant, high-redshift quasars have an abundance of gas surrounding the supermassive black holes. X-ray images reveal their light, which is blocked at optical wavelengths by the surrounding gases. Most quasars are denizens of the distant past, having formed long ago and having used up most of their fuel long ago. Some quasars, such as 3C 273, existed a few billion years ago, but the great majority of quasars are very distant—up to 13 billion light years away. We’re not sure how supermassive black holes could have formed so early in the Universe, but clearly, they did. Quasars fade over time, as the central black holes of galaxies consume the material in their vicinities. They then look like less active galaxies. Eventually, as the accretion disk is depleted of material, the quasar glows less and less, until it disappears and the object looks like a normal galaxy. If quasars fade in this way and if each is just a short stage in the evolution of most galaxies, we conclude that most galaxies have supermassive black

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holes at their centers, which long ago fed on the surrounding accretion disks. If this hypothesis is correct, many—if not most—big, bright, nearby galaxies of today should still have giant black holes in their centers. Our quest, then, is to ¿nd observational evidence for those supermassive black holes. Ŷ

Suggested Reading Begelman and Rees, Gravity’s Fatal Attraction: Black Holes in the Universe. Melia, The Edge of In¿nity: Supermassive Black Holes in the Universe. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Preston, First Light: The Search for the Edge of the Universe. Wright and Wright, At the Edge of the Universe.

Questions to Consider 1. Outline the argument used to infer that the physical size of quasars is very small.

2. Suppose we observe a quasar with a spectral line at 5000 Å that we know is normally emitted at 4000 Å. (a) By what percentage is the line redshifted? (b) By roughly what percentage of the speed of light is the quasar receding? (The non-relativistic formula gives acceptable results, as you can see if you try the relativistic one, too.) (c) At what speed is the quasar receding in km/s? (d) Using Hubble’s law, to what distance (lookback time) does this speed correspond?

3. Does it seem paradoxical that black holes, from which nothing can escape, account for the incredible power of quasars?

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4. What do you think of the hypothesis, favored by a very small minority

Lecture 76: Cosmic Powerhouses of the Distant Past

of astronomers, that quasars are ejected from relatively nearby galaxies and, hence, are not at the distances implied by their redshifts?

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Supermassive Black Holes Lecture 77

“There is strong evidence for the existence of gigantic black holes in the centers of many big galaxies. We will ¿nd that the bigger the bulge … and also the more tightly it’s compressed … those are the ones that tend to have the very biggest black holes. The black hole formation process seems to be linked with the formation process of the bulge.”

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n the previous lecture, we learned that quasars provide evidence for the existence of supermassive black holes in the centers of galaxies. Currently, there is additional strong evidence for the existence of gigantic black holes in the centers of large galaxies. As time passes, a black hole begins devouring all the material in its vicinity, causing the quasar to fade. The galaxy itself then becomes a more normal galaxy, still with a black hole but one whose surroundings no longer shine. Many galaxies probably have intermediate-mass supermassive black holes that weren’t able to devour material quickly; these never became powerful enough to produce genuine quasars, but they still could have been active galaxies. Some active galaxies may have been a lot brighter in the past, with luminous quasars, while others might have been only moderately active, without luminous quasars. The suspicion that many galaxies harbor supermassive black holes came about with the discovery that emission lines from some active galaxies are broad, compared with the more narrow lines in a normal galaxy. The breadth of the lines could be produced by a black hole pulling on the gases, making them move rapidly. However, this evidence is not entirely compelling. After all, stars can explode, ejecting gas very rapidly and giving rise to broad emission lines. Winds from massive stars can also produce broad emission lines. Gas in general is relatively easy to accelerate, creating high-speed (and sometimes chaotic) motions. More compelling evidence for supermassive black holes is the rapid movement of stars in a galaxy’s central region; in fact, only the strong gravitational force of a black hole can move stars at such high speeds. The presence of a rapidly rotating, organized disk of gas also strongly indicates that a supermassive black hole is present.

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The strongest evidence for the presence of supermassive black holes in the central regions of galaxies comes from our own Milky Way Galaxy, toward the constellation Sagittarius. Charles Townes and other astronomers found that the orbital speeds of stars closer to the center of our Galaxy were much faster than the speeds farther away from the center. Plotted on a graph, the speeds of stars correspond to a curve with an inverse-square-root law. Recall from a previous lecture that the rotation speed curve of planets in our Solar System is also an inverse-square-root law—that is, planets closer to the Sun orbit faster than the outer planets. More recently, adaptive optic techniques have shown that the stars are rapidly zipping around a speci¿c point at the center of the Milky Way. One star orbits in just 15 years (reaching a maximum speed of about 5000 km/s at a distance of 125 AU from the central point). An even more extreme example is a star that reaches a speed of about 12,000 km/s at a distance of just 45 AU from the central point. The common central mass derived from these and other rapidly moving The NASA/ESA Hubble Space Telescope stars is about 3.6 million peered into the Sagittarius Star Cloud, solar masses. providing this spectacular glimpse of some of the oldest inhabitants of our galaxy. 384

Hubble Heritage Team (AURA/STScI/NASA/ESA)

Lecture 77: Supermassive Black Holes

So far, the evidence shows that many galaxies have black holes between a million and several billion solar masses. The Hubble Space Telescope has been responsible for providing the best evidence for most of the few dozen galaxies with de¿nitively identi¿ed black holes. One of the most massive black holes known is in M87, the central galaxy of the Virgo Cluster, about 60 million light years away. Spectra of the gas around its nucleus illustrate that the gas is orbiting very quickly, 550 km/s, at a distance of just 60 light years from the galaxy’s center. The black hole has a mass of about 3 billion solar masses.

In addition, the middle of our Galaxy varies in its brightness, another indicator of the presence of a supermassive black hole. This variable brightness suggests that there is an accretion disk around the black hole, which glows at different brightnesses over time as a result of the changing availability of material being devoured. The variable Àaring occurs on a time scale of about an hour, so the Àaring region (presumably the accretion disk) cannot be much larger than 1 light hour across, or about 10 AU. The Schwarzschild radius of a 4-million-solar-mass black hole is about 0.1 AU; thus, the size of the accretion disk is about 100 Schwarzschild radii. This agrees quite well with theoretical expectations. Other galaxies also show evidence of central supermassive black holes. The second-best case (after the Milky Way) is the galaxy NGC 4258, which has a tiny disk of gas in its very central region. Within this disk, the gas clouds produce an intense beam of microwave light—a maser—which is like a laser but at microwave wavelengths. Using special techniques, the gas clouds’ positions and motions can be accurately measured; these measurements show an inverse-square-law relationship for their orbital speed versus their distance from the galaxy’s inferred center. This dominant object, certainly a black hole, has 40 million solar masses, causing the gas clouds to move at 1100 km/s at about 0.4 of a light year from the very center. Our neighboring Andromeda Galaxy, 2.4 million light years away, has a black hole of roughly 140 million solar masses. Interestingly, this galaxy has a concentration of reddish stars in an oblong ring—about 10 light years in diameter—surrounding the nucleus. Immediately around the nucleus, however, the galaxy has an unusual smaller ring (1 light year in diameter) of youngish, blue, hot stars that appear to have formed only 200 million years ago. We don’t yet know how these stars formed so close to a black hole. Let’s look at some other characteristics of supermassive black holes. More massive black holes tend to appear in galaxies with more massive bulges, or nuclear regions, for reasons that we don’t yet fully understand. Also, if the mass of the bulge is spread out, the black hole is less massive; if that mass is concentrated toward the center, the black hole is larger. The black holeversus-bulge correlation indicates that there is a fundamental connection between the growth of galactic bulges and supermassive black holes. 385

Lecture 77: Supermassive Black Holes

There may be a correlation between black holes and globular clusters, although this hypothesis remains controversial. Some astronomers support this hypothesis, believing that the largest globular cluster orbiting the Andromeda Galaxy has a 20,000-solar-mass black hole at its center. However, others think that this globular cluster is actually a galaxy being swallowed by Andromeda and that the black hole formed in this small galaxy long ago. Some astronomers believe that globular cluster M15, in our own Galaxy, has a black hole of 1700 solar masses. However, the motion of stars in the central region could also indicate the presence of a cluster of dead neutron stars. Some star clusters vary so much at x-ray wavelengths that it is possible they have an accretion disk surrounding a comparatively massive object (500 solar masses) in the center. Many of these clusters might actually contain a stellarmass black hole, perhaps having 5 to 10 solar masses, stealing material from a companion star. A 500-solar-mass black hole is big compared to a typical stellar mass, and we don’t expect such massive stars to form. However, some of these objects may really be 500-solar-mass black holes—known as intermediate-mass black holes (larger than the stellar-mass variety but smaller than the supermassive black holes found in the centers of galaxies). They may have started out as smaller, stellar-mass black holes but then grew due to gravitational collapse of the central regions of star clusters. If star clusters do have intermediate-mass black holes and the clusters subsequently merge, they form an even bigger black hole. The merging of black holes should give rise to the emission of gravitational waves. Thus, if supermassive black holes merge, we should be able to detect their radiation using gravitational-wave detectors. We mentioned LIGO (Laser Interferometer Gravitational-Wave Observatory) in Lecture 66; this facility is attempting to detect gravitational waves from supernovae and merging binary neutron stars. The Laser Interferometer Space Antenna (LISA) is another project that has a larger baseline than LIGO and is planned to go online in the next decade or two. LISA will measure gravitational waves and, possibly, the coalescence of supermassive black holes in galactic nuclei. Ŷ

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Suggested Reading Begelman and Rees, Gravity’s Fatal Attraction: Black Holes in the Universe. Ferguson, Prisons of Light—Black Holes. Melia, The Edge of In¿nity: Supermassive Black Holes in the Universe. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Wright and Wright, At the Edge of the Universe.

Questions to Consider 1. Summarize what generally happens to a quasar as it ages. 2. Suppose no nearby galaxies exhibited evidence for the presence of supermassive black holes in their centers. Would this be a problem for the hypothesis of what powers quasars?

3. Explain how we deduce the presence and measure the mass of a supermassive black hole in the center of a galaxy.

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Feeding the Monster Lecture 78

“We have seen that even a quiescent black hole has the chance of being reborn if a new supply of fuel is somehow pushed toward the central region where the black hole exists.”

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Lecture 78: Feeding the Monster

he evidence for the existence of supermassive black holes in the centers of many galaxies is now very strong. But why do black holes have relativistic jets of gas shooting out from their vicinity? Recall that supermassive black holes have accretion disks and pull stars toward them at tremendous speeds with their strong gravitational ¿elds. Astronomers call such black holes “monsters”; thus, as a black hole swallows material, we call this “feeding the monster.” Quasars are the most extreme evidence of this “feeding” activity. But we have seen that even less active supermassive black holes can be rejuvenated by new fuel in their vicinity, perhaps supplied through gravitational interactions with another galaxy. The merging of galaxies can eventually create an even larger central black hole. Even non-merging galaxies can experience a surge in activity if, for example, the central black hole tidally disrupts a nearby star, tearing the star apart and creating new material for the black hole to feed on. The Chandra X-Ray Observatory and the ROSAT x-ray telescope have uncovered evidence of such Àares. They seem to occur somewhere in the sky a few times per decade—consistent with how often we would expect a star to become tidally disrupted. Material escaping from the vicinity of a black hole often travels very rapidly along a highly collimated, or highly focused, jet. Though we don’t fully understand the mechanics, it’s possible that magnetic ¿elds in the accretion disk channel material along the axis of rotation—also the axis of the magnetic ¿eld—causing this tight focusing of jets, similar to what is observed in pulsars. However, the jets from a black hole don’t create the pulsating lighthouse effect that pulsars do, because the direction of ejection remains relatively constant as viewed by us. In some cases, perhaps the collimation is aided by a thicker accretion disk, forming a nozzle along which material is ejected. The narrower the nozzle, the more highly focused 388

is the jet. A tidally disrupted star can also contribute to the accretion disk and, therefore, to the jet as well. Indeed, we have seen cases in which a more extended jet appears following the Àare-up of an active nucleus. Let’s discuss in more detail the evidence for accretion disks and jets, as well as the formation of these collimated jets. In general, most galaxies with disks spin. As material nears the black hole, its spin rate increases as a result of the principle of conservation of angular momentum. Actual evidence for the presence of accretion disks has been hard to ¿nd, but we can look at the spectra of gases for clues. In some cases, the pro¿le of an emission line shows bumps corresponding to both redshifted and blueshifted gases, indicating a spinning disk. One side of the disk is moving away from us (redshift), while the other side is moving toward us (blueshift). More direct evidence for disks shows up at x-ray wavelengths, which allow us to peer closer into a galaxy’s center, where speeds are higher, gases are more compressed, and the gravitational “Some combination of ¿eld is stronger. X-ray astronomers have found evidence that gas in the very magnetic ¿elds and a central regions of some galaxies moves physical obstruction … almost at the speed of light. The gas is so is thought to occur in close to the black hole that its spectrum these objects with jets.” is gravitationally redshifted. If gas is orbiting a spinning black hole and the black hole drags space around it (as described in an earlier lecture), then the gas can glow even more brightly. If space weren’t dragged around a black hole, the gas would glow less brightly. Not only does a supermassive black hole have a rapidly spinning accretion disk, but it also has emerging jets of gas. These jets can actually appear to move faster than the speed of light—superluminal motion. We can determine this movement by measuring clumps, or blobs (knots), in the jets, whose distance from the black hole increases over time. One explanation for the apparent speed is that the blobs are really different materials Àashing on and off at different times but appearing to be one object moving rapidly through space. Another similar model suggests that the observed blobs are actually produced by a beam of light hitting some kind of cosmic screen and appearing to move faster than the speed of light. The most likely explanation for superluminal motion is 389

the creation of an optical illusion by the motion of relativistic particles in a direction nearly, but not exactly, along the light of sight. In other words, the blobs appear to move faster than the speed of light, but really, our viewing angle creates this illusion.

Lecture 78: Feeding the Monster

Quasars can be powerful probes of the matter that exists in the vast distances between Earth and them. A quasar at redshift 3, for example, emits light that travels a great distance, passing through clouds of gas and other galaxies or through galaxies that are still forming. On its way through that gas, some of the quasar’s light is absorbed. Even if we can’t see these other objects, the quasar’s spectrum will reveal them in absorption lines. Low-redshift quasars may show only a few absorption lines because there is naturally less material between Earth and relatively nearby quasars. Conversely, high-redshift quasars will show numerous absorption lines because of the presence of much more material between Earth and distant quasars. As an example, consider a distant quasar with absorption lines produced by neutral hydrogen, in which electrons are moving from the ¿rst to the second energy level. That process absorbs an ultraviolet photon with a rest wavelength of 1216 angstroms. But the absorption lines appear in the spectrum at other wavelengths, corresponding to intervening clouds of gas at various redshifts. Recall the phenomenon of gravitational lensing, which was ¿rst discovered through the observation of two closely spaced quasars whose spectra looked identical. Because no two quasars are alike, this evidence suggested that the two apparent quasars were actually one quasar whose image had been projected twice. The theoretical model made for this particular quasar suggested that the galaxy causing the gravitational lensing was not exactly collinear with the quasar and Earth. Thus, the two images of light had been bent at different angles. Ground-based photographs showed that the galaxy was closer to one image of the quasar than to the other. Hubble Space Telescope photographs also showed that although one galaxy produced most of the lensing, the quasar is actually lensed by a cluster of galaxies. Therefore, we must include the gravitational ¿eld of a galaxy cluster as a whole in order to understand the details of a particular gravitational lens.

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© Digital Vision/Thinkstock

When a misaligned galaxy lenses a quasar into four images, we see a quad, sometimes also known as an Einstein cross, of which we have found many. In many cases, up to ¿ve images of a quasar are actually produced, although the ¿fth one tends to be much fainter than the others and projected on the lensing galaxy. Active galaxies and quasars are truly exciting phenomena that can teach us much about the Universe. Ŷ

A quad, sometimes known as an Einstein Cross.

Suggested Reading Begelman and Rees, Gravity’s Fatal Attraction: Black Holes in the Universe. Cohen, Gravity’s Lens: Views of the New Cosmology. Ferguson, Prisons of Light—Black Holes. Melia, The Edge of In¿nity: Supermassive Black Holes in the Universe. Pasachoff, Astronomy: From the Earth to the Universe, 6th ed. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. `

Questions to Consider 1. Why doesn’t gas generally fall directly into a black hole, instead forming an accretion disk?

2. Is the apparent “superluminal motion” of blobs in a quasar jet a violation of the predictions of Einstein’s special theory of relativity?

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3. Describe how quasars can be used as probes of matter between us and them.

4. How would the presence of dark matter affect the gravitational lensing

Lecture 78: Feeding the Monster

of a quasar?

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The Paradox of the Dark Night Sky Lecture 79

“A deceptively simple question: Why is the sky dark at night? You might say, because the Sun has set … but all those stars are distant suns. … Their combined brightness should far exceed the brightness of our Sun visible during the daytime sky. Not only should the night sky be bright, but the daytime sky should be much, much brighter than it is.”

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e now enter the second unit of the third major section of this course, cosmology—the study of the structure and evolution of the Universe as a whole, its age, shape, size, and future. We begin by asking a deceptively simple question: Why is the night sky dark? It may seem silly, but this question actually has profound implications for the nature of the Universe. There are a number of possible reasons why the sky is dark. Yes, at night, the Sun disappears below the horizon, but the cumulative brightness of all the stars should far exceed the brightness of our Sun visible during the daytime. Thus, not only should the night sky be bright, but the daytime sky should be much brighter than it is. We will initially assume that the Universe is not expanding. In addition, we will assume that the Universe is in¿nitely old, in¿nitely large, and uniformly ¿lled with stars—on average, every place in the Universe has about the same density of stars. If the Universe is in¿nite in size and age and there is an in¿nite number of stars, every line of sight should eventually intersect a star. By analogy, when looking through an in¿nite forest, every line of sight intersects a tree. Therefore, the collective light from all these stars should make the sky at least as bright as the surface of the Sun, a typical star. Although distant stars appear dim according to the inverse-square law of light, their angular area is also inversely proportional to the square of the distance. The linear angle subtended by an object decreases with increasing distance, so its angular area decreases with the square of the distance. Therefore, the surface brightness of a star (its apparent brightness per unit of angular area) is independent of distance, again meaning that the night sky should be very bright.

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Lecture 79: The Paradox of the Dark Night Sky

Why isn’t the night sky bright? This paradox was considered for a long time by such notable scientists as Kepler and Newton. But it wasn’t until the mid19th century that Wilhelm Olbers (17581840) emphasized how profound this concept really is. Olbers’s paradox implies that at least one of our key assumptions about the Universe must be wrong, a profound conclusion. Though we may not know exactly which of the assumptions is incorrect, we can rule out some hypotheses. We know that dust cannot be responsible for blocking so much light because in an in¿nitely old Universe, the dust would heat up so much that it would either glow brightly or completely evaporate. The paradox cannot be blamed on dark matter because that would require so much of it that we would know about its presence in other ways. The most likely explanation is that the Universe is relatively young. Though its estimated age—about 14 billion years—seems old, it’s still too young to have allowed enough time for light from the most distant stars to reach Earth. Thus, we ¿nd many gaps in between them. In a roughly 10-billion-year-old Universe, we can see only 10 billion light years away in every direction. If we were to see out to a distance of about 1023 light years, then the gaps would ¿ll in and we would see stars everywhere. Light from those very distant stars and galaxies has not had time to reach us. The more years that pass, the more of the Universe we see, and the more stars appear in the sky as their light ¿nally reaches us. In addition, because the Universe is expanding, the light from distant galaxies has been redshifted out of our visible window. However, this effect does not adequately explain the paradox, and by far, the more important factor right now is that the Universe is not in¿nitely old. Is the Universe getting brighter? The answer is both yes and no. It is getting brighter with time because we see more and more stars. But at the present time, by far, the dominant contribution to the electromagnetic radiation—the photons in the Universe—comes from the afterglow of the Big Bang, called cosmic microwave background radiation. This background radiation is fading because of the expansion of the Universe and the associated loss of energy, though the starlight contribution is actually growing. How do we know that the Universe is 14 billion years old? One way to estimate the age of the Universe is to say that it must be at least as old as the oldest objects within it. The oldest well-formed objects are globular clusters, 394

whose ages we’ve determined with a reasonable amount of certainty—that is, 12 to 13 billion years old. The Universe could be much older, but we have yet to ¿nd discrete objects older than globular clusters. The ¿rst few generations of stars seem to have occurred before the birth of the globular clusters, possibly preceding them in time by up to 1 billion years, which is why we estimate the Universe’s age at 14 billion years. We know the ages of globular clusters by looking at how long it takes stars of various initial masses to leave the main sequence. Recall the temperature-luminosity (HertzsprungRussell) diagram from Lecture 44. We know approximately how long stars remain on the main sequence, so we can estimate the age of a star cluster by measuring its main-sequence turnoff point. We can also estimate the ages of white dwarfs, retired stars, from their observed dimness. Though we have some ballpark estimate of the Universe’s age based on its oldest objects, our evidence is not completely compelling because there could have been older objects that were wiped out or disappeared because of some cataclysm. “Whatever is the solution to Olbers’s Another way of determining the age of the Universe is to look at the expansion age. paradox, it must be We can extrapolate all the galaxies’ recession something profound from one another backward in time and arrive about our Universe.” at a point when all the material of which they are made was basically in the same place. This place wasn’t necessarily the center of the Universe, because that may be in a different dimension, but at least the density of material was high. If the expansion speed (v) of a given galaxy is constant, then the distance (d) it travels equals speed multiplied by time (t): d = vt. In addition, we know Hubble’s law, v = H0d. If we divide by H0, we get d = v(1/H0). We can denote 1/H0 by T0. Thus, d = vT0 resembles d = vt. Because the two equations have the same mathematical form, we can equate the inverse of the Hubble constant, T0, with the expansion age of the Universe if it has been expanding at a constant speed. T0, the inverse of the Hubble constant, is therefore, the time over which the galaxies have been receding from one another, if at constant speed. However, because of gravity, we would expect the Universe to be slowing down with time. If the Universe had been expanding more quickly in the past, then the total time it has taken

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to reach its current size is less than the time calculated by simply taking the inverse of the Hubble constant. In a decelerating Universe, t0 < T0, where the symbol t0 denotes the present age of the Universe. If H0 = 50 km/s/Mpc, the maximum age of the Universe is 20 billion years. If H0 = 100 km/s/Mpc, the maximum age of the Universe is only 10 billion years. By knowing the current value of the Hubble constant and the expansion history of the Universe, we should be able to determine how much time has passed since the Big Bang. In the next lecture, we will do that. Ŷ

Important Terms cosmic microwave background radiation: Radio electromagnetic radiation that was produced in the hot Big Bang. It now corresponds to T | 3 K because of the expansion and cooling of the Universe.

Lecture 79: The Paradox of the Dark Night Sky

expansion age: The time estimated for the age of the Universe since the Big Bang, determined by measuring the rate at which galaxies are receding from one another; currently thought to be about 13.7 billion years. Olbers’s paradox: The dark night sky; simple arguments suggest that it should be very bright.

Suggested Reading Ferris, Coming of Age in the Milky Way. Harrison, Cosmology: The Science of the Universe. ———, Darkness at Night: A Riddle of the Universe. Lightman, Ancient Light: Our Changing View of the Universe. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

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Questions to Consider 1. Are you convinced that Olbers’s paradox really does present a problem whose main possible solutions are profound?

2. Can you think of any other solutions to Olbers’s paradox, besides those discussed here?

3. What are two ways of estimating the age of the Universe?

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The Age of the Universe Lecture 80

“Galaxies have been expanding away from each other, and if we know the current rate at which they are receding from one another, and we know the history of that expansion rate, we can calculate the expansion time, the time since the Big Bang.”

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Lecture 80: The Age of the Universe

n the last lecture, we learned how astronomers estimate the age of the Universe by measuring its expansion time since the Big Bang. Let’s review this concept. Throughout time, galaxies have been receding away from one another because of the expansion of space. If we know the current recession rate, as well as the historical rate, we can calculate the expansion time—that is, the time since the Universe began with the Big Bang. Any two galaxy clusters are separated by some distance, but in general, all of them recede from one another by the same factor in some amount of time. If this expansion speed has been constant, then the expansion time is simply the inverse of the Hubble constant (1/H0). If galaxies recede at a constant speed, then their distance apart grows linearly with time, beginning at time zero to the current time; that time difference is denoted by T0. Age = T0 = 1/H0. Remember that H0 has units of inverse time—kilometers per second per megaparsecs (km/s/Mpc). Because kilometers and parsecs are both units of length, when we divide them, the lengths cancel each other out, though we need to keep track of unit conversion factors. Properly correcting for conversion factors, if H0 = 50 km/s/Mpc, the reciprocal would be 20 billion years, or 20 gigayears (Gyr). If H0 = 100 km/s/Mpc, the Universe is expanding twice as quickly, and the reciprocal is only 10 Gyr. The greater the Hubble constant is, the younger is the Universe. If the expansion slows down with time because all galaxies exert a gravitational pull on each other, then the speed of recession of a given galaxy decreases with time. Thus, the true age of the Universe would be less than T0, or less than 1/H0. More speci¿cally, the Universe would be only about 2/3 of H0 in the scenario historically preferred by theorists (to be discussed in 398

more detail later). If H0 = 50 km/s/Mpc, then T0 § 20 Gyr, or t0 § 13 Gyr (2/3 of 20). If H0 = 100 km/s/Mpc, T0 § 10 Gyr, or t0 § 7 Gyr. If H0 = 71 km/s/ Mpc —which appears to be roughly correct—then T0 § 14 billion years, or t0 § 9 Gyr. To get a close approximation for the age of the Universe, we need to know the present-day value of the Hubble constant, H0, but arriving at this value has not been easy. Throughout the 1970s and 1980s, many astronomers tried to measure H0, but each arrived at different values. One of the leaders, Allan Sandage, used many different methods to measure H0, arriving at what seemed to be reliable values. For many years, Sandage’s best value was 50 km/s/Mpc, which would make the Universe somewhere between 13 and 20 Gyr old. This “This was one of seemed roughly consistent with the ages of the the key reasons globular clusters, which had been thought to be 14 to 17 billion years old, but only if there was that the Hubble little or no deceleration of the expansion. Space Telescope was built … to take Another astronomer, Gerard deVaucouleurs, the measure of obtained a value closer to 100 km/s/Mpc; thus, the maximum age of the Universe would be 7 the Universe.” to 10 Gyr, inconsistent with the inferred ages of the globular clusters. Clearly, either our measurements or our assumptions were faulty. Later, we more accurately determined that the globular clusters were younger than we had thought— about 12 to 13 Gyr old. To arrive at a value for H0 (a constant of proportionality), we must ¿rst determine the recession speeds of galaxies by measuring the redshift of the galaxies’ spectra. Also, we must know the distances of galaxies, which are much harder to determine. One method is to measure the apparent angular size of an object of constant physical size, but this is dif¿cult. For example, even galaxies at the same distance can differ in physical size; galaxies span a wide range of sizes. How, then, do we know if an apparently smaller galaxy is farther away than a larger galaxy, or if it’s simply physically smaller?

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We can determine distances more accurately by measuring the apparent brightnesses of objects having a known luminosity. If we know L (luminosity) and measure the apparent brightness (b) of an object, then according to the inverse-square law, b = L/(4ʌd2), we can determine the object’s distance (d). For this technique to work, we must know the luminosity, L, for a certain class of objects. If the value of L is always the same, or nearly the same, among members of this class, then we call such objects standard candles. For example, we know the distance of the star Betelgeuse in the constellation Orion, and from its apparent brightness, we can, therefore, calculate its luminosity, L. Then, we measure the apparent brightness of a physically similar star in a galaxy of unknown distance and solve for the star’s distance using the inverse-square law of light. This also gives us the distance of the galaxy to which the star belongs.

Lecture 80: The Age of the Universe

Cepheid variables were historically used as standard candles because we know their period-luminosity relationship, and they have an easily recognized light curve. As discussed in Lecture 69, measuring the period of the Cepheid’s light curve, we can get the Cepheid’s average luminosity from the period-luminosity relationship. Measuring the Cepheid’s average apparent brightness and comparing with the average luminosity, we can then derive the Cepheid’s distance and, hence, the distance of the galaxy to which it belongs. The Hubble Space Telescope was built, in part, to measure Cepheid light curves in relatively distant galaxies, allowing us to determine the distances of the galaxies. In 1994, the ¿rst Hubble Space Telescope measurements of Cepheids were made in a few galaxies—one in particular—and these were compared to their distances, allowing astronomers to get a tentative value for H0. Provisionally, H0 had been said to equal 80 km/s/Mpc, considerably larger than Sandage’s value (50) but somewhat smaller than de Vaucouleurs’s value of roughly 100. The Universe, therefore, would be between 8 and 12 billion years old—12 if it hasn’t been slowing down and 8 (2/3 of 12) if its rate of slowdown were equal to the theoretical preference. In 1994, we thought globular clusters were 14 to 17 billion years old, which would have meant that globular clusters were older than the Universe itself. This crisis shook the astronomical community!

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NASA

One problem, even with the Hubble Telescope, is that Cepheids are not easily visible in very distant galaxies. Cepheids are more visible in nearby galaxies, such as those in the Virgo Cluster. However, the Milky Way Galaxy and our entire Local Group pull gravitationally on the Virgo Cluster; thus, it isn’t receding from us as quickly as it should be. Furthermore, we don’t know the masses of the galaxies nor exactly how much they are slowing one another down. Thus, in order to get a more reliable value for H0, we need to use a very distant galaxy whose recession speed is dominated by the expansion of the Universe and not affected by the random gravitational inÀuences of our own Galaxy and others. Unfortunately, we cannot clearly see Cepheid variables in distant galaxies, so their use as a standard candle is limited.

Supernova remnant N63A is a member of a star-forming region in the Large Magellanic Cloud.

More luminous standard candles are Type Ia supernovae, whose peak luminosity is extremely high—nearly 1010 solar luminosities. They can be seen at very great distances. If we measure the peak brightness of a nearby Type Ia supernova that occurs in a galaxy of known distance (that is, near enough to use Cepheids to determine the galaxy’s distance and, hence, the supernova’s distance), then we can determine the supernova’s luminosity by using the inverse-square law of light. Type Ia supernovae should be nearly standard candles because these exploding white dwarfs should have roughly the same mass (recall the Chandrasekhar limit from Lecture 54). Even though they don’t all have exactly the same peak luminosity, we can account 401

for the discrepancy by recording how they fade. The more luminous Type Ia supernovae produce more radioactive nickel, whose decay makes the ejected gases hotter and causes them to become more opaque, increasing the time interval over which energy leaks out. We also must account for dust that might obscure a supernova’s light. We do this by measuring how much the supernova has been reddened (selectively extinguished at blue wavelengths compared with red wavelengths). This reddening effect differs from the redshift produced by the expansion of space. When we measure the distances of galaxies using supernovae, we ¿nd that H0 = 72 ± 7 km/s/Mpc. Combining this value with the history of the expansion rate (to be discussed in an upcoming lecture), the derived expansion age of the Universe is about 13.7 billion years. We now think that the globular clusters are only 12 to 13 billion years old, which makes more sense. There is no longer any apparent discrepancy between the expansion age of the Universe and the age of its oldest inhabitants. But astronomers must continue their studies to see whether the ages of globular clusters and the expansion age of the Universe remain consistent as new data are gathered and interpreted. Ŷ

Lecture 80: The Age of the Universe

Name to Know Sandage, Allan (1926 ). American astronomer and disciple of Edwin Hubble, he has made fundamental contributions to the determination of globular cluster ages, the distances of galaxies, the Hubble constant, the age of the Universe, and the rate at which the expansion of the Universe is changing.

Suggested Reading Ferris, The Whole Shebang: A State-of-the-Universe(s) Report. Goldsmith, Einstein’s Greatest Blunder? The Cosmological Constant and Other Fudge Factors in the Physics of the Universe. Hogan, The Little Book of the Big Bang: A Cosmic Primer.

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Overbye, Lonely Hearts of the Cosmos: The Story of the Scienti¿c Quest for the Secret of the Universe. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Silk, A Short History of the Universe.

Questions to Consider 1. Suppose the expansion rate of the Universe were increasing (rather than decreasing) with time for some reason. Would the true expansion age be less than or greater than T0?

2. Describe how the current value of Hubble’s constant is measured. Why can relatively nearby galaxies give erroneous values?

3. Do you think the derived ages of globular clusters could be way off?

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When Geometry Is Destiny Lecture 81

“The expansion rate as a function of time is intimately tied to the global, or overall, geometry of the Universe. Those, in turn, are intimately tied to the ultimate fate of the Universe.”

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Lecture 81: When Geometry Is Destiny

e believe that we have reliably determined the age of the Universe—roughly 14 billion years. Now, we will look at the overall (global) geometry of the Universe and discuss its implications. Recall that to derive the Universe’s age, we need to know both the current expansion rate, or Hubble constant (H0), and the history of the expansion rate. This expansion rate as a function of time and the ultimate fate of the Universe are intimately tied to the overall geometry of the Universe, at least in the simplest models. Mathematically, the best way to treat the entire Universe (encompassing all of its mass and energy) is to use Einstein’s general theory of relativity. To simplify the calculations, we also must make some justi¿ed assumptions about the Universe. Two fundamental assumptions (which make up the cosmological principle) are needed, in addition to the assumption that the general theory of relativity is the correct, most valid theory for the large-scale properties of the Universe. The ¿rst assumption is that the Universe is homogeneous; it has the same average density everywhere, regardless of localized lumps. That is, averaged over suf¿ciently large volumes, the density of the Universe is the same everywhere. The second assumption is that the Universe is isotropic; it looks the same in all directions. There is no preferred axis of rotation, for example, and the galaxies are not all aligned in the same direction. The cosmological principle may seem manifestly incorrect, but because we apply it to the largest scales—the clusters of galaxies, stars, and voids averaged over regions hundreds of millions of light years in diameter—we ¿nd that the Universe is roughly homogeneous and isotropic. On large scales, the evidence for the principle is that the largest obvious structures in the Universe are superclusters of galaxies. There are superclusters and voids, but beyond that, superclusters don’t group much. If we average over progressively larger volumes, we come to a progressively better approximation of the Universe 404

as uniform. The average density of the Universe can change with time and still be consistent with the cosmological principle, as long as, at any given time, it looks homogenous and isotropic. Another assumption we make, at least temporarily, is that there are no longrange forces other than gravity. A proton and an electron separated by 1 billion light years, technically, will “feel” each other. But because most matter is electrically neutral, only on small scales are electromagnetic forces typically strong. Only gravity acts on large scales. In 1917, Einstein introduced the idea of a repulsive effect—working against gravity—which he called the cosmological constant. At that time, the Universe was thought to be static, neither expanding nor contracting. Edwin Hubble had not yet discovered the general recession of galaxies. Because the galaxies and stars gravitationally pull on one another, the Universe should theoretically be collapsing in on itself. To prevent “the sky from falling,” so to speak, Einstein reluctantly introduced his cosmological constant. He didn’t know its physical origin— only that this effect was big enough to counterbalance the attractive force of gravity. Einstein didn’t like the cosmological constant because it made his equations messier, less aesthetically pleasing. Moreover, there was no laboratory evidence for such an effect, and it implied that the vacuum has an energy density that is nonzero. In addition, the strength of this repulsive effect had to be exactly equal to the strength of gravitational attraction, but in the “Einstein didn’t need opposite direction. This seemed unlikely. A dozen years later, Hubble discovered this cosmological that the Universe is expanding rather constant. … He than static, making the cosmological renounced it, and in constant unnecessary. fact, anecdotally, he called it the ‘biggest After the publication of Einstein’s general theory of relativity, Russian astrophysicist blunder of his career.’ ” Alexander Friedman came up with three possible geometries and two possible fates for the Universe. The three possible geometries (together with their fates) depend on the average density of matter and gravitationally attractive energy. 405

Lecture 81: When Geometry Is Destiny

We de¿ne Omega matter (:M) as being equal to the ratio of the average density of the Universe (Uave) to the critical density of the Universe (Ucrit), or :M = Uave/Ucrit. The critical density is given by Ucrit = 3H02/(8SG). Its value varies with time because of the changing Hubble constant. Currently, Ucrit = 9.5 u 1030 g/cm3, equivalent to the presence of just 6 hydrogen atoms per cubic meter. Thus, whether a cubic meter has fewer than 6 or more than 6 hydrogen atoms dictates the geometry and fate of the Universe! This dependence on whether the result is slightly more or less than 6—and we know that we’re somewhere near this critical density—shows just how empty most of the Universe is. If the average density exceeds the critical density—that is, ȍM> 1—then the expansion will ultimately stop and reverse, ending in a Big Crunch; the density of the Universe is so great that it will pull the material back in. If the average density equals the critical density, ȍM = 1, then the expansion will eventually stop (at time t = in¿nity) but will not quite turn back to re-collapse. If the average density is less than the critical density, ȍM< 1, then the expansion will slow with time, but it will not come to a complete stop at t = in¿nity; the gravitational attraction between galaxies is not enough to completely halt the expansion. Let’s consider the global geometry implied by these three possibilities of density. Where ȍM = 1 (average density equals critical density), the Universe is described by the laws of Euclidean geometry. In particular, Euclid’s ¿fth postulate (the parallel postulate) is satis¿ed: For a given line and a point not on that line, there is only one parallel through the point that is parallel to the line. Such a universe must be in¿nite in volume, in its simplest form, though mathematicians have found spatially ¿nite versions as well. It expands forever, but just barely; it will come to a complete stop at t = in¿nity, but of course, in¿nite time is never actually reached. Where ȍM > 1 (average density exceeds critical density), the Universe must be described by spherical geometry (positive curvature). For any given line and a point not on that line, there are no parallel lines that can be drawn through the point; Euclid’s ¿fth postulate is violated. This universe has a ¿nite, or closed, volume; it wraps around itself with no boundaries or edges. Such a universe begins hot and dense in the Big Bang, expands and becomes cooler, and then re-collapses (the Big Crunch) into a hot, dense state. Where ȍM < 1 (average density is less than critical density), the universe has negative curvature—hyperbolic geometry. For any given line and a point not on that line, there are in¿nite 406

parallels to the line; Euclid’s ¿fth postulate is again violated. The simplest case of a hyperbolic universe is in¿nite in volume, though there are certain cases where it could be ¿nite. This universe expands forever, and the speed of a given galaxy approaches some constant greater than zero as t moves toward in¿nity. To visualize the geometry of these three possible universes, it helps to use analogues in two dimensions, embedded in our three-dimensional space. The ¿rst case, a Àat universe, is like an in¿nite sheet of paper. But the real universe would have three dimensions instead of two. In the second scenario, a two-dimensional analogue is a sphere like the rubber of a balloon, or the surface of the Earth, wrapped around a third mathematical (but not physically accessible) dimension. In three dimensions, such a universe is a hypersphere wrapped around a fourth inaccessible dimension. The third scenario might look like a horse’s saddle or potato chip to some extent, though this particular analogue does present a problem with isotropy. Again, in three dimensions, space would curve around a fourth (inaccessible) dimension. Given these three possible universes, according to Alexander Friedman and subsequent physicists, our challenge is to ¿gure out which sort of universe we live in. Ŷ

Important Terms closed universe: A universe having ¿nite volume. cosmological constant: In Einstein’s general theory of relativity, a term (/) that produces cosmic repulsion that can counterbalance the attractive force of gravity. Recent evidence suggests that its value is nonzero and somewhat larger than originally postulated by Einstein, causing the observed acceleration of the Universe’s expansion. cosmological principle: The Universe is homogeneous and isotropic (that is, uniform) on the largest scales. critical density: The average density of the Universe if it were poised exactly between eternal expansion and ultimate collapse, if the cosmological constant is zero.

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Àat (critical) universe: A universe in which the laws of Euclidean geometry hold. homogeneous: The same (density, temperature, and so on) at all locations. open universe: A universe whose volume is in¿nite.

Suggested Reading Harrison, Cosmology: The Science of the Universe. Hawking, The Universe in a Nutshell. Hogan, The Little Book of the Big Bang: A Cosmic Primer. Osserman, Poetry of the Universe. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Silk, A Short History of the Universe.

Questions to Consider

Lecture 81: When Geometry Is Destiny

1. Discuss why ȍM, the ratio of the average matter density to the critical density of the Universe, is such an important parameter.

2. Given that humans, the Earth, our Solar System, our Galaxy, and our Local Group all have densities in excess of the Universe’s critical density, why don’t they collapse?

3. Which prospect do you ¿nd more depressing: eternal expansion or the ¿ery Big Crunch? Or perhaps you ¿nd neither one depressing—all things must die, and the Universe is no exception.

4. Can you visualize what our Universe might look like if it’s the threedimensional analogue of the two-dimensional surface of a balloon?

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The Mass Density of the Universe Lecture 82

“A dense Universe that has a lot of galaxies per unit volume pulling on each other is positively curved, like a sphere, and must re-collapse … ending in ¿re. … A lower-density Universe—one whose average density is equal to a critical value called the critical density—must be Àat, like a Euclidean sheet of paper, and must expand forever. … That Universe becomes cold, and dilute, and dark—in a sense, ending in ice.”

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n the previous lecture, we learned that the average mass density of a uniform, homogeneous, isotropic universe determines not only its overall geometry but also its ultimate fate. Let’s examine how we determine the average density of matter and compare it with the critical density. It is dif¿cult to measure the average density of the Universe because when we look into space, we see clusters of galaxies, voids, and superclusters. How do we know what is representative, and how do we look over a big enough volume to measure every galaxy? How do we know how much dark matter there is? One method of measuring the average density and, hence, the global geometry of the Universe is to compare the current expansion rate with the past expansion rate and calculate the change over time. Measuring the historical expansion rate is dif¿cult because we must look back to very large distances, which are hard to measure accurately. Another method is to look at the Universe’s geometric properties directly. For example, we could ¿re two laser beams and see if they ever meet. If they do, we live in a positively curved universe; if they don’t, we live in a Àat or negatively curved universe. Obviously, this particular method isn’t practical because we can’t follow the laser beams to in¿nity to see if they ever meet. We could also look at the Universe’s geometrical properties by constructing triangles and seeing whether their interior angles add up to 180 degrees, as required in the case of Euclidean geometry. If we draw a triangle on a sphere, its interior angles always add up to more than 180 degrees. In the horse’s saddle analogy—a negatively curved universe—the angles add up to less than 180 degrees. Both results violate the laws of Euclidean geometry. Recently, this method has been used to determine the overall geometry of 409

Lecture 82: The Mass Density of the Universe

the Universe, as will be discussed in a subsequent lecture. Another way of probing the Universe’s geometrical properties is to count the number of galaxies within a volume having progressively greater radius (distance). In a Àat universe, we would encounter progressively more galaxies in proportion to the square of the distance from our point of origin. At twice the distance, there would be four times as many galaxies within the volume. In a positively curved universe (or hypersphere), as distance increases from the point of origin, the total number of galaxies would also increase but more slowly than in proportion to the square of the radius. In a negatively curved universe (analogous to a horse’s saddle), as distance increases, we would see more galaxies at a rate greater than in proportion to the square of the radius. This technique is dif¿cult to apply in practice because galaxies evolve with time, changing their luminosity and sometimes merging. Yet another geometric method is to measure the angular size of a galaxy as a function of its distance. In Àat space, the angular size of a galaxy of known physical extent is inversely proportional to its distance. In positively curved space, the angular size does not decrease as quickly. In fact, a distant galaxy can, in principle, look just as big as a nearby galaxy under some circumstances. In a negatively curved space, distant galaxies look even smaller with increasing distance than they do in Àat space. This technique is, once again, dif¿cult to apply in practice because galaxies evolve with time, changing their physical size. We can also observe the apparent brightness of an object and see how it changes as a function of distance. In Àat space, the object would dim with increasing distance according to the inverse-square law of light. In positively curved space, the object would dim more gradually than expected from the inverse-square law. Under some circumstances, extremely distant objects might, in principle, even grow brighter with increasing distance as their light rays converge rather than diverge. In negatively curved space, the light rays would dim more quickly than expected from the inverse-square law. One problem with looking at apparent brightness as a function of distance is that most objects (such as galaxies) evolve in luminosity. We avoid this problem by using Type Ia supernovae, which explode in much the same way regardless of where in the Universe they exist and regardless of the lookback time. We could also measure the motions of galaxies and galaxy clusters. 410

From the amount by which clusters of galaxies perturb one another, we can determine their mass and, hence, the average density of the Universe. But this method takes into account only the clumped material, not any uniformly distributed matter. Throughout the 1980s and 1990s, measurements began to converge on a value for Omega matter (ȍM), the ratio of the average density to the critical density of the Universe. That value was ȍM § 0.3; thus, the average density of matter in the Universe was thought to be about 30% of the critical density. If this is true, the Universe should be decelerating somewhat. But because this value is below the critical density, galaxies won’t reach 0 velocity at t = in¿nity. In addition, the spatial geometry of the Universe should be negative, according to this value of ȍM. But most of the measurements used to derive the value of ȍM = 0.3 were based on clusters of galaxies—their masses, distribution, and gravitational inÀuence on one another. Uniformly distributed matter and other possible effects (i.e., the cosmological constant) were not taken into account. There were few tests of global deceleration or geometry. Moreover, there were theoretical reasons for believing that :total = 1, where now we include the possibility of exotic contributions to :. If only normal gravitationally attractive matter and energy exist, then we expected :M = 1. If :M were not exactly 1, it should have deviated very far from 1 by the present time, according to the standard cosmological equations. A value of 0.3 would be highly unlikely. To resolve this dilemma, other measurements were needed of either the global geometry of the Universe or its expansion history. The most direct way of determining the deceleration rate is to measure the expansion rate as a function of time by looking at very distant objects. We can look at representative galaxies at redshift z = 1 and calculate what their distances (lookback times) would be as a function of the historical expansion of our Universe. The lookback time, then, is a function of the expansion history of the Universe. The key is to look at galaxies at different redshifts, measure their distances, and determine the possible curves they follow in a plot of redshift (recession speed) versus distance. It turns out that 1 + z = R(tnow)/R(temitted), the ratio of the galaxy’s distance now to the galaxy’s distance at the time it emitted the light we are now seeing. For example, if z = 1, then 1 + 1 = 2; therefore, the light that we are now seeing (tnow) was 411

Lecture 82: The Mass Density of the Universe

emitted when the galaxy was half of its current distance from us (temitted), because 1/½ = 2, and 1 + 1 = 2. For a given recession speed, or redshift, a dense universe has a smaller lookback time and, hence, a smaller distance than a less dense universe. Progressively less dense universes provide a greater lookback time and, hence, a greater distance for a given speed of recession. If we measure the redshifts and distances of numerous galaxies, we can plot them on a graph to see which of the three possible curves our Universe follows. This will determine its historical expansion rate and predict its future expansion. “The distant galaxy can actually look In order to accurately measure these great distances, we again turn to Type Ia supernovae, just as big as the those that are produced by exploding white nearby galaxy in a dwarfs. We can measure the peak apparent positively curved brightness of a Type Ia supernova in a distant geometry.” galaxy and compare that with the known luminosity of a nearby Type Ia supernova to derive its distance and, hence, the distance of its galaxy. These measurements are fairly accurate because most Type Ia supernovae have about the same peak luminosity; that is, they are all white dwarfs that explode around the Chandrasekhar mass limit. We can then plot these distances (and the corresponding redshifts) on a graph to see which curve they tend to follow: ŸM > 1, ŸM = 1, or ŸM < 1 (a special case of this last possibility being ŸM = 0, an empty universe). Based on past measurements, we would expect the Type Ia supernovae to land on the curve corresponding to ŸM = 0.3, in which the Universe is decelerating only a little bit. In the early 1990s, two teams—the High-z Supernova Search Team (HZT, led by Brian Schmidt) and the Supernova Cosmology Project (SCP, led by Saul Perlmutter)—began measuring the distances of distant Type Ia supernovae. I was a member of both teams, although my primary af¿liation is with the HZT. Over the course of a few nights, each team took many deep, wideangle photographs of the sky, capturing the images of tens of thousands of galaxies. After obtaining new photographs of the same regions of the sky a few weeks later, computer programs and humans were used to search for 412

candidate supernovae in the new images. Optical spectra of the candidates were obtained, often with the Keck 10-m telescopes, to determine whether they were Type Ia supernovae and to measure the redshifts (recession speeds) of their host galaxies. We will next learn about the stunning results of these studies. Ŷ

Suggested Reading Goldsmith, Einstein’s Greatest Blunder? The Cosmological Constant and Other Fudge Factors in the Physics of the Universe. Harrison, Cosmology: The Science of the Universe. Hogan, The Little Book of the Big Bang: A Cosmic Primer. Kirshner, The Extravagant Universe: Exploding Stars, Dark Energy, and the Accelerating Cosmos. Livio, The Accelerating Universe: In¿nite Expansion, the Cosmological Constant, and the Beauty of the Cosmos. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. Summarize the different methods for determining the value of ȍM. What are the dif¿culties in actually implementing these methods?

2. Hubble’s law states that a galaxy’s speed of recession is proportional to its distance. Why, then, do different values of ȍM correspond to different curves in the graph of recession speed versus distance?

3. Why are exploding white dwarf stars so useful for measuring the distances of galaxies?

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Einstein’s Biggest Blunder? Lecture 83

“In the early 1990s, two teams set out to measure the peak brightnesses of Type Ia supernovae, and from those peak brightnesses, to determine their distances and the lookback times. What they found stunned the world of physics. … Einstein’s ‘biggest blunder’ may have actually been his greatest triumph.”

T Lecture 83: Einstein’s Biggest Blunder?

o determine the expansion history of the Universe, two teams set out in the early 1990s to measure the peak apparent brightness of Type Ia supernovae to determine their distances. Recall that by comparing the true peak luminosity of Type Ia supernovae of known distance with the peak apparent brightness of distant supernovae, we can determine the distance of the latter and, hence, their lookback time. Using the Keck telescopes in Hawaii, the High-z Supernova Search Team (HZT) and the Supernova Cosmology Project (SCP) took spectra of Type Ia supernova candidates in distant galaxies. They also measured their peak brightnesses, as well as the rate of decline, with various telescopes. The HZT data analysis was led by Adam Riess, a young postdoctoral scholar working as part of my research team at the University of California, Berkeley. The teams discovered that the supernovae were so faint that their implied distances were farther than possible given the age of the Universe, if the Universe were behaving in any of the ways described by Alexander Friedman (see Lecture 81). The supernovae and, hence, the galaxies in which they were located seemed to have traveled farther than they possibly could have. The distances were too great to even be compatible with a constant expansion rate, let alone a decelerating rate of expansion. The detailed argument turns out to be independent of the age of the Universe. It is based on the curves in the plot of recession speed (redshift) versus distance, discussed in the previous lecture. Therefore, the galaxies must be accelerating with time, rather than decelerating, as had been expected. The two teams concluded that the expansion of the Universe has been speeding up over the past 4 or 5 billion years. This stunned the world of physics.

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For a given redshift, distance depends on the Universe’s density; dense universes have smaller distances than progressively less dense universes. The data seemed to imply that :M < 0, yet we know that the average density of our Universe is greater than 0 because we exist, as do galaxies and clusters of galaxies! Instead, there might be some kind of strange energy having a repulsive gravity—like Einstein’s cosmological constant—that counters the force of gravity. In the past 4 or 5 billion years, this cosmic pushing apart has been dominating over the tendency of galaxies to attract one another, causing expansion to accelerate over time. “These supernovae … were farther away than they could have gotten, even if the Universe had not decelerated at all. The Universe’s expansion recently has been speeding up.”

Einstein’s cosmological constant, ȁ, equals 8ʌG multiplied by the density of the vacuum, and it has the desired repulsive effect. However, as discussed in Lecture 81, this had originally been introduced to account for an apparently static Universe, neither collapsing nor expanding. Einstein renounced his cosmological constant after Edwin Hubble discovered that the Universe is expanding. After all, no repulsive effect was needed to account for the expansion if the Universe was born in an expanding state. Thus, we’ve resuscitated Einstein’s concept, not to make a static Universe, but to make one that (over large scales) is expanding faster with time. Of course, gravity dominates on Earth, in our Galaxy, and in galaxy clusters. But over billions of light years of essentially empty space, “antigravity” dominates. What Einstein referred to as his “biggest blunder”—his cosmological constant— may have actually been his greatest triumph, though motivated by the wrong reasons. Einstein’s only error was in making the cosmological constant have a particular, ¿nely tuned value: that which perfectly balances gravity on large scales. Because their ¿ndings were so unusual and unexpected, the two teams were careful to make sure no other factors could be affecting their measurements or interpretation. Space dust could not account for the faintness of distant supernovae because dust would also have made the supernovae appear 415

Lecture 83: Einstein’s Biggest Blunder?

redder, which was not the case; recall that dust selectively blocks out blue light. The teams measured the light curves through different ¿lters to rule out the possibility of dust. Another potential problem was that perhaps white dwarfs at very great distances don’t explode in the same way as nearby ones, making the peak luminosity of distant supernovae dimmer than that of nearby ones. But comparisons of spectra of nearby supernovae and distant ones showed great similarity, suggesting that the explosions were indeed nearly the same. The result that the Universe is accelerating was based on observations of supernovae at average redshifts of about 0.4 to 0.5—so the lookback time is 4 to 5 billion years. Thus, in the last 4 or 5 billion years, the Universe has been accelerating. But what would we see at even greater lookback times? In a subsequent project led by Adam Riess, the Hubble Space Telescope found even higher-redshift supernovae (the highest, z = 1.7, corresponding to a lookback time of about 10 billion years). The measurements indicated that the Universe was slowing down, not speeding up, back then! Indeed, for the ¿rst 9 or so billion years of its existence, after the Big Bang, the Universe had slowed down in its expansion. But something took over, causing expansion to accelerate during the past 4–5 billion years. The transition from deceleration to acceleration is mathematically known as a jerk. What might account for this jerk? When the galaxies were close together, gravitational forces were strong, pulling the galaxies toward each other. If the cosmological constant—or whatever the repulsive effect is—is associated with space itself, then the cumulative amount of this effect was small, because the distances between galaxies were small. We would expect the repulsive effect to begin dominating over the attractive force of gravity as the galaxies receded farther apart. With time, the attractive gravitational force declined, whereas the cumulative effect of repulsion increased. Thus, the expansion of the Universe eventually began to accelerate. For their leadership roles in discovering the accelerating (but initially decelerating) universe and dark energy, Saul Perlmutter, Adam Riess, and Brian Schmidt were awarded the 2006 Shaw Prize in Astronomy—sometimes called the “Nobel Prize of the East” (it is awarded in Hong Kong). The current acceleration of the Universe, driven by some sort of mysterious dark energy (which we will discuss in another lecture), has some important 416

implications. We would expect the expansion to continue forever unless dark energy becomes gravitationally attractive in the future. Unless the expansion reverses itself, the Universe will expand forever at an accelerating rate, becoming cold, dark, and dilute. Within a few tens of billions of years, the galaxy clusters we see now will be beyond the range of visibility through telescopes. This dark energy also implies that the Universe could be closed— that is, positively curved (like a sphere) and ¿nite—yet still expand forever. The principle that “geometry is destiny” (Lecture 81) would no longer apply. If we combine the current rate of expansion (the Hubble constant) with this history of expansion, we determine that the expansion age of the Universe is about 14 billion years. Moreover, the data tell us how much repulsive dark energy there is: Measured in units similar to ȍM, we arrive at a ¿gure of ȍ/ § 0.7. If we then add this to the associated energy of gravitationally attractive matter (ȍM § 0.3), then the density of dark energy plus the density of normal energy and matter equals 1.0 (:total = 1). Recall that this is exactly what some theoretical physicists said it should be, taking into account the total amount of matter and energy in the Universe. Finally, dark energy is sometimes considered to be the most important unexplained phenomenon in all of physics. Perhaps it is caused by quantum Àuctuations (discussed in Lecture 87). It will probably necessitate a uni¿cation of the two great pillars of modern physics—general relativity and quantum physics. Any uni¿ed theory must be able to explain the observed properties of dark energy; otherwise, it is not a viable candidate theory. Ŷ

Suggested Reading Goldsmith, Einstein’s Greatest Blunder? The Cosmological Constant and Other Fudge Factors in the Physics of the Universe. Kirshner, The Extravagant Universe: Exploding Stars, Dark Energy, and the Accelerating Cosmos. Livio, The Accelerating Universe: In¿nite Expansion, the Cosmological Constant, and the Beauty of the Cosmos. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. 417

Questions to Consider 1. Besides cosmic evolution of Type Ia supernovae and the possible presence of obscuring dust, can you think of any other astrophysical reason (not having to do with accelerated expansion) why high-redshift Type Ia supernovae might appear fainter than expected?

2. What do you think Einstein’s reaction would have been to the discovery that the cosmological constant might actually be nonzero, after he renounced it as his “biggest blunder”?

3. If the dark energy is a property of space, then as the Universe grows,

Lecture 83: Einstein’s Biggest Blunder?

the cumulative amount of antigravity increases, and space expands exponentially. Does this mean that two galaxies can eventually recede from each other faster than the speed of light? If so, how is this conclusion consistent with Einstein’s special theory of relativity?

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The Afterglow of the Big Bang Lecture 84

“The most important aspect of the CMBR, or this cosmic microwave background radiation, was that it played a crucial role in eliminating one of the major cosmological theories, the so-called ‘steady-state theory,’ which was the big alternative to the hot big bang theory.”

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n the past 4 or 5 billion years, the Universe has been accelerating because of some kind of weird dark energy. How can we learn more about this dark energy? First, let’s look at a few theories. In 1927, a Belgian scientist and priest, Georges-Henri Lemaître, suggested that an expanding universe must have begun in a hot, compressed state, a singularity from which everything then expanded. Unaware of Friedman’s equations, Lemaître independently used Einstein’s general theory of relativity to conclude that the Universe was expanding and not static. He called this hot state a primeval atom or cosmic egg that then exploded for reasons unknown. The observed expansion of the Universe suggests but does not demand that it did begin in a hot, compressed state. However, it could instead have been expanding forever, with no beginning and no end. Fred Hoyle proposed this steady-state theory. He criticized the primeval atom hypothesis, jokingly calling it the Big Bang, which ironically, stuck. Recall from Lecture 81 that the cosmological principle states that the Universe is uniform, with the same average density everywhere; in addition, it’s isotropic—appearing the same in all directions. But density can change with time; in an expanding universe with a beginning, density decreases with time. Hoyle’s steady-state theory was based on the perfect cosmological principle: The properties of the Universe don’t change with time on average. Thus, there was no beginning, there will be no end, and the average density doesn’t decrease with time. Hoyle had to postulate that new matter is constantly created out of nothing (empty space) to keep the overall density constant. We’ve been taught that energy and matter can be transformed, but the total—matter plus energy—is conserved. However, the creation of

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energy and matter in Hoyle’s hypothesis was too slow to conÀict with any experimental measurements of this “law” of conservation of energy—only about 1 hydrogen atom per cubic meter per billion years (1 H/m3/109 years). Thus, we wouldn’t notice an extra hydrogen atom appearing in the room; no experiment can measure the occasional addition of one hydrogen atom in a volume this size.

Lecture 84: The Afterglow of the Big Bang

The steady-state theory turned out to be wrong, but it provided a great impetus for theoretical physicists to critically examine their assumptions and for cosmologists to search for observational evidence supporting the Big Bang. We know that Hoyle was wrong for a number of reasons. For example, the discovery of quasars revealed that at one time, the Universe had many quasars per unit volume, but now, it has very few or no quasars. More recently, we’ve witnessed the evolution of galaxies. Today, we see granddesign spiral galaxies. Looking back a few billion years, we see amorphouslooking galaxies that presumably coalesced. The Universe’s appearance has changed with time, and the steady-state theory doesn’t support this. The fatal blow to the steady-state theory is the existence of an afterglow from the Big Bang with a temperature of only 3 degrees above absolute zero—the overall temperature of the Universe. At this temperature, the Universe itself is glowing similar to a black body—the afterglow of the time long ago when the Universe was very hot and dense. In 1964–1965, astronomers Arno Penzias and Robert Wilson unwittingly discovered this glow when they tried to map emission from neutral hydrogen in our Galaxy. Because the hydrogen emission was faint, they had to eliminate all sources of “noise” (interference) in their electronic gear. Most of the noise was eliminated except for a tiny amount whose origin they couldn’t locate. Gradually, they were convinced that the noise came from everywhere in the sky; regardless of where or when they looked, the noise had the same intensity and was uniformly found throughout the sky. The noise intensity, if interpreted as coming from a black body, corresponded to a temperature of about 3 degrees above absolute zero. Subsequent measurements made by others also showed that it had the spectrum of a black body, suggesting that the Universe glows at a temperature of 3 K. Because the wavelengths are

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comparable to the radiation emitted by a microwave oven, this noise is now called the cosmic microwave background radiation (CMBR). If the Universe was hot long ago and had a lot of radiation corresponding to short wavelengths, then as the Universe expanded, the short waves that existed back then would also expand. Electromagnetic waves are not gravitationally bound; thus, they would “Only when you have expand with the Universe, assuming that it, too, expanded. Thus, if the Universe started competing hypotheses out hot, eventually, expansion would cool are experimentalists the Universe and transform those short and observers wavelengths into very long wavelengths, stimulated a lot to like those of the observed CMBR. really work hard and Let’s look at the production mechanism probe all possibilities of these waves in more detail. When to the degree that they the Universe was hot, whatever photons should. That’s what existed bounced around from one electron science is all about.” to another. The atoms were ionized; the electrons were not bound to the protons, and the electrons weren’t bound to whatever helium nuclei existed either. With such a plasma of free electrons, electromagnetic radiation—in the form of photons—is impeded and scattered. Thus, the plasma was opaque, impeding light’s ability to travel through it in straight lines. As the Universe cooled and expanded (about age 380,000 years), it cooled to about 3000 K. At that point, electrons could combine with protons to form neutral hydrogen atoms. This physical process is called recombination, though here it was happening for the ¿rst time in the Universe. Similarly, electrons could combine with helium nuclei to form neutral helium atoms. The Universe became transparent after this recombination period because atoms absorb only radiation that corresponds to the energy differences between their well-de¿ned electronic energy levels. As space expanded, the photons stretched. In essence, the cosmic microwave background photons come from an opaque wall at a redshift of about 1000. We cannot see electromagnetic

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Lecture 84: The Afterglow of the Big Bang

radiation from beyond this wall because the Universe before that time was opaque, like thick fog. This marks the boundary of the observable Universe; that is, we cannot see light from a time before about 380,000 years after the Big Bang. Because the radiation has the same intensity everywhere in the sky, the early Universe from which the radiation originated must have been incredibly homogeneous and isotropic. The steady-state theory cannot account for the CMBR, yet the Big Bang theory naturally predicts it. In the late 1940s and the early 1950s, George Gamow, Ralph Alpher, and Robert Herman predicted the existence of the CMBR. They thought that the elements in the Universe were produced by nuclear reactions early in its history; thus, the Universe must have been hot and dense. They were partly right; the lightest elements were indeed produced when the Universe was young, hot, and dense, but heavier elements were subsequently cooked up in stars, a fact that wasn’t recognized until later. They predicted that, given the temperature needed in the Universe at the time when the elements were produced, it would now have a temperature of about 10 degrees above absolute zero. They were wrong by a factor of 3 or 4, but they got the right order of magnitude. Years later, some Princeton physicists independently predicted the existence of the CMBR based on similar arguments. They and their colleagues subsequently started to build a radio telescope that could detect the radiation. However, Penzias and Wilson were the ¿rst to actually measure the noise, despite not speci¿cally searching for it or even recognizing its importance (until they were told by others). Their careful research earned them the 1978 Nobel Prize in Physics. Ŷ

Names to Know Gamow, George (19041968). Russian-American physicist; he suggested that the Universe began in a hot, compressed state and predicted the existence of the cosmic background radiation that was later discovered by Arno Penzias and Robert Wilson. Also devised a theory of radioactive decay.

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Hoyle, Fred (19152001). English astronomer; proposed the steady-state theory of the Universe, which stimulated much important work in cosmology. Also made fundamental contributions to the understanding of the origin of the chemical elements. Coined the term Big Bang.

Important Term steady-state theory: A model of the expanding Universe based on the assumption that the properties of the Universe do not change with time. Matter must be continually created to maintain constant density.

Suggested Reading Ferris, The Whole Shebang: A State-of-the-Universe(s) Report. Gribbin, In Search of the Big Bang: The Life and Death of the Universe. Harrison, Cosmology: The Science of the Universe. Hogan, The Little Book of the Big Bang: A Cosmic Primer. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Silk, A Short History of the Universe.

Questions to Consider 1. Philosophically, which universe makes you more uncomfortable: one that has no beginning and no end in time or one in which there was a de¿nite beginning?

2. Can you think of any possible explanation for the cosmic microwave background radiation in the context of Hoyle’s steady-state theory of the Universe?

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3. Describe the origin of the cosmic microwave background radiation and the reason it now corresponds to a very low temperature.

4. Would you believe the announcement of the discovery of a galaxy at

Lecture 84: The Afterglow of the Big Bang

redshift 10,000?

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Ripples in the Cosmic Background Radiation Lecture 85

The ultimate origin of density variations in the Universe came from small quantum Àuctuations very early in its history.

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he cosmic microwave background radiation (CMBR) is of fundamental importance in cosmology. It implies the existence of an early hot, dense phase for the Universe, a Big Bang, from which the Universe expanded. Recall that the CMBR comes from about 380,000 years after the birth of the Universe, when the temperature had cooled to around 3000 K, suf¿ciently low to allow the recombination of electrons with atomic nuclei to form neutral atoms. (Even though the process was happening for the ¿rst time in the Universe, we call it recombination because in the past, physicists had ionized gases in their laboratories many times, then watched the electrons recombine with atomic nuclei.) The discovery of the CMBR emanating from the Big Bang was monumental. Penzias and Wilson’s work set off a whole industry of measurements of ever-greater precision to determine whether this radiation corresponded to a thermal black body. Indeed, in 1990, measurements made with NASA’s Cosmic Background Explorer (COBE) satellite showed that the spectrum is that of a black body. John Mather of the NASA/Goddard Space Flight Center won half of the 2006 Nobel Prize in Physics for his role as leader of the team that measured the perfect black-body spectrum of the CMBR. The other half of the Nobel Prize was awarded to George Smoot, of UC Berkeley, for the discovery of tiny variations in the temperature of the CMBR, which will be discussed later in this lecture. The CMBR was actually detected several times in the 1940s, but its importance was not recognized. The detection was through optical observations of cyano radicals—carbon combined with nitrogen (CN), which astronomers often refer to informally as “cyanogen molecules.” CN has various vibration, rotation, and electronic energy levels. Normally, from the ground state, there is only one possible excitation to a higher energy level (an excited vibration, rotation, and electronic state). The absorption line corresponding to such an excitation is in the violet (or “near-ultraviolet”) 425

NASA

Lecture 85: Ripples in the Cosmic Background Radiation

part of the optical spectrum. However, CN can go from the ground state to an excited rotation state by absorbing a microwave background photon. From this level, there are three possible violet (near-ultraviolet) absorption lines instead of just one, corresponding to various higher energy levels. The spectrum of a distant star or quasar through a cloud of gas containing CN molecules shows three absorption lines, indicating the presence of microwave photons. Also, we know that the CMBR corresponded to a higher temperature in the past through studies of the CN clouds at higher redshift, which show how the relative strengths of these absorption lines change.

Observed sky from Cosmic Microwave Background Explorer (COBE) telescope.

We know that the microwave background photons come from far away because of the Sunyaev-Zel’dovich effect, named after two Soviet physicists. They correctly predicted that hot electrons in large clusters of galaxies would scatter (reÀect) some microwave background photons as they traveled through the cluster, boosting them to a slightly higher energy—that is, giving them a slight blueshift. Indeed, the microwave background photons in the direction of distant, hot clusters of galaxies are slightly blueshifted relative to the ones not passing through clusters of galaxies, showing that the microwave background photons did indeed originate from a greater distance than the clusters.

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From any perspective in the Universe, we would see photons coming from a sphere (that is, from all directions) nearly 14 billion light years in radius. Overall, those photons are redshifted by the expansion of the universe. A map of the microwave radiation in the sky shows that radiation is basically the same in all directions, with a temperature of 2.725 ± 0.002 K. The actual observed temperature varies across the sky by a greater amount than the statistical uncertainty quoted above: about 0.2%. This variation is explained by the fact that our Sun moves around in the Milky Way Galaxy at about 200 km/s, and our Galaxy moves around inside the Local Group, which itself is pulled around by other moving galaxy groups. Adding all these motions together, our Sun’s motion relative to the smooth expansion of the Universe as a whole (the Hubble Àow) is about 600 km/s. Compared to 300,000 km/s, the speed of light, the Sun’s relative motion is about 2 parts in 1000, or 0.2%. Therefore, in one region of the sky, photons look somewhat blueshifted (“hotter”) relative to the average, and in another part of the sky, they look somewhat redshifted (“cooler”) relative to the average. Apart from this, for a long time, no variations in the temperature of the microwave background had been observed that could not be explained by the Sun’s so-called “peculiar” motion through the Universe. The extreme isotropy of the CMBR is actually puzzling. If clusters of galaxies formed from the gravitational collapse of initial density variations in the Universe, we would expect to see some corresponding temperature variations in the microwave background radiation, as well. Photons escaping from denser regions should have a slightly different redshift than those escaping from less dense regions. Such variations are also called Àuctuations, inhomogeneities, non-uniformities, anisotropies, and ripples in various books and articles. Several effects can produce them, but one of the simplest to understand is the gravitational redshift. Photons emitted from an overdense region lose some energy going away from the strong gravitational ¿eld and, therefore, become slightly more redshifted. Conversely, photons emitted from an underdense region actually gain some energy as they go toward a stronger gravitational ¿eld, so they appear slightly less redshifted (and, hence, blueshifted relative to the average redshift). If the Universe was exceedingly smooth at very early times, how could clusters of galaxies form? It turns out that large ripples aren’t needed in the beginning to achieve gravitational collapse and subsequently form galaxy clusters and superclusters. The 427

Lecture 85: Ripples in the Cosmic Background Radiation

Universe can be quite smooth initially, yet it must have some small ripples, some small variations in density, in order for gravitational collapse to form such structures as clusters of galaxies. For a long time, astronomers were unable to ¿nd these Àuctuations, or ripples, even with rather precise measurements. In fact, some speci¿c models of galaxy and cluster formation were ruled out by the absence of visible Àuctuations in the microwave background radiation. If the next generation of powerful telescopes had also failed to ¿nd these variations, then we would have had to completely rethink our ideas about how the largescale structure of the Universe formed. In 1992, a breakthrough occurred when the COBE satellite found variations, or ripples, in the temperature of the microwave background radiation. As predicted, the CMBR (also known as the “microwave sky”) actually does have ripples, but they’re tiny—only a few parts per 100,000 (105). These tiny variations correspond to clumps in the matter distribution at early times. Even COBE, whose improved resolution was still low, was able to see only large ripples, the smallest of which are about 10 degrees across the sky and correspond to sizes 10 to 20 times bigger than superclusters. These ripples were the seeds from which slightly overdense and slightly underdense regions in our Universe had formed. The small variations presented by these ripples are too small to violate the principle of isotropy, wherein the Universe—beyond the supercluster stage—is basically uniform. In fact, despite the gargantuan size of some ripples, we don’t see giant supersuperclusters of galaxies because these slight density variations, although visible from near the beginning of the Universe, haven’t had time to collapse into anything signi¿cant in today’s Universe. George Smoot of the University of California, Berkeley, won half of the 2006 Nobel Prize in Physics for his role as leader of the team that used COBE to discover the temperature variations in the CMBR. The ultimate origin of variations in the Universe came from small quantum Àuctuations very early in its history. Shortly after its birth, the Universe went through a huge growth stage, known as inÀation, which will be described in future lectures. Prior to and during inÀation, quantum Àuctuations occurred and became the seeds of clusters of galaxies, superclusters, and beyond. After 428

COBE, our measurements became progressively better. Such balloon-based measurement projects as BOOMERANG and MAXIMA noted structures on smaller angular scales, typically 1 degree instead of COBE’s 10 degrees. The most prominent Àuctuations were found to occur at a scale of about 1 degree, about twice the size of the full Moon in the sky. It turns out that certain “preferred” physical sizes are expected theoretically. In particular, the most prominent physical size is equal to the distance a sound wave could have traveled in the 380,000 years before recombination of the electrons and protons. This conclusion is quite robust; it is essentially independent of the detailed model for the early history of the Universe. But the mathematical relationship between the physical and angular sizes of an object depends on the overall geometry of space; recall our discussion in Lecture 82. With Àat Euclidean geometry, light travels along familiar straight lines, and the angular size of an object of given physical size is inversely proportional to its distance. With spherical (i.e., positively curved) geometry, light travels along paths that are curved in such a way that an object of given physical size and distance looks larger than in Àat (Euclidean) space. With hyperbolic (i.e., negatively curved) geometry, light travels along paths that are curved in such a way that an object of given physical size and distance looks smaller than in Àat (Euclidean) space. The observed angular diameter of the most prominent variations, when combined with the calculated physical diameter, corresponds to what is expected in Àat space. Thus, the CMBR maps tell us that the Universe is Euclidean (spatially Àat) on very large scales. Since 2001, a satellite known as the Wilkinson Microwave Anisotropy Probe (WMAP) has measured the structure of the CMBR even better than before, con¿rming that space is Àat, at least over the distances that we can see. We may, nonetheless, live in something that is, overall, shaped more like a giant sphere, or a saddle; however, the scale over which the Universe curves would be much, much larger than the distance to which we can see. That is, either the Universe really is Àat globally, or else it’s so big that we see only a tiny fraction, which looks Àat as far as we can see. Either conclusion has grand implications for much of cosmology. Ŷ

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Suggested Reading Harrison, Cosmology: The Science of the Universe. Hawley and Holcomb, Foundations of Modern Cosmology. Hogan, The Little Book of the Big Bang: A Cosmic Primer. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Rowan-Robinson, Ripples in the Cosmos: A View Behind the Scenes of the New Cosmology. Smoot and Davidson, Wrinkles in Time. Wilkinson Microwave Anisotropy Probe, map.gsfc.nasa.gov.

Lecture 85: Ripples in the Cosmic Background Radiation

Questions to Consider 1. Explain why the CMBR actually looks slightly hotter in one direction of the sky, and slightly cooler in the opposite direction.

2. Discuss the signi¿cance of tiny variations (inhomogeneities, or ripples) in the CMBR. What is their origin, and what did they later become?

3. How do the observed temperature variations in the CMBR help us decipher the overall geometry of the Universe?

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The Stuff of the Cosmos Lecture 86

“[Cosmic microwave background] radiation provides so many details about the fundamental contents of our Universe. It still amazes me how much they get from these studies.”

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e turn to the fundamental contents of our Universe, beginning with a review of conclusions from studies of the cosmic microwave background radiation (CMBR). Recall that the CMBR tells us that the Universe is geometrically Àat over the very large scales that we can see. Indirectly, this provides strong supporting evidence for the presence of dark energy that is currently accelerating our Universe, as was ¿rst somewhat directly inferred from studies of high-redshift Type Ia supernovae. Speci¿cally, the data show that the most prominent variations (Àuctuations) in the CMBR have the angular scale expected if light travels through the Universe along Euclidean straight lines. Thus, according to general relativity, the average density of all the stuff in the Universe divided by the critical density equals 1 (ȍtotal = 1). As discussed in Lecture 82, we already knew that ordinary and dark matter (and normal energy), largely in galaxy clusters, add up to only ȍM = 0.3. This implies that the Universe must be 70% something other than normal matter, normal energy, and dark matter. What exactly is this other 70% of “stuff,” and do we have proof that it exists? We call this “stuff” ȍȁ or, if we don’t believe in the cosmological constant, ȍX, in which X is some unknown quantity. The relevant equation is ȍȁ = ȁc2/(3H02). This ratio is similar to the equation we previously discussed for matter (ordinary and dark) and ordinary energy, where ȍM was ȡaverage/ ȡcritical, and ȡcritical = 3H02/(8ʌG). Suf¿ce to say that ȍȁ is a measurement of the contribution of the cosmological constant, or whatever the dark energy is, to the total contents of the Universe. What if our Type Ia supernova measurements are wrong and this extra 70% isn’t actually countering the effects of gravity and accelerating expansion? What could the material be? If it were slowly moving and cold, then this extra stuff would occur in galaxy clusters, and we would have detected it through gravitational lensing or the induced motions of clusters. Given that we see only the ȍM = 0.3 associated 431

with clusters, it must be something more spread out and not associated with clusters of galaxies. However, if the extra stuff were hot and moving very fast (at speeds close to the speed of light, like neutrinos), it would wipe out the formation of the smaller-scale structures, such as galaxy clusters, in the large-scale structure of the Universe. In other words, the Universe would look different than it does.

Lecture 86: The Stuff of the Cosmos

We call this unknown material dark energy. We have evidence for its existence and for the fact that it exerts a repulsive effect that stretches out space faster than we would expect if it didn’t exist. Recall the WMAP satellite images from Lecture 85 that showed little variations in temperature across the Universe. These are the ¿ngerprints of small density inhomogeneities from which large-scale structure gradually grew due to gravity. Dark energy, stretching space, affects the growth of galaxies and clusters of galaxies. Using computer simulations, when we include the effects of dark energy in the formation of the Universe’s large-scale structure, the results closely resemble what we observe. Another observational effect that points to dark energy stretching space at an increasing rate is associated with the CMBR. When we remove the SunyaevZel’dovich effect (Lecture 85), in which hot gas in clusters of galaxies scatters CMBR photons and makes them more energetic, we notice that the photons are slightly more blueshifted in the direction of superclusters than they are away from the superclusters. In an expanding universe that isn’t accelerating, the photons passing through the gravitational ¿eld of a supercluster will emerge from that ¿eld with no net gain or loss in energy. But in an accelerating universe, the gravitational ¿eld of the supercluster becomes weaker as the supercluster expands, and the photons gain a slight amount of energy to become blueshifted. By 2003, we had a good deal of evidence for dark energy. Speci¿cally, as discussed above, the Àatness of the Universe inferred from the WMAP map (hence, ȍtotal = 1), together with ȍM = 0.27 (a more re¿ned value, compared with the previous ȍM = 0.3), indicated that ȍȁ = 0.73. These values agree very well with results of studies of hundreds of high-redshift Type Ia supernova: ȍM = 0.28 and ȍȁ = 0.72. The Type Ia supernova results were vindicated, providing great comfort to the two teams that had announced the accelerating universe in 1998.

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But the WMAP map can actually tell us even more about the fundamental contents of the Universe. The map shows the microwave background radiation coming from all directions around us. We detect small hot spots and cold spots (ripples) of varying sizes. Plotting the square of the temperature deviations of the hot and cold spots against the scale over which we are looking, from a few tenths of a degree all the way to 90 degrees, gives us the power spectrum. At certain scales, the temperature Àuctuations have a higher amplitude than at other scales; the peak of the distribution occurs at 1 degree. We think these ripples, or variations, are acoustic waves that formed early in the Universe from quantum Àuctuations in density. The ripples caused compression and rarefaction waves in the plasma of the early Universe. Remember, before recombination, photons were trapped in the plasma and could not travel freely through it. They were mixed with dark matter and normal matter. The overdense regions were pulled in by gravity, but photon pressure, or radiation pressure, pushed out. This combination of both an attractive force and restoring force is what is “There was a ‘Àuid’ needed to perpetuate sound waves. Indeed, we can in the Universe “hear” the sounds of the early Universe if we turn consisting of these acoustic oscillations into something audible photons, dark to the human ear. matter, and normal In a wind instrument, a wave of compression matter mixed occurs where air is blown in, with a rarefaction together.” at the very end; between the compression and rarefaction, the air has some intermediate density. In a similar way, these sound waves moving through the early Universe had regions of maximum compression and maximum rarefaction. The fundamental corresponded to length scales over which one full compression had occurred by an age of 380,000 years, the time of recombination. The ¿rst overtone corresponded to length scales on which one full compression was followed by one full rarefaction. The second overtone corresponded to one compression, followed by a rarefaction, then another compression. After recombination, the photons traveled freely through the Universe and no longer participated in the compressions and rarefactions. The power spectrum of the temperature variations reveals the amplitude of the compressions and rarefactions at the time of recombination. The relative strengths of peaks and valleys in the spectrum tell us about the details of the early Universe and its composition. 433

NASA/WMAP Science Team

In 2003, the WMAP team reported its ¿rst results, and in 2006, it provided essentially the same (but re¿ned) values. The team determined a Hubble constant of 73 ± 3 km/s/Mpc, an age of the Universe of 13.7 ± 0.2 billion years, ȍM = 0.25, and ȍȁ = 0.75. The precise values for the amounts of matter and dark energy depend on the assumptions, but a mixture of ¼ matter (and normal energy) and ¾ dark energy is a good average. Moreover, ȍM is only 0.04 if we just look at neutrons, protons, and other normal matter. If 0.04 of that 0.25 is normal matter, then 0.21 must be some kind of exotic dark matter.

Lecture 86: The Stuff of the Cosmos

The WMAP map of microwave light gives us a more precise understanding of the contents of the Universe.

What is the Universe composed of? As we said, dark energy accounts for 75% of all the stuff of the Universe. Cold dark matter, most likely WIMPs (weakly interacting massive particles), is 21%, and normal atoms, most of which don’t glow, constitute only 4% of the Universe. Of the 4% normal matter, only 0.5% (that is, ȍM = 0.005) is stuff that glows at optical wavelengths, such as stars and nebulae. Three percent (ȍM = 0.03) is what we used to think of as dark matter, but it has been found recently to glow at X-ray wavelengths. Half a percent (ȍM = 0.005) might be MACHOs (massive compact halo objects), but not much more because very few MACHOs are found in our Galaxy’s halo. Perhaps up to a third of a percent (ȍM = 0.003) consists of neutrinos. Given that only 4% of the Universe as a whole consists 434

of normal atoms, the rest (96%) is made up of dark energy and some sort of exotic dark matter that isn’t protons and neutrons. However, elaborate devices have not yet de¿nitively detected the presence of WIMPS, though we think they constitute most of the dark matter. It’s disconcerting that 75% of the Universe’s energy is dark energy, and we don’t know what it is. There is much left to be done in the world of astrophysics and physics before we truly understand the Universe. Ŷ

Important Terms accelerating universe: The model of the Universe based on recent observations that its expansion is speeding up with time. cold dark matter: Nonluminous matter that moves slowly, such as neutron stars and exotic particles.

Suggested Reading Greene, The Fabric of the Cosmos: Space, Time, and the Texture of Reality. Harrison, Cosmology: The Science of the Universe. Hawley and Holcomb, Foundations of Modern Cosmology. The Once and Future Cosmos (special edition of Scienti¿c American, 2002). Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Smoot and Davidson, Wrinkles in Time. Wilkinson Microwave Anisotropy Probe, map.gsfc.nasa.gov.

Questions to Consider 1. Do you ¿nd the arguments for the presence (indeed, the dominance, over large scales) of dark energy compelling?

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2. Think of possible candidates for dark matter that consists of normal neutrons and protons but would be hard to detect observationally. How could you con¿rm them or rule out their existence?

3. How do you feel about the conclusion that normal matter and energy,

Lecture 86: The Stuff of the Cosmos

such as that of which we consist, make up only a small percentage of the Universe? Are we the debris of the Universe, the afterthought of creation?

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Dark Energy—Quantum Fluctuations? Lecture 87

“The important point to take away initially, however, is that dark energy is not the same thing as dark matter. … Dark matter pulls; it has a gravitationally attractive effect. Dark energy, whatever it is, pushes; it stretches space more and more quickly.”

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he evidence for dark energy is now compelling; Type Ia supernovae show that the expansion of the Universe is accelerating, and studies of the cosmic microwave background radiation independently suggest the presence of dark energy. The concept is shaking the foundations of theoretical physics. Many physicists think the nature of dark energy is the single most important, observationally driven, unsolved problem in physics. Note that dark energy is not the same as dark matter, despite what one might naively conclude from Einstein’s famous equation, E = mc2. Dark matter has a gravitationally attractive effect; dark energy stretches space at an accelerating speed. Before we consider the possible physical mechanisms that might explain dark energy, let’s review the general theory of relativity. In general relativity, normal, outward-pushing pressure adds to the gravitational attraction of a body, though this is quite counterintuitive. For example, the mass of Earth gravitationally attracts us, but it also exerts an outward (positive) pressure, warping space and time a bit and causing local gravity to be stronger than it would be had there been no pressure. Thus, two sources of gravity—matter and energy density (ȡ) and pressure (P)—both contribute to an object’s gravitational ¿eld. There is also the possibility of a substance with a pressure contributing to the deceleration of the Universe. In general relativity, the rate of change of the expansion rate is proportional to –(ȡc2 + 3P), or the density of normal matter and energy multiplied by the speed of light squared, plus 3 times the pressure of the substance under consideration. In most cases, energy density and pressure are both positive. In the equation above, a positive result multiplied by –1 becomes negative; that is, the expansion rate slows with time for normal matter, energy, and pressure. If we have a substance or effect with negative pressure (P < 0) and, more speci¿cally, P  (1/ 3)Uc 2 , the quantity (ȡc2 + 3P) 437

is negative. A negative of a negative is a positive, which means that the rate of change of expansion increases—the Universe accelerates with time. We think dark energy has a positive energy density but negative pressure, which when multiplied by 3, more than compensates for the positive energy density. This causes the expansion of the Universe to accelerate.

Lecture 87: Dark Energy—Quantum Fluctuations?

What is negative pressure? The normal outward (positive) pressure of the Earth pushes on us and keeps us from falling to the center of the Earth. Negative pressure is similar to the inverse of that. As an analogy, a stretched rubber band doesn’t push out on the person stretching it. Instead, the rubber band pulls in, with a kind of negative pressure. In general relativity, negative pressure is somewhat like “antigravity,” an effect acting opposite to that of gravity. A stretched rubber band, however, doesn’t cause the Universe to accelerate (the analogy fails), but real dark energy (with negative pressure) might. As we will see in subsequent lectures, we think that in the ¿rst few moments after the birth of the Universe, an exponential growth phase called inÀation occurred—this was, in essence, the “Big Bang.” The Universe grew to a truly gargantuan size in a very short time, driven apart by dark energy having a negative pressure. What is dark energy, and why would it have negative pressure? One idea is that dark energy may result from a non-perfect cancellation of quantum Àuctuations—changes in the space vacuum, where virtual particles are created out of nothing. Recall from Lecture 64 the Heisenberg uncertainty principle; one form of this says that the uncertainty in the energy of any measured physical process multiplied by the uncertainty of the length of time over which the observation is made is greater than Planck’s constant divided by 2ʌ. Any real observation is thus constrained by the equation ('E 't ) t (h / 2S) . But virtual particles can form out of nothing if ('E 't )  (h / 2S) , which can be thought of as a temporary quantum violation of the law of conservation of energy. Virtual particles spontaneously form out of nothing, living for a short time, then annihilating each other. This happens everywhere, not just in a vacuum, but in the air of a room and inside the very structure of atoms. If the energy was instead “borrowed” from the vacuum, leaving a negativeenergy hole, then positive-energy Àuctuations cancel negative ones, leaving no net energy—in other words, not even a quantum violation of the law of conservation of energy. 438

Virtual particles don’t last long enough to be isolated and studied, but they can affect the properties of matter. The theory of quantum electrodynamics says that quantum Àuctuations really occur and they affect the structure of atoms, for example. The interaction between two real particles is mediated by virtual particles—virtual photons, in the case of electromagnetic interactions. Two electrons interact by exchanging virtual photons. The Feynman diagram is one of many tools that allows us to determine the electromagnetic forces between protons and electrons, for example. The diagram is a simple graph of time on the vertical axis versus position on the horizontal axis. In 1947, Willis Lamb observed that energy levels of electrons in a hydrogen atom are not exactly where we expect them to be if quantum Àuctuations don’t occur. This slight discrepancy, beyond a certain decimal place, is known as the Lamb shift. Quantum electrodynamics explains this shift because it includes the effect of virtual photons, allowing us to exactly explain the measured energy levels of the hydrogen atom. (The energy levels of other elements are more complicated to predict, but they, too, show general agreement with the measurements.) Virtual photons interact with electrons and change their effective mass and energy level. Let’s return to quantum Àuctuations, and then discuss the concept of in¿nity. For a long time, many physicists assumed that there were just as many negative-energy Àuctuations as there were positive-energy ones. Positive energy cancels negative energy for a net effect of E = 0. But rather than an exact cancellation of positive- and negative-energy Àuctuations, there could be a slight excess of positive energy. This vacuum energy is exactly the kind of energy associated with negative pressure: P = Uc2. Space would expand at an accelerating rate wherever this vacuum energy dominated over more normal forms of energy. Strong experimental evidence, seen in the Casimir effect, is consistent with virtual particles altering the energy and pressure of the vacuum. Set up two thin, essentially massless (so that gravity can be ignored), highly conducting metal plates very close to each other with their faces parallel. Because the plates are grounded, they have no free charges. The plates will actually move closer to each other because of virtual particles. Vacuum quantum Àuctuations occur both outside the plates and between the plates. Outside 439

Lecture 87: Dark Energy—Quantum Fluctuations?

the plates, the waves associated with the virtual particles can be any length, with no restrictions. Between the plates, however, wavelengths are restricted to that con¿ned space, with a node (stationary point) at each plate. That is, the waves Àuctuate in their middles but not at their ends; electric currents are produced in the plates that force the waves to have a node at each plate. The waves between the plates are called standing waves, and they can occur in multiple lengths: O = 2L/n, in which O is wavelength, L is the distance between the plates, and n is an integer (1, 2, 3, 4, and so on). They are analogous to sound waves in a wind instrument having two closed ends. We might think there would be an in¿nite number of waves both between the plates and outside; therefore, the pressure pushing out should equal that pushing in, and the plates shouldn’t move toward each other. However, the in¿nity between the plates is smaller than the in¿nity outside the plates! Recall our discussion in Lecture 72, where we said that even though sets of numbers can be in¿nite, the sets can have different densities, in a sense. For example, we can count to in¿nity using all the counting numbers or we can leave out the even numbers. The former has a denser set of numbers than the latter, yet we are still counting to in¿nity in both cases. Moreover, there are just as many rational numbers as there are counting numbers, even though the rational numbers are denser. Each of the above sets of numbers is called a countable in¿nity; it can, in principle, be placed into a one-toone correspondence with the counting numbers (positive integers). There are also uncountable in¿nities, which do not have a one-to-one correspondence with the positive integers; they are a bigger set of numbers. For example, irrational numbers—such as S, e, Se—constitute an uncountable in¿nity that is larger than the countable in¿nity of the positive integers or the rational numbers. The number of standing waves between the plates is a countable in¿nity; many possible wavelengths are missing because they cannot all ¿t between the plates. Outside the plates, on the other hand, an uncountable in¿nity of waves exists. Thus, the plates are pushed toward each other. Likewise, dark energy could represent an incomplete cancellation of positiveenergy and negative-energy quantum Àuctuations, subtracting a smaller in¿nity from a larger in¿nity to get a net positive energy. That positive vacuum energy has the property of negative pressure, and that negative pressure causes the Universe to expand at an accelerating rate. The Universe, though 440

accelerating, is not yet growing at an exponential rate (that is, doubling in size during each unit of time) because there are still considerable amounts of gravitationally attractive matter resisting exponential growth. The size of the Universe is increasing, and there is a ¿nite number of normal-matter and darkmatter particles in this expanding box. However, the amount of dark energy increases as space expands, because dark energy is a property of space itself. Eventually, repulsive dark energy will vastly dominate over gravitationally attractive matter; thus, the expansion will become exponential—a runaway Universe, which if the process continues, has no end. Ŷ

Suggested Reading Goldsmith, Einstein’s Greatest Blunder? The Cosmological Constant and Other Fudge Factors in the Physics of the Universe. Greene, The Fabric of the Cosmos: Space, Time, and the Texture of Reality. Guth, The InÀationary Universe: The Quest for a New Theory of Cosmic Origins. Kirshner, The Extravagant Universe: Exploding Stars, Dark Energy, and the Accelerating Cosmos. Livio, The Accelerating Universe: In¿nite Expansion, the Cosmological Constant, and the Beauty of the Cosmos. The Once and Future Cosmos (special edition of Scienti¿c American, 2002). Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. Given that E = mc2 (an equation many of us learned at our mother’s knee), stating the equivalence of mass (matter) and energy, can we conclude that dark matter is the same as dark energy?

2. Can you think of some kind of analogy that might make the concept of negative pressure more intuitive and understandable?

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3. Given that we cannot directly detect virtual particles, does it make sense to consider them as part of the Universe?

4. Do you think there could be more than one kind of uncountable in¿nity?

Lecture 87: Dark Energy—Quantum Fluctuations?

Consider what is called the superset of a set—the set of all possible subsets of a given set. What if (as, in fact, is the case) the superset of any set other than the null set is strictly larger than the set itself?

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Dark Energy—Quintessence? Lecture 88

“Virtual particles come into existence and out of existence and create this energy, which, if there’s a net positive amount of it, has a negative pressure that accelerates the stretching of space. … These Àuctuations, being a property of space, grow in total number as space grows. The more space gets bigger, the more of these quantum Àuctuations there are.”

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n the previous lecture, we considered the possibility that dark energy consists of quantum Àuctuations in the vacuum of space. If there is net positive energy with a negative pressure, space should stretch in opposition to gravity, causing the expansion rate of the Universe to accelerate. The number of quantum Àuctuations (and, hence, the associated positive energy) grows as the volume of space increases. However, as the Universe expands, no additional total energy is introduced because the positive energy of quantum Àuctuations is exactly cancelled by negative gravitational energy.

The hypothesis of quantum Àuctuations as dark energy is interesting, but there are at least two major problems. It seems to require an extraordinary amount of “¿ne tuning.” First, the cosmological constant that we measure from observations of Type Ia supernovae and the CMBR is very small: ȍȁ = 0.75. After some simple calculations, we ¿nd that ȍȁ should be at least 1050, or even 10120, if not in¿nite! Based on our existence alone, ȍȁ cannot be that big. If it were, the Universe would have expanded so quickly early on that no galaxies would have formed, nor stars, nor ourselves. Second, ȍȁ and ȍM, right now, are roughly equal. The ratio of ȍȁ = 0.75 to ȍM = 0.25 is about 3, fairly close to 1. (The ratio could have been anything, such as 109 or 10–6; that’s why we say it is roughly 1.) But both ȍM and ȍȁ should be changing dramatically with time. Ten billion years ago, ȍM was much larger than ȍȁ; in the future, ȍȁ will be much larger than ȍM. Looking at the history and future of the Universe, at most times, the ratio of these densities differed greatly from 1. Interestingly, we are living during a time near when the two densities are nearly equal. 443

Lecture 88: Dark Energy—Quintessence?

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There must be some theoretical reason why ȍȁ is a very small yet nonzero number right now and why its size is close to that of ȍM. Quantum Àuctuations give no real insight. Instead, theorists have been seeking a more natural solution to the dark-energy problem. The most extensively investigated alternative to quantum Àuctuations is a set of theories generically called quintessence, similar to Aristotle’s celestial ¿fth essence, the material of the heavens. His other four Portrait of Greek philosopher Aristotle. elements were ¿re, earth, water, and air. Quintessence is like an extra energy ¿eld that happens to be repulsive, similar to quantum Àuctuations, but it’s not, strictly speaking, quantum Àuctuations themselves. It can be thought of as the latent heat of space associated with an unbroken (or a recently broken) symmetry. For example, a spherical droplet of water has perfect symmetry. It looks the same when viewed from any direction. A snowÀake is less symmetrical than a spherical droplet of water because the snowÀake looks the same only when viewed from certain directions. There is a preferred axis of symmetry, unlike the case for a water droplet. Latent heat is a certain energy that is released when a substance changes phase. Water has latent heat that must be removed in order for it to freeze into ice, for example. However, a substance can sometimes be supercooled below a temperature at which it normally releases its latent heat and changes phase. In that case, the latent heat keeps the substance in its previous phase. Some form of extra energy, or latent heat, might be what is currently accelerating the Universe. (Here, the analogy with supercooled water breaks down because its latent heat does not accelerate it.)

We can plot a curve of the energy of a system versus its symmetry parameter (often denoted by M) for a variety of temperatures. A ball on the curve represents the actual state of the system. Above a certain critical temperature, the lowest energy state is one of unbroken symmetry (M = 0). The ball simply rolls down to the bottom of the curve. Below the critical temperature, the curve’s character changes. The lowest energy state is one of broken symmetry. However, the system can remain in a state of unbroken symmetry if the curve has the right shape— for example, a dimple at M = 0 in which the ball can sit. The latent heat is the extra energy that the system now contains. If the system is perturbed, the ball can pop out of the dimple and roll down the curve, breaking symmetry and releasing its latent heat. Different substances have different curves, some of which can be quite Àat, wherein the breaking of symmetry occurs slowly. In the case of the Universe, the latent heat is dark energy that drives the accelerated expansion. As long as that energy is nonzero, accelerated expansion can occur. Recall from Lecture 82 that different expansion histories will lead to different curves for the graph of observed peak brightness of a supernova versus its redshift. By observing hundreds of distant supernovae, we are looking back in time to see which of these curves the Universe actually follows. A team called ESSENCE, or Equation of State: SupErNovae Trace Cosmic Expansion, is one of several attempting to measure the equationof-state parameter of the Universe, or w. Mathematically, w = Ɋ/(ȡc2), in which w is the pressure of the dark energy (P) divided by its energy density (ȡc2, its mass or energy times the speed of light squared). The density ȡ is proportional to (volume)–(1 + w). For normal non-relativistic matter, w = 0. For example, if there are 1000 particles in a box and the box expands but still has 1000 particles, the density is proportional to the reciprocal of the volume. For photons, w = 1/3 because they stretch with the Universe. For the cosmological constant (ȁ), w 1 . Because 1 + –1 = 0, the density remains constant, independent of the volume. For quintessence models, w  –1. Thus, we would like to measure w to see if it equals –1 or is clearly inconsistent with –1. Surprisingly, our initial results, and those of other teams, are that w is consistent with –1. Moreover, there is no clear observational evidence that w is changing with time, but in generic quintessence models, it does change with time. Thus, currently, it appears 445

as though the vacuum energy provided by the quantum Àuctuations is at least as good an explanation for dark energy as any quintessence models. Some quintessence models predict a value of w close to –1; thus, the fact that we measure it to be –1 doesn’t prove that dark energy consists of vacuum Àuctuations. It might be a type of quintessence that yields nearly the same answer. But we can rule out forms of quintessence that have values of w very different from –1.

Lecture 88: Dark Energy—Quintessence?

Some quintessence models predict a value of w more negative than –1, which means that the vacuum density increases (gets stronger) with time. In such a scenario, the vacuum energy density will come to dominate gravity within galaxy clusters, ripping them apart. Eventually, galaxies, planetary systems, stars, planets, people, and even atoms will Ày apart in a so-called “Big Rip.” Even if such a hypothesis were supported by observations (which is not clearly the case), the Big Rip wouldn’t happen for a very long time. It’s also possible that the character of the dark energy or the quintessence will change in the future. Instead of being gravitationally repulsive and stretching space, it could become gravitationally attractive. If so and if ȍtotal > 1.00, the Universe might end in a Big Crunch—but not sooner than in 30 billion years, at the very least. These various explanations of dark energy are rather abstract, dif¿cult to comprehend, and still incomplete. We don’t know whether the dark energy will ever change sign, becoming gravitationally attractive. Though the Universe might expand forever, continued research is needed to know with more certainty. Ŷ

Important Terms quintessence: A new particle or ¿eld in physics that can lead to repulsive dark energy. supercooled: The condition in which a substance is cooled below the point at which it would normally make a phase change.

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Suggested Reading Guth, The InÀationary Universe: The Quest for a New Theory of Cosmic Origins. Greene, The Fabric of the Cosmos: Space, Time, and the Texture of Reality. Kirshner, The Extravagant Universe: Exploding Stars, Dark Energy, and the Accelerating Cosmos. Krauss, Quintessence: The Mystery of the Missing Mass. Livio, The Accelerating Universe: In¿nite Expansion, the Cosmological Constant, and the Beauty of the Cosmos. The Once and Future Cosmos (special edition of Scienti¿c American, 2002). Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. Do you consider the near equality of the energy densities of gravitationally attractive matter and dark energy to be surprising?

2. If you are decreasing the temperature of water in a freezer tray in order to make some ice, is it suf¿cient to remove just enough heat from the water to bring it down to 32° F (0° C, the freezing point of water), or is something extra needed?

3. What do you think living in the Universe would be like, far in the future, if the Big Rip were to happen?

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Grand Uni¿cation & Theories of Everything Lecture 89

“To get a much more complete understanding of the dark energy, we will probably require something like a ‘theory of everything,’ a uni¿ed theory of the fundamental forces, and particles, and ¿elds of physics.”

Lecture 89: Grand Uni¿cation & Theories of Everything

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more complete understanding of dark energy will almost certainly require a uni¿ed theory, a so-called theory of everything (TOE), reconciling all the known fundamental forces of nature. Dark energy provides an opportunity to test modern TOEs that attempt to unify the forces of nature into a single comprehensive framework. Moreover, some potential causes of dark energy might be directly related to other important concepts. Traditionally, there are four fundamental forces in nature. The ¿rst is gravity, which acts on all matter and energy and has an in¿nite range. The second is electromagnetism, which is roughly 1039 times stronger than the force of gravity, but it acts only on charged particles. The third is the strong nuclear force, which binds protons and neutrons together in an atom’s nucleus. One hundred times stronger than electromagnetism, it is a residual effect of something more fundamental and stronger, called the color force, which binds quarks in protons and neutrons. The fourth is the weak nuclear force, having roughly 10–6 the strength of the electromagnetic force. This force governs certain types of radioactive decay (such as the decay of neutrons into protons, electrons, “The idea of uni¿cation and antineutrinos). theories is to try to see whether we can Uni¿cation theories attempt to understand understand these these different forces as different different forces as manifestations of some greater force. For example, in the past few decades, being actually different electromagnetism and the weak nuclear manifestations of some force have been uni¿ed into something greater, more uni¿ed, called the electroweak force. The two more fundamental force.” forces are different at low energies, but when protons collide with energies 448

corresponding to 100 to 1000 proton masses, they behave in a similar manner; they are indistinguishable from each other. As an analogy, consider a coin. If we spin it rapidly, with high energy, it appears symmetric (the same from all directions), neither heads nor tails. But when it comes to rest, we see either heads or tails. In 1865, James Clerk Maxwell showed that electricity and magnetism are fundamentally related—the electromagnetic force. The uni¿ed equations explained the phenomenon of light. Ideally, a grand uni¿ed theory would unite the strong nuclear force and the electroweak force. Candidate theories have been developed, but we don’t yet have proof for any of them. Our current grand uni¿ed theories generically say that a proton, like a neutron, is a fundamentally unstable particle, but though the neutron decays after 15 minutes, the proton could take 1040 years. Given that the Universe is only 1010 years old, not many protons have decayed! Such theories also predict that there are supersymmetric partners to particles, called selectrons for the electrons, sneutrinos for the neutrinos, and photinos for the photons. None of these partner particles has ever been observed, but at least they are testable predictions. Even more ideal, a superuni¿ed force in a TOE would unite the grand uni¿ed force with the gravitational force. Some type of supersymmetry might bring it all together. In short, the goal is to ¿nd one theory, or force, from which everything else can be derived. Discovering a superuni¿ed force and TOE has two major obstacles. First, we don’t know why gravity is so weak. We can observe this by watching how a nail clings to a small magnet; the force of gravity—exerted by the entire Earth—is weaker than the magnetic attraction. In order for the gravitational force between a proton and an electron in an atom to be comparable to the electric force, protons and electrons would need to have 1019 proton masses, known as the Planck mass. Second, the two great pillars of modern physics— general relativity and quantum mechanics—are mutually incompatible. Quantum mechanics describes the properties of matter on small scales (molecules, atoms, subatomic particles), while general relativity describes the Universe over large scales (stars, galaxies, galaxy clusters). There is no theory describing the properties of large masses in small volumes, no quantum theory of gravity reconciling the two pillars. For example, the singularity in a black hole has a nonzero mass in a very small volume, but we 449

don’t have a theory that explains it. Similarly, if the Universe has a nonzero total mass and energy and, initially, its mass was compressed into a small volume, we need to consider both quantum mechanics and general relativity to explain the Big Bang.

Lecture 89: Grand Uni¿cation & Theories of Everything

Even without the Big Bang and black-hole singularities, the incompatibility between the two theories affects all of empty space. According to the Heisenberg uncertainty principle, over smaller and smaller distances (probed by shorter and shorter time scales), the uncertainty in energy progressively increases: 'E 't ! h / 2S, in which h is Planck’s constant. Therefore, energy must be Àuctuating at all times in a chaotic, unpredictable way. If it didn’t, we could determine the energy of every point in space and know what it is—but this isn’t allowed by the Heisenberg uncertainty principle. Energy changes quickly and chaotically over time through the creation of virtual pairs of particles; at every point in space, they occur all the time. If we probe space on smaller scales, quantum theory predicts that larger amounts of energy are chaotically created and annihilated. According to general relativity, any energy is also associated with space-time curvature. Thus, the space-time curvature is extreme and chaotically Àuctuating, but general relativity describes only smooth variations, not chaotic and giant Àuctuations. If we extrapolate this known physical process—that space teems with activity—down to the smallest imaginable scales, we see in¿nite energy Àuctuations and, hence, in¿nite (and rapidly varying) curvature in space-time. Zooming in to scales of 10–33 centimeters, the so-called Planck length, the associated energies of these virtual particles created out of nothing are 1019 times the mass of a proton, the Planck mass. At that mass, gravity becomes just as important as the other forces, further muddling the theories. Even stopping at the Planck length, the problems persist. We expect the vacuum energy density (cosmological constant, :/) to be 10120, yet the observed value is merely 0.75. If we postulate a perfect cancellation of the quantum ¿elds, in which positive-energy Àuctuations balance out negative ones, the vacuum energy density should be precisely 0, yet the measured value is 0.75.

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Perhaps we can avoid the in¿nite energy and in¿nite curvature Àuctuations by appealing to something called string theory. String theory forbids consideration of in¿nitesimally small points or even regions of space. Space itself and the particles that occupy space have a minimum size—the Planck length, 10–33 centimeters; anything smaller is forbidden. These particles are thought to be little packages of energy in a loop, or a one-dimensional string. Different types of strings vibrate at different rates and in different ways to form what we think of as different kinds of particles. The strings can be closed or open-ended, and they vibrate on the Planck scale in other dimensions. Because string theory says we can’t consider particles smaller than 1033 cm, we avoid the problem of in¿nite Àuctuations in energy and the space-time curvature. However, the vacuum energy should still be 10120, because everything is Àuctuating at the Planck mass scale; vacuum energy is essentially the Planck mass raised to a power of 4. The goal of string theory is to explain all physical properties of forces and particles with no unknowns—there should be only one way in which the Universe is built. We expect the typical particle energies in string theory to be 1019 proton masses, but we have not detected any such particles. How, then, do we arrive at the masses of observed particles—protons, electrons, photons? String theory says that most vibrations come in pairs and cancel each other out, lowering the expected masses of the particles. This is supposedly how low particle masses are achieved. A complete cancellation gives rise to a massless particle, called a graviton, the quantum carrier of the gravitational force. Unfortunately, no string theories have yet explained any of the observed particle masses—other than the hypothetical graviton, which has never actually been observed. Furthermore, despite their alluring mathematical elegance, string theories have not yet made any predictions that can be uniquely tested. Ŷ

Important Terms electroweak force: The uni¿cation of the electromagnetic and weak nuclear forces. grand uni¿ed theory (GUT): A theory that uni¿es the strong nuclear (“color”) and electroweak forces into a single interaction. 451

string (superstring) theory: A possible uni¿cation of quantum theory and general relativity in which fundamental particles are different vibration modes of tiny, one-dimensional “strings,” instead of being localized at single points. symmetric: Forces that are symmetric act identically. They act differently when the symmetry is broken. weak nuclear force: Governs the decay of a neutron into a proton, electron, and antineutrino.

Suggested Reading Calle, Superstrings and Other Things: A Guide to Physics.

Lecture 89: Grand Uni¿cation & Theories of Everything

Davies, Superforce: The Search for a Grand Uni¿ed Theory of Nature. Greene, The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. ———, The Fabric of the Cosmos: Space, Time, and the Texture of Reality. Kaku, Hyperspace: A Scienti¿c Odyssey through Parallel Universes, Time Warps, and the 10th Dimension. The Of¿cial String Theory Web Site, superstringtheory.com. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. t’Hooft, In Search of the Ultimate Building Blocks. Weinberg, Dreams of a Final Theory: The Scientist’s Search for the Ultimate Laws of Nature.

Questions to Consider 1. Why is it that we rarely think about (or seem to feel) electromagnetic forces, given that they are much stronger than gravity?

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2. The Planck mass is very large compared with typical masses of known subatomic particles. Compare the Planck mass with the size of some familiar objects. Is it as large as the mass of a proton, a bacterium, a grain of dust, a baseball, or an elephant? Conversely, the Planck length is exceedingly small. How many Planck lengths are a proton (1013 cm), a marble, and a car?

3. Do you think a theory that has few, if any, testable predictions in today’s Universe should be considered as serious science?

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Searching for Hidden Dimensions Lecture 90

“[String theories] … are these ideas that particles come in little fundamental packets of energy, almost shaped like a one-dimensional string. It’s the different vibrational modes of that string that correspond to different particles. … It turns out that for the vibrations to work … the vibrations have to occur in additional unseen dimensions—spatial dimensions that don’t correspond to the normal x, y, and z.”

Lecture 90: Searching for Hidden Dimensions

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hysicists are now attempting to unify all four forces of nature, and the leading set of hypotheses are generically called string theories. As we learned in Lecture 89, string theories suggest that particles come in tiny fundamental packets of energy, something like a one-dimensional string. Each has a different vibration mode that corresponds to different particles—neutrinos or electrons, for example. In order for the vibrations to work, they must occur in unseen spatial dimensions that are inaccessible on a macroscopic scale. We need at least a total of 10 dimensions, including time, in order for string theories to work. (These include the 3 known spatial dimensions and 6 additional spatial dimensions.) In fact, the most modern string theories work best with 11 dimensions; these are called M theories for “membrane.” Membranes can occur in two, three, or four dimensions or, in general, P dimensions (P-branes). The extra dimensions are not visible to us because they could be wrapped up at sizes comparable to the Planck length, 10–33 centimeters. As an analogy, a sheet of sandpaper seen from a distance might appear two-dimensional. But as we zoom in on smaller and smaller scales, the sand particles become visible, and clearly, the sandpaper is not twodimensional. Similarly, a garden hose might look like a one-dimensional object, a string of sorts, from a distance. But upon closer inspection, it wraps around another dimension. Ants can crawl around the surface of the hose and avoid one another, but if the hose were only one-dimensional, crawling ants would eventually bump into one another.

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The Kaluza-Klein theory is a historical precedent to the idea of extra dimensions. In 1919, Theodor Kaluza suggested the possibility of four spatial dimensions. He found that electromagnetism theory comes naturally from general relativity written in four spatial dimensions, and there may be a deep connection between the two. In 1926, Oscar Klein re¿ned this idea, postulating that the extra dimension curls up on a tiny scale. Though initially intriguing, the theory was soon forgotten because it seemed to conÀict with the properties of electrons. But other forces and particles weren’t known yet, and the possibility of even more additional dimensions was not suf¿ciently tested. The idea was resuscitated 50 years later, and it has met with more success. The three known spatial dimensions of x, y, and z are macroscopically large. Why, then, would the other seven dimensions curl up on the Planck scale? We don’t know. We also don’t know why they are so tiny or how they are shaped; they could be spheres, loops, or donuts, for example. The mathematics is complex, but it reveals seven curled-up spatial dimensions of a generic class called Calabi-Yau spaces. What are some of the predictions of string theories, and are they testable? All string theories predict the graviton, the quantum carrier of gravitational waves. Although no gravitons have yet been observed (technology is still insuf¿cient to do so), they are widely believed to exist. However, other theories predict gravitons; thus, they aren’t unique to string theories. String theories are also able to correctly predict the number of quantum states in a theoretical, specially constructed, tiny black hole. However, we are not likely to ¿nd a black hole of this sort anytime soon. A third theory predicts the presence of supersymmetric partners of particles, such as selectrons and squarks, but this prediction isn’t unique to string theories either. Some, but not all, string theories predict the occurrence of fractionally charged particles. If we found fractionally charged particles, we could throw out certain classes of string theories, but no such particles have yet been found. Many physicists don’t like string theories because they seem like fantasy. There are just too few—or maybe no—testable predictions. However, any string theory that categorically denies the possibility of dark energy must either be wrong or provide an entirely new framework to explain the accelerating Universe. Thus, dark energy does provide at least some test of string theories.

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Lecture 90: Searching for Hidden Dimensions

The latest string theories suggest that some of the extra dimensions might be macroscopically big compared to the Planck scale. For example, suppose gravity resides mostly in another spatial dimension, and only some of it leaks into our three large, experiential dimensions. If electromagnetic and other forces “feel” our “The math works three dimensions but not a fourth dimension, and gravity resides mostly in this fourth out best right now dimension, this could explain why gravity is so … with these 11 weak. One way to test for the presence of other dimensions in total.” dimensions is to study the collision of highenergy particles in accelerators. If gravitons are formed and escape to another dimension, there will be an apparent violation of the law of conservation of energy in our dimension because the energy of the incoming reactants might be greater than the total energy of the outgoing products. Such experiments are currently being conducted. Gravitons produced by core-collapse supernovae might also escape into other dimensions. For example, the supernova explosion SN 1987A was measured to have a certain energy. This measurement was shown to be incompatible with the existence of only four spatial dimensions, but it has not ruled out the possibility of ¿ve, six, or seven dimensions. Oddly, the more spatial dimensions there are, the less energy is lost. Let’s take a closer look at gravity. Suppose there are dimensions that are large compared to the Planck length but small compared to the scale over which gravity normally works. If gravity “feels” (has access to) this extra dimension, then it might spread out in a way incompatible with the 1/r2 law for gravity observed in three-dimensional space. In a two-dimensional space, the circumference of a circle is 2ʌr; thus, gravity spreads out over a progressively larger circumference, which grows in proportion to r, its radius. The gravitational force would be proportional to 1/r in twodimensional space, not to 1/r2 (the inverse-square law in three-dimensional space). Similarly, in a one-dimensional space, such as a line, gravity would be constant (that is, not diminish in strength) as distance increases along the line. However, if space had one large dimension, together with a small, wrapped-up dimension (like a sheet of paper curled into a tight cylinder), then 456

we would see a 1/r force law at small distances and a force independent of distance at large distances. Thus, we expect different gravity laws depending on how much gravity spreads out, which depends on how many dimensions there are. If we experimentally probe gravity on small scales, we might see that the force law deviates from 1/r2. Laboratory physicists are now checking for deviations at scales of 1 millimeter or less. If there are ¿ve spatial dimensions, then gravity should decline according to 1/r4, not 1/r2, because there are ¿ve (rather than three) dimensions into which the lines of force can spread out. Five-dimensional spreading of gravity is also consistent with some theories that postulate what dark energy could be. What about the largest scales? Could there be some very large extra dimensions? For example, perhaps our Universe is embedded in some bigger hyperspace, and material in that hyperspace is pulling on us from the outside. This is an alternative to the usual theory that the Universe is accelerating because of dark energy within it. Or perhaps dark matter (say, coincident with clusters of galaxies) is actually matter that exists in other dimensions. Maybe the Universe wraps around in such a way that we can feel the gravity of a very distant galaxy, but the gravity travels through another dimension— through a shortcut. We don’t see anything there, but we feel the effects of gravity, mimicking dark matter. There are other wild hypotheses, but we hope that someday, we will have experimental evidence con¿rming (or excluding) at least some of the possibilities. Ŷ

Suggested Reading Calle, Superstrings and Other Things: A Guide to Physics. Greene, The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. ———, The Fabric of the Cosmos: Space, Time, and the Texture of Reality. Kaku, Hyperspace: A Scienti¿c Odyssey through Parallel Universes, Time Warps, and the 10th Dimension.

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———, Parallel Worlds: A Journey through Creation, Higher Dimensions, and the Future of the Cosmos. The Of¿cial String Theory Web Site, superstringtheory.com. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Randall, Warped Passages: Unraveling the Mysteries of the Universe’s Hidden Dimensions.

Questions to Consider 1. What other examples, besides sandpaper and a garden hose, illustrate the presence of some macroscopically large as well as small dimensions?

2. Would the absence of deviations from the inverse-square law (1/r2) for gravity on 0.1-mm scales necessarily indicate that gravity can’t go into other dimensions?

3. Can you think of additional methods by which the presence of hidden or Lecture 90: Searching for Hidden Dimensions

invisible dimensions might eventually be discerned?

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The Shape, Size, and Fate of the Universe Lecture 91

“Is the Universe like some sort of a bubble, embedded in some higher dimensional space, a hyperspace, as represented here, for example? Or is it in¿nite; is its extent in¿nite, regardless of whether it is embedded in some higher-dimensional hyperspace?”

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he discussion of possible extra dimensions in the previous lecture rekindles our interest in the shape, size, and future of the Universe. Let’s start by considering its shape and size. As discussed in Lecture 85, measurements of the angular size of the most prominent tiny variations in the temperature of the CMBR indicate that the Universe is nearly Àat: ȍtotal = 1.0 ± 0.02, the ratio of the total mass and energy density to the critical density. If ȍtotal is, on average, exactly equal to 1.00 (to an in¿nite number of decimal places) throughout the entire Universe, then globally, the Universe is perfectly Àat. However, if ȍtotal differs even slightly from unity (1.00), then the overall geometry of the Universe is not exactly Àat. It might look basically Àat from our perspective, but really, it would be positively curved if ȍtotal is slightly greater than 1.00; it would wrap around itself like a sphere but in three dimensions (a hypersphere). If ȍtotal is slightly less than 1.00, the Universe would be negatively curved, shaped more like a horse’s saddle or a potato chip, but again, in three dimensions. It is probable that we see an apparent Àatness because we observe only a tiny fraction of the entire Universe, yet there are still slight spatial variations in overall density. This is known as cosmic variance. In the regions where ȍtotal > 1, the Universe is positively curved. In the regions where ȍtotal < 1, it’s negatively curved. We might never know the true overall geometry of the Universe because we can measure ȍtotal only in our observable part of the Universe. Although the simplest solutions to the Friedman equations discussed in Lecture 81 suggest that a precisely Àat Universe, as well as a negatively curved one, would necessarily be in¿nite, it turns out that both can be ¿nite. Universes that are isotropic from our perspective but not globally isotropic— 459

Lecture 91: The Shape, Size, and Fate of the Universe

not the same from all perspectives—could be ¿nite. For example, a donut could be Àat or negatively curved. Though the two-dimensional surface of a donut embedded in our three-dimensional space does not seem to be isotropic at any point (the measured curvature depends on the observed direction, for example), it can be isotropic if embedded in a larger multidimensional space. Positively curved universes can also have a geometry “The Universe, if it differing from that of a sphere. For example, does wrap around there may be dodecahedral universes (which, in itself, only does so two dimensions, have 12 faces). Such unusual on a scale larger ¿nite universes evolve in the same manner as their normal counterparts. The Àat and negatively than 78 billion curved ones expand forever, regardless of whether light years.” they contain any repulsive dark energy; they have ȍtotal < 1. Positively curved universes eventually collapse unless they contain a signi¿cant amount of repulsive dark energy, in which case, they can expand forever (unless the dark energy eventually becomes gravitationally attractive, causing ultimate collapse). How do we determine whether our Universe is in¿nite or ¿nite, and how do we map its global topology? In 1900, Karl Schwarzschild realized that in a ¿nite universe that wraps around itself, light can travel around the wrap, in principle, perhaps multiple times if the universe is suf¿ciently small. For example, looking in one direction, we would see light from Earth, from long ago, wrapping around the Universe and returning to our eyes. Light from even longer ago might wrap around twice. We might see multiple images of Earth, depending on the direction we look, because some directions might not wrap around or, at least, not on the same physical scale. The multiple images create a “hall of mirrors” effect. Essentially, we would see different snapshots of Earth at different points in time because of the ¿nite speed of light. The CMBR has provided the best test of this idea. Using the WMAP data of 2003, astronomers have been trying to ¿nd hot spots that might turn out to be two different images of the same density Àuctuation early in the Universe. As of yet, we have not found any that indicate the Universe wraps around itself. If it does, we live in a Universe at least 78 billion light years in diameter. 460

Astronomers are also speculating about what might happen to our Universe in the distant future. Although the expansion is accelerating with time right now, it could reverse and collapse in 30 to 40 billion years. If it doesn’t collapse, the Universe could live trillions or quadrillions of years or, possibly, even an in¿nite amount of time. The book The Five Ages of the Universe: Inside the Physics of Eternity, originally published in 2000 by astrophysicists Fred Adams and Greg Laughlin, has some very interesting views on what might happen to the Universe and its contents, which are summarized below. Because further discoveries have been made since the book’s initial publication, some of its conclusions have been revised in a 2006 edition. The book describes the notion of a cosmological decade, denoted by n, in which the age of the Universe at the beginning of a decade is 10n years. For example, at the beginning of the cosmological—not the real—decade 9, the Universe is 1 billion (109) years old. The authors identify ¿ve major eras in the Universe’s past and future. The Primordial Era marks the age of less than 1 million years: t < 106 years, roughly the time scale of recombination when the CMBR was released. (It was released at about 380,000 years, but this is close enough to 106 for order-of-magnitude–type arguments.) For our purposes, we will refer to the Primordial Era as n < 8 because before t = 108 years, stars didn’t exist. The Stelliferous Era—¿lled with stars—lasts from 108 to 1014 years after the Big Bang. This is followed by the Degenerate Era (1014 to 1040 years), which will have only white dwarfs, brown dwarfs, neutron stars, and other degenerate objects. Next, the Black Hole Era (1040 to 10100 years) will have only black holes, after all protons decay into other particles. Finally, there is the Dark Era (>10100 years), when the Universe will contain only electrons, positrons, neutrinos, and photons. We live in the Stelliferous Era, a time of much star formation, which will continue until hydrogen gas is no longer available to generate new stars or to fuel existing ones. Main-sequence stars that survive toward the end of this era will be the low-mass, slowly fusing red dwarfs. When they ¿nally burn out all the hydrogen in their cores, they will become degenerate white dwarfs. As far as the Earth and Sun are concerned, most of the interesting events in this era will occur shortly after the present time, at about 10 billion years, whereas not much will occur at 1013 years. For example, the Sun will glow 461

brighter in the next half-billion to 1 billion years and evaporate our oceans. Shortly after that, our atmosphere will evaporate. In 5 billion years, the Sun will bloat into a red giant, causing Earth to eventually spiral toward it and become vaporized. The Milky Way and Andromeda Galaxies will begin to collide in about 6 billion years, eventually forming a larger elliptical galaxy.

Lecture 91: The Shape, Size, and Fate of the Universe

If the Universe continues to expand at an accelerating rate, only gravitationally bound groups and clusters of galaxies will remain together. For example, we would see only nearby galaxies, but our Galaxy will consume all the galaxies in the Local Group before that time. By about 100 billion years, n = 11, most galaxies and clusters will have separated to the extent that an observer anywhere in the Universe would see nothing beyond his or her own galaxy or local cluster. The end of the Stelliferous Era will come when the hydrogen-burning stars burn out. Some clouds of gas might form a few new stars, but eventually, all the hydrogen in a typical galaxy will be depleted. The end of the Stelliferous Era will herald a colder, darker Universe. Following the Stelliferous Era, 100 trillion years from now, the Universe will consist of degenerate brown dwarfs (which were never full-Àedged stars undergoing normal hydrogen fusion; see Lecture 50), white dwarfs, and neutron stars. Some stellar-mass black holes will exist, and supermassive black holes will remain in galactic nuclei. A few other types of nondegenerate objects will also be present, such as planets, dark matter, and dark energy. During this Degenerate Era, the only activity will be sporadic visible radiation. This could be produced when brown dwarfs occasionally coalesce to turn into low-mass stars that will shine for a while. White dwarfs might merge to create a supernova. Also, white dwarfs should collect dark matter particles that annihilate each other and release some energy. Indeed, dark matter annihilation will become the dominant energy source in the Universe. This will end as white dwarfs are ejected from a galaxy and the supply of dark matter is depleted. By about year 1020, galaxies will have Àung out most of the stars and planets through gravitational interactions, reducing the material in galaxies. Remaining stars and planets will be devoured by black holes. By year 1030, galaxies will have been destroyed, leaving behind black holes and lone, wandering white dwarfs or neutron stars. These will eventually disintegrate 462

through proton decay. We don’t yet know the typical lifetime of a proton, though recent experiments suggest that it is longer than 5 u 1033 years. Theories predict that protons will decay by about 1042 years, certainly by 1045 years. Cosmological decade n = 40 is a compromise guess for the end of protons and the Degenerate Era. After the degenerate objects have disintegrated, only black holes will remain, marking the Black Hole Era. But even they don’t last forever. Recall the idea of Hawking radiation from Lecture 64. Particles and antiparticles can emerge from black holes as long as their partner particles and antiparticles enter the black holes with negative energy, as viewed by us. Stellar-mass black holes will evaporate after about 1065 years; million-solar-mass black holes, after 1083 years; the largest supermassive black holes, after about 10100 years. Once black holes evaporate, all that remains are elementary particles— electrons, positrons, neutrinos, and some very long-wavelength photons— because by this time, the Universe will have stretched so much that electromagnetic radiation will have stretched enormously with it. Beyond 10100 years, we enter the Dark Era, with no new source of light other than the occasional meeting and annihilation of electrons and positrons. Or an electron and positron can become weakly electrically bound to each other in an “atom” of positronium, but even they eventually decay and will be mostly gone by cosmological decade 110. In the end, the Universe will be made of elementary particles and radiation. It’ll be huge, but too old for any complex matter to exist. We might think life will end when the Stelliferous Era ends, at cosmological decade 14, but Freeman Dyson proposes that other life forms could arise. This is known as the cosmological time principle: We do not live at a special time, the only one that permits life. Instead, life of unknown forms might be possible far in the future. Though any speci¿c interactions will probably be slow, the available time scale for interactions will be very long. Ŷ

Suggested Reading Adams and Laughlin, The Five Ages of the Universe: Inside the Physics of Eternity.

463

Davies, The Last Three Minutes: Conjectures about the Ultimate Fate of the Universe. Hawley and Holcomb, Foundations of Modern Cosmology. Kaku, Parallel Worlds: A Journey through Creation, Higher Dimensions, and the Future of the Cosmos. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed.

Questions to Consider 1. Why does the measurement ȍtotal = 1 not necessarily tell us that the global geometry of the Universe is precisely Àat?

2. What ultimate fate would you philosophically “prefer” for the Universe:

Lecture 91: The Shape, Size, and Fate of the Universe

eternal expansion (and, hence, a cold, dark, vacuous ending) or ultimate collapse (and, hence, a hot, bright, dense ending)?

3. Do you think there will be any life in the Universe after the end of the Stelliferous Era?

464

In the Beginning Lecture 92

“We can learn about conditions in the early Universe, and the physics of very hot gases, by seeing what kinds of effects those gases and those conditions had on the current large-scale properties of the Universe.”

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sing well-established physics, we can reasonably postulate how the Universe began back to time (t) = nearly zero. In the early Universe, gases consisted of interacting particles, antiparticles, and photons. Everything was in thermal equilibrium, at the same temperature. This early Universe was relatively simple; few fundamental laws governed the physics of its hot gas. At t = 1 second, conditions in the Universe would have been similar to that of the central regions of stars. Because we understand the nuclear physics of stars and stellar life cycles, and we know the abundance of their various elements, we can reasonably assume that these conditions match those of the Universe at age t = 1 second. We’re also con¿dent about what happened at t = 10–12 seconds, when gas temperatures were about 1016 K, thanks to particle accelerators that can reproduce the behavior of matter under such temperatures. Even at t = 10–35 seconds, when gas temperatures were about 1028 K, particles, antiparticles, and photons would exist in thermal equilibrium; thus, we think we can understand these gases to some extent (though not entirely), despite the fact that we cannot reproduce these temperatures experimentally. However, by observing the current large-scale properties of the Universe, we can learn more about its early history. In a sense, the history of the Universe is our great particle accelerator in the sky. Though it’s dif¿cult to imagine, a lot could have happened in the ¿rst 10–35 seconds in the existence of the Universe. Particles would have been extremely close together, and with such tiny interaction distances and time scales, an enormous number of interactions could have taken place in almost no time. At t = 10–43 seconds, the Planck time, temperatures would have been 1032 K, and typical particle masses would have been 1019 proton masses. The space465

Lecture 92: In the Beginning

time curvature associated with those masses is huge; thus, we would need a quantum theory of gravity. Time and space might have been packaged in bundles, possibly bundles on the scales of the Planck time and the Planck length. Some physicists postulate a space-time foam, with packages of time and space Àitting into and out of existence. String theories or competing theories of everything may someday tell us more about conditions at the Planck time. Despite uncertainties, we begin to feel comfortable about our established physical models at t = 10–35 to 10–6 seconds. Between t = 10–35 and 10–6 seconds—a millionth of a second—temperatures dropped from 1028 K to 1013 K, while the Universe expanded. Particles, antiparticles, and photons existed in equilibrium. “Murray Gell-Mann, Particle-antiparticle pairs annihilated each other, producing high-energy photons; conversely, who won the Nobel high-energy photons spontaneously formed Prize in Physics in particle-antiparticle pairs. We think that quarks 1969 for his studies (constituent particles of protons and neutrons) of elementary were the main fundamental particles at that particles, ... was time. Initially, they were unbound, but they later formed bound pairs and triplets, producing just struck with normal matter. Quarks come in different types, the word ‘quark.’ or Àavors—up, down, strange, charmed, It comes from truth (or top), and beauty (or bottom)—and Finnegan’s Wake by in different colors—blue, green, and red. The terms Àavor and color are whimsical, used James Joyce.” simply to distinguish among different kinds of quarks; they don’t reÀect any real character. Quarks are bound to each other by gluons. Normal matter consists of up and down quarks, electrons, and electron neutrinos. A proton is two up quarks (each with a charge of +2/3) and one down quark (with a charge of –1/3). A neutron is one up quark and two down quarks. In this early Universal mixture, many particle reactions occurred. Quarks and antiquarks combined to form high-energy photons—gamma rays—which, in turn, spontaneously reformed as quarks and antiquarks. But at some stage, a slight imbalance of quarks over antiquarks must have formed—that is, an 466

imbalance of matter over antimatter, at a level of only about 1 part in a billion, to which we owe our existence. At t = 10–6 seconds, temperatures were 1013 K. As before, photons formed from the annihilation of protons, neutrons, and the antiparticles of both, but at this temperature, the typical photon energy was too low to re-create protons and neutrons. Protons, neutrons, and their antiparticles were annihilated for the last time, producing gamma rays; no new protons, neutrons, and their antiparticles formed thereafter. The slight imbalance of matter over antimatter left some extra protons and neutrons. Neutrons and protons could rapidly convert between each other. Neutrons combine with neutrinos to form protons and electrons, protons and electrons combine to form neutrons and neutrinos, neutrons and positrons combine to form protons and antineutrinos, protons and antineutrinos combine to form neutrons and positrons. The protons were slightly favored over the neutrons in these interactions because protons are a little less massive and, therefore, easier to create. As expansion continued; what happened at t = 1 second and later? Temperatures were about 10 billion K, and photons were no longer energetic enough to spontaneously create electron-positron pairs. The ¿nal annihilation of electrons and positrons formed more photons, contributing to a sea of photons that eventually became the cosmic microwave background radiation. There was an excess of electrons, the result of the previously generated asymmetry of matter over antimatter. These electrons were free, not yet bound to atomic nuclei because neutral atoms had not yet formed. Neutrons began to decay into protons, electrons, and antineutrinos, increasing the relative excess of protons over neutrons. Between t = 1 and 10 seconds, particles collided to form a heavier nucleus for a short time, only to be unbound again by more collisions. At t = 100 seconds, the Universe had cooled to about 1 billion K, and bound particles created by collisions among protons and neutrons could persist much longer. This was the era of primordial nucleosynthesis, when protons and neutrons combined to form deuterium nuclei, or deuterons, plus photons. Deuterons combined to form helium-3 nuclei (a lighter form of helium than the more common helium-4) and neutrons; additionally, they could combine to form tritons (tritium nuclei)—an unstable form of hydrogen—and protons. The helium-3 nuclei and tritons combined with deuterons to form helium-4 467

nuclei and either protons or neutrons. Most of the helium formed when the proton-to-neutron ratio was about 7:1 and made up about 25% of the Universe by mass; hydrogen made up the remaining 75%. A tiny sliver of lithium also formed. Because densities and temperatures were too low, no heavier elements could form until later, in stars. Primordial nucleosynthesis ended at about t = 10 minutes.

Lecture 92: In the Beginning

When did the ¿rst stars form? After primordial nucleosynthesis, the Universe was still a hot plasma, an ionized gas; electrons were not bound to atomic nuclei. The Universe was opaque until the time of recombination (380,000 years). Eventually, neutral atoms formed, and they, too, expanded and cooled. The ¿rst stars formed between 200 million and 400 million years after the Big Bang, when slightly overdense regions gravitationally collapsed by a suf¿cient amount. The Dark Ages (not the same as the Dark Era from Lecture 91) lasted from recombination to the ¿rst star formation, so called because the only extant light came from the hot plasma of the Big Bang. The ¿rst generation of massive stars produced supernovae, ejecting newly formed heavy elements, such as carbon, oxygen, and iron, into interstellar space. Thereafter, the average heavy-element abundance of the Universe continued to increase as more stars formed and exploded. The ¿rst few generations of stars produced much ultraviolet radiation, which reionized the neutral Universe. Today, most of the hydrogen in the Universe, apart from neutral clouds of gas within galaxies, is in a very low-density ionized state. The early Universe also produced lots of dust, ¿ne particulate matter, when the outer envelopes of stars expanded to become red supergiants. If we assume that we don’t see much of the early star formation because of dust that blocks our view, the derived star formation rate as a function of time differs from what we thought a few years ago. We previously thought that the star formation rate peaked around 4 billion years after the Big Bang. In the new model, however, the peak is closer to 1 billion years. Either way, the star formation rate in today’s Universe pales with what happened early in the Universe’s history. Though we’ve seen young (high-redshift) galaxies with the Hubble Space Telescope and the afterglow of the Big Bang with WMAP, the James Webb Space Telescope (proposed to launch in 2013) may give us a clearer picture of the very youngest galaxies, looking back to when the Universe was perhaps only a half-billion years old. Ŷ 468

Important Term nucleosynthesis: The creation of elements through nuclear reactions, generally nuclear fusion.

Suggested Reading Adams and Laughlin, The Five Ages of the Universe: Inside the Physics of Eternity. Barrow, The Origin of the Universe. The Once and Future Cosmos (special edition of Scienti¿c American, 2002). Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Tre¿l, The Moment of Creation: Big Bang Physics from Before the First Millisecond to the Present Universe. Weinberg, The First Three Minutes: A Modern View of the Origin of the Universe.

Questions to Consider 1. Explain why we can consider with some con¿dence the behavior of the Universe early in its history, even before it was 1 second old.

2. Consider the Universe at an age of 1013 seconds. If typical interactions between particles took only 1023 seconds, how many such interactions could a given particle have experienced by that time? Does this make it easier to understand why time intervals that to us seem ridiculously short were actually very signi¿cant soon after the birth of the Universe?

3. If hydrogen in the Universe remained neutral at all times after recombination (t = 380,000 years), would we expect to see any ultraviolet radiation from quasars at rest wavelengths shorter than 912 angstroms? (Note that 912 angstroms is the wavelength at which photons become energetic enough to ionize hydrogen from its ground state.) Such radiation is, in fact, seen from quasars. 469

The InÀationary Universe Lecture 93

“The Big Bang theory … doesn’t say that the big bang was an explosion in some preexisting space. It says that it was space itself that got created in some way that we don’t yet understand.”

T

Lecture 93: The InÀationary Universe

he Big Bang theory postulates that the Universe began long ago in a very hot, dense, compressed state, which then began expanding and cooling. The Big Bang theory is widely accepted. Its foundation and its predictions are supported by a number of observations, as follows. The Universe is expanding with time; clusters of galaxies are receding from us, as shown by Hubble’s law. Through various measurements, such as the surface brightness (the brightness per observed unit of area) of galaxies as a function of redshift, we know that the space between clusters of galaxies is growing. Galaxies are not like bullets Àying through some preexisting space; instead, space itself expands with time in the Big Bang theory. Contrary to popular belief, the Big Bang wasn’t an “explosion” in preexisting space. The Universe has a ¿nite age, 13.7 ± 0.2 billion years. We know of no older objects; globular clusters are 12 to 13 billion years old, and some of the oldest white dwarfs are comparable in age. The cosmic microwave background radiation (CMBR) is not much older than the oldest stars. The Universe evolves. Distant galaxies and clusters, seen as they were long ago, generally look different from nearby galaxies. Moreover, quasars were visible in the distant past, at high redshifts, but are now very rare. The CMBR is a sea of photons left over from the Big Bang. The COBE satellite shows that the CMBR has a perfect black-body spectrum that corresponds to a single temperature, 2.725 K, about the temperature expected for an initially hot universe that has been expanding for 14 billion years. The CMBR has very small variations, or Àuctuations, in its observed temperature. The WMAP picture of the Universe nicely shows hot and cold spots, the seeds from which giant clusters and superclusters of galaxies formed, together with the voids between them. The abundance of helium in the Universe (roughly 25% by mass) is what we would expect if the helium had formed during primordial nucleosynthesis—a process that took place during the ¿rst 10 minutes 470

of the Universe’s life. Moreover, the helium abundance is nearly uniform throughout the Universe, as expected if it formed when the Universe was young. Heavy elements were produced later by stars, which ejected them into the cosmos in a spotty distribution—as expected in the Big Bang theory because primordial nucleosynthesis could not produce heavy elements. Despite the large amount of evidence strongly supporting the Big Bang theory, the original, standard form of the theory has several important problems, two of which are discussed here. The Big Bang theory cannot explain the overall smoothness, or uniformity, of the Universe: In all directions, the temperature of the CMBR corresponds to 2.725 K. How could widely separated regions of the Universe be in thermal equilibrium with each other when such vast regions cannot be traversed by signals traveling at or below the speed of light? In other words, if we are just now detecting photons from one direction in the sky that were emitted 13.7 billion years ago, there is no way those photons (or any other signals) could have reached the opposite part of the sky—yet the temperature in the other direction is the same. For example, a radiator takes a while to heat a room. It ¿rst heats the air particles next to it. Those heated particles heat the ones next to them, and so on, in a chain reaction that eventually heats the entire room. In fact, the Universe has always been larger than the distance light or any other signal could have traveled since the birth of the Universe. Thus, in the standard Big Bang theory, we must assume that different parts of the Universe were simply born with essentially the same temperature everywhere. Physicists would prefer to have a logical explanation for the incredible observed uniformity of the Universe. On the largest scales, the Universe is observed to be Àat, ȍtotal = 1.0 ± 0.02, which means that it must have begun its existence almost exactly Àat. In the standard Big Bang theory, the curvature of the Universe rapidly deviates from Àatness if it wasn’t Àat to begin with. If ȍ had exceeded 1 by even a small amount a long time ago, then with time, ȍ would have rapidly grown to a very large value (for example, 105) by now. If ȍ had been less than 1 by even a small amount a long time ago, then with time, ȍ would have quickly deviated to a very small value (typically, 10–5) by now. For ȍ to have deviated so little from 1 by this advanced age, it had to have started out exceedingly close to 1, which seems like a ¿nely tuned Universe. This is an

471

Lecture 93: The InÀationary Universe

assumption of the standard Big Bang theory, yet physicists would prefer to have a logical explanation for this incredible Àatness. To account for these and other problems with the standard Big Bang theory, in 1980, Alan Guth and Andrei Linde independently postulated that the early Universe began much smaller than we initially thought. It subsequently went through a period of exponential expansion (inÀation), perhaps doubling in size every 10–37 seconds (or less) for a period of 10–35 seconds. An initial tiny volume could theoretically be in thermal equilibrium because there would have been enough time for a uniform temperature to permeate the entire area. Suddenly, the Universe expanded exponentially, but its temperature (although plummeting from “If our part of the the expansion) remained uniform because Universe … is only the Universe expanded by the same amount everywhere. What about the Universe’s observed a tiny fraction of Àatness? If it began tiny, then inÀated to some all that there is, giant region much bigger than the parts we can then it will look see, then the parts we see look Àat because they Àat regardless of are only a tiny fraction of the whole Universe. the shape of the Let’s take a closer look at the Universe’s size. At overall Universe.” the present time, the radius of the observable part of the Universe is roughly 1027 meters. If we use the standard Big Bang theory to extrapolate back to time t = 10–40 seconds, we see that the Universe was still too large to accommodate thermal equilibrium. However, if the Universe instead had a radius of about 10–52 meters at time t = 10–40 seconds, its size was small enough for thermal equilibrium to have been achieved. Additionally, assuming that the Universe expanded exponentially during its inÀationary period, a size of 10–52 meters at t = 10–40 seconds can easily account for the current size of the observable Universe. The Universe can grow by a huge factor, and different inÀation theories give different numerical values for the expansion factor. We don’t really know how much it might have expanded because we don’t understand the physics of extremely hot, compressed gases very well. In extreme cases, the expansion factor might have been as large as (1010)12. It’s entirely possible that the ratio of the radius of the total Universe to the radius of the observable Universe 472

may be larger than the ratio of the radius of the observable Universe to the radius of a proton, about 1041. In other words, all that we can see compared with all that there is might be similar to, or smaller than, the fraction of the observable Universe occupied by a proton. This exponential growth of the Universe’s size is not a violation of Einstein’s special theory of relativity, which says that no material object can travel through space at a speed exceeding that of light. Space itself can expand faster than the speed of light. If the Universe expanded by truly gargantuan factors or is in¿nite in extent, there are a huge number of physically independent regions that all began in the same place. Further, the laws of physics would be the same in all of these independent regions. Some physicists postulate that if our observable Universe has a ¿nite number of particles—and assuming that they can be arranged in only a ¿nite number of ways—then there could be other regions of the Universe that look identical to ours; that is, somewhere, there may be copies of ourselves. However, there may be an uncountable number of possibilities for how the particles can be arranged and how they could interact, just as we have uncountable in¿nities in irrational numbers. Moreover, our own volume of space is not completely isolated from all other volumes. We may not see beyond 14 billion light years, but objects near the edge of our observable part of the Universe can “see” and interact with objects near them—at distances beyond where we can see. Ŷ

Name to Know Guth, Alan (1947 ). American physicist; proposed the inÀationary theory of the Universe to eliminate some glaring problems with the standard Big Bang model. His perspective was that of an elementary particle physicist, not an astronomer; he was most troubled by the absence of magnetic monopoles.

Important Term inÀationary universe: A modi¿cation of the standard Big Bang theory. Very early in its history (e.g., t | 1037 seconds), when the Universe was exceedingly small, it began a period of rapidly accelerating expansion, making its ¿nal size truly enormous. Subsequently, the regular Big Bang expansion ensued. 473

Suggested Reading Barrow, The Origin of the Universe. Ferris, The Whole Shebang: A State-of-the-Universe(s) Report. Guth, The InÀationary Universe: The Quest for a New Theory of Cosmic Origins. The Once and Future Cosmos (special edition of Scienti¿c American, 2002). Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Tegmark, “Parallel Universes,” Scienti¿c American, May 2003, p. 40. Tre¿l, The Moment of Creation: Big Bang Physics from Before the First Millisecond to the Present Universe.

Questions to Consider 1. Are you troubled by the great uniformity of the Universe and by its global Àatness in the context of the standard Big Bang theory?

Lecture 93: The InÀationary Universe

2. To illustrate exponential growth, try folding a newspaper in half repeatedly, getting a progressively thicker stack of pages. How many times do you think you could fold it with your own hands and muscles? How many times would you need to fold it to get a stack as high as your room’s ceiling or a skyscraper?

3. Suppose that during inÀation, the size-doubling time scale was only 1038 seconds. If inÀation started at t = 1037 seconds and continued until t = 1035 seconds, about how many doublings occurred? If the Universe started out with a diameter of 1033 cm (the Planck length) at t = 1038 seconds, what would its diameter be at the end of inÀation?

4. How do you feel about the possibility that there are exact duplicates of ourselves elsewhere, leading exactly the same lives or lives that begin to differ with each passing second of time?

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The Ultimate Free Lunch? Lecture 94

“InÀation—or something like it, something with a similar effect—is widely accepted by cosmologists these days because it removes some of the unphysical, arbitrary-sounding assumptions of the standard Big Bang theory, and it also produces testable predictions that, in fact, agree with observations.”

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he inÀationary concept that the Universe began miniscule in size, then grew by a gargantuan factor in the ¿rst blink of its existence, sounds like a wild idea. Yet this or a similar effect is widely accepted because it removes some of the arbitrary assumptions of the standard Big Bang theory and has testable predictions. How might inÀation have occurred? Recall that quantum Àuctuations in the density of the Universe occurred shortly after its birth, before and during rapid inÀation that increased the physical size of the Àuctuations. These, in turn, became the seeds for the formation of giant galaxies, clusters, superclusters, and voids, as seen by WMAP and its predecessors. In the last few billion years, an accelerated expansion began again—reminiscent of, but much weaker than, the initial and rapid inÀation of the Universe. We don’t know why inÀation occurred, but its physical mechanisms may have been similar to quintessence models for dark energy. Quintessence is a repulsive energy ¿eld, the latent heat of space associated with an unbroken or a recently broken symmetry. InÀation might have been caused by an unbroken or recently broken symmetry, such as the splitting of the grand uni¿ed force into the strong nuclear force and the electroweak force. At t = 10–37 seconds, the temperature was 1029 K. Everything was in thermal equilibrium, and at least three forces—the strong nuclear force, the weak nuclear force, and electromagnetism—were uni¿ed. As the Universe cooled, the grand uni¿ed force should have split into the electroweak force and the strong nuclear force, an asymmetry. However, suppose the Universe cooled below 1029 K without breaking symmetry; that is, the strong and electroweak forces remained uni¿ed as the grand uni¿ed force at age t = 10–37 seconds. In such a scenario, the Universe would have contained latent heat—that is, too much energy for its temperature, like water 475

Lecture 94: The Ultimate Free Lunch?

supercooled to below 0° C without freezing. It is possible that this latent heat of a supercooled Universe drove inÀation, essentially giving the Big Bang its “bang.” It would have lasted only a tiny fraction of a second. The inÀation propelled the Universe by repulsive energy, a latent heat called an energy of the false vacuum—false because it has an extra energy associated with it. When the transition to a broken symmetry eventually occurred, the standard Big Bang theory subsequently took over. This might have occurred around an age of t = 10–35 seconds. The grand uni¿ed force split, and the “The early inÀation latent heat (the energy of the false vacuum) was of the Universe released, turning it into particles, antiparticles, may have been and photons. what gave the Big The predictions of inÀation theory are Bang the ‘bang.’ ” spectacular. As discussed in Lecture 93, inÀation can account for the uniformity (homogeneity and isotropy) and Àatness of the Universe. InÀation theory can also account for the absence of magnetic monopoles, or unmatched north and south magnetic poles: They were abundantly created at early times, then inÀation pushed them away from each other, thereby making them very rare in any given volume. InÀation can explain why the Universe is probably much bigger than we can observe. If the Universe does have an edge, it must be way beyond what we can see because we detect no clear evidence for any inhomogeneities on the largest scale. InÀation theory also explains the observed distribution of matter over various size scales in the Universe. In the ¿rst tiniest fraction of a second after t = 0, quantum Àuctuations in density gave rise to density variations in the Universe. InÀation expanded those small variations to proportions from which superclusters of galaxies, voids, and clusters of galaxies could emerge through the attractive force of gravity. The total energy of the Universe appears to be zero or close to it. Matter, antimatter, and photons together have an equal amount of energy but opposite in sign to the gravitational energy associated with them. InÀation theory also has a total energy of zero; it would take only a spark to jumpstart inÀation. Here is where inÀation theory becomes quite speculative: Where did the spark come from? One logical possibility for the spark is a quantum 476

Àuctuation produced out of nothing at all. Recall an interesting consequence of Heisenberg’s uncertainty principle that virtual particles can arise from empty space if they have ǻEǻt < h/2ʌ. If one such Àuctuation lasted suf¿ciently long, inÀation could get a jumpstart and take over, creating a gigantic universe out of the quantum Àuctuation. If that Àuctuation grew according to inÀation theory and that growth conserves energy, it still has zero, or essentially zero, energy; no new energy would be created at all. Effectively, we have a universe from nothing—the ultimate free lunch! Even before the development of inÀation theory, some physicists had speculated that the whole Universe might have been a quantum Àuctuation out of nothing. In particular, looking at Heisenberg’s uncertainty principle, if ǻE = 0 and ǻt is in¿nity, the product of those is still less than Planck’s constant. If the Universe truly has zero total energy or nearly so, it may itself have been a quantum Àuctuation out of nothing, and it still exists because the uncertainty principle allows for it. Though we don’t know the details of the mechanism yet, nor how much the Universe expanded and what energies and ¿elds were involved, inÀation theory seems to explain many of the things that we otherwise can’t explain in the standard Big Bang theory. Are there alternatives to inÀation? One creative possibility was proposed by Paul Steinhardt of Princeton University. He suggested that inÀation didn’t really occur; rather, the Universe goes through cycles. The idea is based on certain extensions of modern-day string theory known as brane theory—for membranes. Our three-dimensional Universe is like a membrane Àoating around within a larger fourth spatial dimension (known as the bulk). Assuming there are multiple membranes Àoating in this fourth dimension, they can collide with each other and create something like a Big Bang. The theory avoids the need for a singularity, a point-like particle from which everything appeared, but it does not seem to account for the existence of membranes themselves. Our Universe might hit other planes in the future, causing additional Big Bangs. This cyclic model of the Universe—which is sometimes called ekpyrotic (“born in ¿re”) because of the heat supposedly generated when the membranes hit each other—lacks compelling evidence at the present time. One possible test of the hypothesis might be whether we can see the inÀuence of gravitational waves on the cosmic background

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radiation. In inÀation theories, gravitational waves are abundantly produced in the early Universe, whereas they are not in the Ekpyrotic model.

Lecture 94: The Ultimate Free Lunch?

Another possibility is that the speed of light is variable. If light traveled much faster in the past, then very widely separated parts of the Universe might have been able to communicate with one another to arrive at a uniform temperature. A variable speed of light, however, doesn’t explain some of the other great successes of inÀation theory. It doesn’t account for all of the size scales for the observed structure of the Universe, for example. There is little evidence for a changing value of the ¿ne-structure constant, which is a measure of the strength of electromagnetic interactions in atoms: D e2/(hc/2S). If D were changing, there might be changes in the charge of the electron (e), Planck’s constant (h), or the speed of light (c). However, the claimed changes in D are too small to disprove the accelerating universe yet too large for consistency with existing theories. Another possibility is that general relativity is wrong. One suggestion is that the rotation curves of galaxies are not an indication of the presence of dark matter but, rather, an indication that general relativity is wrong for regions with very low gravitational ¿elds—that is, very far out in the outskirts of rotating galaxies. Speci¿cally, the theory called modi¿ed Newtonian dynamics (MOND) is used to explain the observed rotation curves of galaxies in a way that doesn’t require dark matter. It applies at accelerations below 108 cm/s2 (compared with about 1000 cm/s2 at Earth’s surface). The inverse-square law of gravity is modi¿ed. However, applied to clusters of galaxies ¿lled with hot, X-ray–emitting gas, the predictions of MOND do not match what we actually observe, whereas theories that incorporate dark matter and normal general relativity give much better agreement. Again, inÀation theory is on reasonably solid ground, even if the speci¿c mechanisms are unclear. But what happened before inÀation? Even more interesting, what was the Universe, or the space in which it’s embedded, like before time = zero? Ŷ

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Suggested Reading Barrow, The Origin of the Universe. Davies, Superforce: The Search for a Grand Uni¿ed Theory of Nature. Ferris, The Whole Shebang: A State-of-the-Universe(s) Report. Guth, The InÀationary Universe: The Quest for a New Theory of Cosmic Origins. Lederman and Schramm, From Quarks to the Cosmos: Tools of Discovery. The Once and Future Cosmos (special edition of Scienti¿c American, 2002). Pagels, Perfect Symmetry: The Search for the Beginning of Time. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Rees, New Perspectives in Astrophysical Cosmology. Tre¿l, The Moment of Creation: Big Bang Physics from Before the First Millisecond to the Present Universe.

Questions to Consider 1. Discuss what should have happened to the grand uni¿ed force as the Universe expanded and cooled at an age of about 10–37 seconds. Outline how the Universe may have supercooled, leading to inÀationary expansion by an almost arbitrarily large factor when the Universe was only 10–35 seconds old.

2. What do you think of the argument that the Universe has a total energy of zero and that it arose from a quantum Àuctuation out of “nothing”?

3. Does it even make sense to include times before t = 0 in a scienti¿c discussion, given that science is supposed to deal with predictions that are testable in principle?

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A Universe of Universes Lecture 95

“Though we don’t know what preceded inÀation, there are a number of speculative, though physically reasonable, possibilities. … A quantum Àuctuation out of literally nothing—nothing at all … the Universe just appeared—is a physically reasonable idea, but it raises some interesting questions. If there was nothing, not even the laws of physics, prior to the quantum Àuctuation, how did it know that it could occur?”

Lecture 95: A Universe of Universes

A

lthough we don’t know what the Universe was like before inÀation, a number of speculative yet physically reasonable hypotheses exist. In the last lecture, we explored the possibility of a quantum Àuctuation, which may have created the Universe out of nothing. But this idea creates further speculation. Heisenberg’s uncertainty principle says that quantum Àuctuations are an inherent property of the Universe. Perhaps, then, the laws of physics were created and a quantum Àuctuation occurred simultaneously. Or maybe the Àuctuation occurred in some preexisting, higher-dimensional space, which already had laws of physics. Both possibilities are based on reasonable physics. However, by their very nature, they are currently at the boundary of science or, in one sense, even beyond the realm of science because we don’t yet know of a way to experimentally test them, even in principle. In any case, the quantum Àuctuation hypothesis suggests that there may be multiple universes, perhaps in¿nitely many. Quantum physics supports the notion that multiple physically disconnected universes could exist. Unfortunately, we haven’t seen any, and we don’t have any physical access to other dimensions, so we don’t know. Perhaps independent, bubble-like universes Àoat around in a grander hyperspace. Each universe might even be governed by a unique, self-consistent set of fundamental laws of physics. A less extreme possibility is that the bubble universes all have the same set of mathematical equations, but the values of the physical constants—such as the speed of light, ¿ne-structure constant, or Newton’s constant of gravity—differ among these universes. If constants depend on the details of how symmetry broke among the uni¿ed forces, the physical constants associated with that breaking of symmetry might differ

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from one universe to another. For example, all snowÀakes have a general hexagonal symmetry dictated by the structure of the water molecule. But every snowÀake looks different in detail because of the differing molecular motions of the water at the time each snowÀake started to form. Or, perhaps different regions in a single large, inÀating space undergo symmetry breaking at different times, giving rise to many “universes” separated by still inÀating space. The symmetry breaking could have occurred differently in the various regions, giving rise to different values for the physical constants. Multiple universes might also arise from eternal inÀation, where a single inÀating domain—created by quantum Àuctuations—continues to produce numerous baby domains within it, which themselves inÀate and branch off eternally. Again, the physical constants might differ among these domains, or “universes.” Some physicists think black holes may connect multiple universes, through hypothetical connections called wormholes (see Lecture 63). Black holes might even create new universes—like a baby universe sprouting from the other side of a black hole. Emerging baby universes might look like their parents but with a few mutations, thus perhaps allowing a kind of “genetic evolution” of universes, an idea suggested by Lee Smolin in The Life of the Cosmos. Again, though the possible existence of other universes is a reasonable conclusion based on physics, we know of no way to experimentally test for their presence. Thus, by its very nature, this deduction removes itself from the realm of science, at “Maybe other universes least temporarily. are pulling outward on our Universe, causing An independent argument for multiple acceleration.” universes—multiverses—is based on one form of anthropic reasoning that says our existence can be used to make certain deductions about the Universe’s properties. The Universe seems to be ¿nely tuned for the emergence of complexity, culminating in life. Indeed, its pinnacle would be human intelligence. We can play with the equations of physics, changing the values of the seemingly arbitrary physical constants. Even slight changes can result in a much more boring universe, in which nothing interesting develops. For example, if the strong nuclear force were 20% weaker relative to the electromagnetic force, then only hydrogen 481

Lecture 95: A Universe of Universes

would be stable. There would be no nuclear energy to power stars, nor any heavy elements for life. If the strong nuclear force were 2% stronger than the electromagnetic force, then only helium would be formed during the Big Bang. There would be no hydrogen-burning stars, no water, no hydrocarbons. If the weak nuclear force were appreciably stronger, all hydrogen would have fused into iron during the Big Bang. Again, there would be no hydrogen, no fusion of hydrogen in stars, no carbon, no oxygen, nor any of the elements essential for life of our kind. If the weak nuclear force were weaker, then only helium would be formed during the Big Bang, but no hydrogen. If proton and neutron masses were more nearly equal, then, again, only helium would have formed during the Big Bang—just helium, or just neutrons, depending on how equal the proton and neutron masses were. If the mass of the neutron were somewhat higher relative to the proton, neutrons would not exist; there would be only hydrogen. Of course, a possible interpretation of the apparently “¿ne-tuned universe” is that a divine creator made only one universe, and we’re special. This anthropocentric suggestion is essentially one form of the “intelligent design” theory, but such an argument for God cannot be scienti¿cally proved or disproved; thus, we won’t consider it further in this science course. We could also argue that the Universe is special by happenstance, with or without God, and it happens to be just right for our existence by accident. Or, again, with or without God, multiple universes could span a wide range of physical properties, and we necessarily live in one with conditions suitable for the emergence of life. To some degree, our Universe is ¿nely tuned and special, but this would be expected assuming multiple universes spanning a wide range of physical properties. Ours is not necessarily the only interesting universe or the most interesting one; it is simply one island in a vast cosmic archipelago, and the majority of the other islands are boring or even “stillborn,” devoid of complexity. In a sense, the idea of multiple universes is a grand extension of the Copernican principle. However, many scientists despise anthropic reasoning because it’s not real science and it emphasizes our limited perspective. When we resort to such reasoning, some think we then stop seeking explanations for why the fundamental constants are as they are.

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Fred Hoyle’s studies illustrate another use for anthropic reasoning. He made some speci¿c quantitative predictions about the properties of the carbon nucleus, simply based on the observed abundance of carbon and oxygen in the Universe, and experiments later con¿rmed his predictions. Can we know for certain that other universes exist? The answer is no, at least not right now. The multiverse is a logical possibility that is based on science, yet by its very nature, it removes itself from the realm of science, at least temporarily. We 483

© Hemera Technologies/AbleStock.com/Thinkstock

On the other hand, the utility of anthropic reasoning can be illustrated by considering an ancient Greek philosopher contemplating the origin of Earth’s properties. In Aristotelian cosmology, the Earth was unique, a constant of the Universe. It had certain properties and was the only way it could have been because it was created that way. Going a step further, the philosopher might wonder what fundamental physics governed the properties of the Earth. Similarly, string theorists wonder what fundamental physics determines the mass of the proton or the vibration mode of a neutrino. The Greek philosopher might also reason that the properties of Earth are not uniquely speci¿ed but can take on a range of values depending on local details—where the clump of material happened to be from which the Earth formed. He could reason that these Copernicus and Galileo. properties must be within a certain window for us to exist. We can’t exist on Mercury or Neptune. We live in the place that’s just right because that’s one of the few places we could have lived. The philosopher might then wonder if there were an ensemble of objects—planets in this case—covering a wide range of properties. From this line of reasoning, he could conclude that other planets exist without ever having seen one. Though not rigorous proof, it is plausible.

may also ask why any universes should exist. However, we will probably never know why the laws of physics had to have been in place to begin with. Science alone probably cannot provide all the answers. But science can allow a systematic exploration of the Universe based on its observed properties, and experiments, and hypotheses, providing an ever-better working model of how this Universe “ticks.” Ŷ

Important Terms anthropic reasoning (or anthropic principle): The idea that given that we exist, the Universe must have certain properties or it would not have evolved so that life formed and humans evolved. multiverse: The set of parallel universes that may exist, with our observable Universe as only one part.

Suggested Reading Davies, The Accidental Universe. Ferris, The Whole Shebang: A State-of-the-Universe(s) Report.

Lecture 95: A Universe of Universes

Gribbin and Rees, Cosmic Coincidences: Dark Matter, Mankind, and Anthropic Cosmology. Leslie, Universes. Linde, “Future of the Universe,” in The Origin and Evolution of the Universe. The Once and Future Cosmos (special edition of Scienti¿c American, 2002). Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Rees, Before the Beginning: Our Universe and Others. ———, Our Cosmic Habitat. Smolin, The Life of the Cosmos. Velan, The Multi-Universe Cosmos. 484

Questions to Consider 1. De¿ne what is meant by the term universe. 2. Discuss how the observed properties of the Universe depend on the values of the physical constants.

3. Do you consider the possibility of multiple universes to be an extension of the Copernican revolution on the grandest scale?

4. How, in principle, might you test for the existence of other universes? If the presence of other universes cannot be directly tested, do you consider them to be outside the realm of science?

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ReÀections on Life and the Cosmos Lecture 96

“The Universe is truly vast, and this may make you feel small and insigni¿cant. … We now think the Universe extends far, far beyond just those parts that we can see. The parts we can see might be like a proton in the Universe. It might be so big, ¿lled with galaxies all over the sky, and our Milky Way Galaxy is just like one of these specks.”

Lecture 96: ReÀections on Life and the Cosmos

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e come to the ¿nal step in our extensive journey through the Universe, for a grand overview and some philosophical comments. The vastness of the Universe may make us feel small and insigni¿cant. After all, images of the Hubble Ultra Deep Field reveal 100 billion galaxies up to 14 billion light years in all directions—and that’s just in the part of the Universe we can see! We now think the Universe extends far beyond what we see. Indeed, all that we can see, if compared to what we cannot see, might be no more than the size of a proton when compared to our entire visible Universe. Our home Galaxy, the Milky Way, is just one typical galaxy among billions, each containing tens or hundreds of billions of stars. The Sun, a typical star, is a tiny part of the Milky Way Galaxy—even at 1.4 million kilometers across. The Sun is surrounded by a system of planets extending over billions of kilometers. Typically, the planets are separated by tens or even hundreds of millions of kilometers—a vast Solar System on a human scale but tiny compared to the entire Galaxy. Earth is just one of these planets, and a rather small one at that, and we occupy just a tiny fraction of Earth’s surface. Yet of all the ways the Universe could have developed, here we are. Consider what could have been. After the Big Bang, the Universe could have expanded too quickly or too slowly. Density variations might not have formed and grown—Àuctuations that gave rise to clusters of galaxies, stars, planets, and ¿nally, life as we know it. Heavy elements were cooked up within stars and subsequently expelled into the cosmos by gargantuan explosions, supernovae. Alter the physical constants just a little and, in many cases, stars don’t explode. But in our

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Universe, they did. Chemically enriched gases from supernovae spread throughout our Galaxy, gradually mixing with other nebulae. Eventually, they gravitationally collapsed, forming dark, dense clouds whose central regions subsequently fragmented into numerous stellar embryos and, ¿nally, into clusters of stars. Many newly formed stars were surrounded by disks of gas and dust from which planets coalesced. Suf¿cient quantities of heavy elements allowed rocky, terrestrial planets to form—planets close enough to their central stars to be bathed with light and heat, providing conditions conducive for the development of complexity. One of these planets was Earth, at just the right distance from a long-lived, stable star to allow the formation of ponds and oceans of water. Had our Solar System not been swept clean by a giant planet, like Jupiter, the remaining debris might have continued to crash into the Earth for billions of years, probably extinguishing any life. Had the giant planets been placed in highly eccentric orbits, Earth would soon have been ejected from the Solar System. Over time, natural processes increased the concentration of organic matter in ancient ponds, and somehow, somewhere, self-replicating organisms formed in the primeval broth and began to evolve. Life eventually evolved into humans with highly advanced brains, great dexterity, insatiable curiosity, and unlimited creativity—creatures that could gaze upon the heavens and wonder about our purpose, how we came to be, where we’re headed, and what makes the Universe tick. We are enormously complex structures. Even the simplest cell is far more complex than inanimate objects, such as rocks, stars, globular clusters, and galaxies. It is almost as though the Universe has developed a way to know itself, through us—the explorers, brains, and conscience of the Universe. Maybe it took in¿nitely many attempts for the multiverse to achieve a suitable universe with physical properties conducive to the formation of highly complex brains and an innate curiosity about the cosmos. Perhaps even within our own Galaxy, we are rare creatures to have achieved such a level of intelligence, curiosity, and mechanical ability. If the probability for intelligence forming is 1 over trillions or quadrillions, then even with hundreds of billions of stars, there may not be much intelligence in our Galaxy. Moreover, even if simple life does appear, it may take a long time for such complexity to develop, as in the case on Earth. Only in the 487

Lecture 96: ReÀections on Life and the Cosmos

last few million years of the 4.5-billion-year history of Earth have hominidlike creatures existed. And only in the last few hundred thousand years have there been Homo sapiens. Earth had to have certain conditions to allow our existence. For example, it needed a large Moon to stabilize its axis of rotation. Also, most other stars are less abundant in heavy elements and wouldn’t have formed rocky, Earth-like planets. The famous physicist Enrico Fermi wondered, if intelligence is common throughout the Galaxy, why have other life forms not contacted us? Why do we see no evidence of others? There could be intelligent life elsewhere—we may not be unique—but we are probably rare. We may not know about other life, but we do have a good understanding about much of the Universe. And who knows where future discoveries will take us? The late, celebrated physicist Richard Feynman wrote a poem expressing his great joy at thinking about nature. He ends by saying that we are matter with consciousness and curiosity, able to wonder about our own ability to wonder, and able to explore nature. Each of us, in a sense, is both a “It is almost universe of atoms and an atom in the Universe, but as though the a very special atom in this Universe. Universe has developed a way What is the purpose of the Universe? Why does to know itself, it even exist? Science can’t answer that, but we can explore how the Universe works. Einstein through us.” said, “The most incomprehensible thing about the Universe is that it’s comprehensible.” If some of us did not pursue the challenge of deciphering the cosmos, we would be letting ourselves down. Socrates said, “Education is the kindling of a Àame, not the ¿lling of a vessel.” Likewise, I hope these lectures have kindled your Socratic Àame and inspired you to study in more detail those parts of the Universe that most interest you. To help you follow some of the progress in science, some useful Web sites are included in the readings below. Some discoveries have practical spin-offs, such as Newton’s development of the laws of gravitation and calculus or the realization that the long-term

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NASA, ESA, Hubble Heritage (STScI/AURA)

survival of humans depends on our ability to thwart collisions with meteoroids or comets. Other discoveries simply advance our knowledge of the cosmos, allowing us to better understand the intricate workings of nature and to better appreciate our place within it. Perhaps the next time you look up at the dark sky, you will ponder the magni¿cence of the Universe and its contents— and the amazing fact that, through careful experiments, observations, and thought, humans are discovering what makes it all happen.

The Coma Cluster of Galaxies is one of the densest clusters known, containing thousands of galaxies.

Finally, astronomy is surely good for the soul, whatever that may be. Referring to astronomy, Socrates said, “In every man there is an eye of the soul which… is puri¿ed and re-illuminated [by such studies], and is more precious by far than ten thousand bodily eyes, for it alone sees truth.” May you continue to enjoy the wonders of the heavens! Ŷ

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Suggested Reading Astronomical Society of the Paci¿c, astrosociety.org. The Astronomy Café, astronomycafe.net. Feynman, Dyson, and Leighton, Classic Feynman: All the Adventures of a Curious Character. NASA, “Astronomy Picture of the Day,” antwrp.gsfc.nasa.gov/apod/. Pasachoff and Filippenko, The Cosmos: Astronomy in the New Millennium, 3rd ed. Rees, Before the Beginning: Our Universe and Others. Space News, space.com. Space Telescope Science Institute, hubblesite.org.

Questions to Consider

Lecture 96: ReÀections on Life and the Cosmos

1. Do you think some form of “life” could arise in most universes, almost regardless of the values of the physical constants?

2. What do you think is the purpose of the Universe? 3. Find news articles that describe new developments in astronomy, especially in areas covered by these lectures. How have things changed? Science is a dynamic process—nothing is cast in stone!

4. For you, what is the most important unanswered question about the cosmos, a discovery that you would like to see during your lifetime?

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Useful Symbols

In these course notes, the following mathematical symbols are used:

Symbol ~ § • ” >> 1014 years, assume the Universe expands forever.) “0” seconds ..................................... The birth of the Universe, perhaps from a quantum Àuctuation. 10í43 seconds.................................... Space-time foam? Gravity and grand uni¿ed force become separate. 10í37 seconds? ................................. InÀation begins. 10í35 seconds? .................................. InÀation ends. Strong nuclear and electroweak forces become separate. 10í11 seconds .................................... Weak nuclear and electromagnetic forces become separate. 10í6 seconds ..................................... Matter/antimatter annihilation; slight excess of protons and neutrons. 1 second .......................................... Electrons and positrons annihilate; slight excess of electrons. 102 seconds ...................................... Nucleosynthesis of lightest elements from protons and neutrons. 4 × 105 years (1013 seconds) ............ Formation of neutral atoms; Universe transparent.

Universe Timeline

3 × 106 years (1014 seconds) ............ First stars begin to form but not in galaxies. 109 years (3 × 1016 seconds) ............. Many galaxies form and begin assembling into clusters. 1010 years ......................................... Solar System forms (4.6 billion years ago). 1.4 × 1010 years ................................ Present age of the Universe.

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2 × 1010 years................................... Sun becomes a red giant and subsequently a white dwarf. 1014 years ......................................... Last low-mass stars die. 1020 years ......................................... Most stars and planets gravitationally ejected from galaxies. 1030 years ......................................... Black holes swallow most of the remaining objects in galaxies. 1038 years? ....................................... All objects except black holes disintegrate, due to proton decay. 1065 years ......................................... Stellar-mass black holes evaporate due to Hawking process. 10100 years........................................ Largest galaxy-mass black holes evaporate. 10110 years? ...................................... Positronium atoms (electron-positron pairs) decay, producing photons.

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Solar System Timeline

(Given in terms of years ago; 0 = today.) 4.6 billion years............................... Solar System forms. 3.9 billion years............................... Heavy bombardment of Earth by planetesimals subsides. 3.8 billion years............................... Possible formation of primitive life (de¿nitely by 3.5 billion years). 2 billion years.................................. Free oxygen begins to accumulate in atmosphere due to photosynthesis. 600 million years............................. Present atmosphere essentially complete. Multicellular life Àourishes. 550 million years............................. Cambrian explosion—formation of complex, hard-bodied animals. 240 million years............................. Mesozoic era—earliest dinosaurs appear. 65 million years............................... Extinction of the dinosaurs, along with two-thirds of all living species. 4.5 million years.............................. The ¿rst hominids appear. 160,000 years .................................. Early homo sapiens appear. Solar System Timeline

3000 years ....................................... Beginning of Iron Age. 250 years ......................................... Industrial Revolution. 100 years ......................................... Radio communication.

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Glossary

absolute magnitude: Logarithmic measurement of the luminosity of stars; assumes all the stars to be at the same distance of 10 parsecs from Earth. absorption line: A wavelength (or small range of wavelengths) at which the brightness of a spectrum is less than it is at neighboring wavelengths. accelerating universe: The model of the Universe based on recent observations that its expansion is speeding up with time. accretion: The transfer of matter to the surface of a star or a black hole. When the transferred matter goes into orbit around the object, an accretion disk is formed. active galaxy: A galaxy whose nucleus emits large quantities of electromagnetic radiation that does not appear to be produced by stars. (Radio galaxies are one example of active galaxies.) adaptive optics: Optical systems providing rapid corrections to counteract atmospheric blurring. analemma: The apparent ¿gure-8 path made by the Sun in the sky when photographs of the Sun’s position taken at a given time of day throughout the year are superimposed on each other. angstrom (Å): A unit of length commonly used for visible wavelengths of light; 1 Å = 108 cm. angular momentum: A measure of the amount of spin of an object; dependent on the object’s rotation rate, mass, and mass distribution.

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anthropic principle: The idea that given that we exist, the Universe must have certain properties or it would not have evolved so that life formed and humans evolved. antiparticle: A particle whose charge (if not neutral) and certain other properties are opposite those of a corresponding particle of the same mass. An encounter between a particle and its antiparticle results in mutual annihilation and the production of high-energy photons. apparent brightness: The amount of energy received from an object per second, per square centimeter of collecting area. It is related to luminosity and distance through the equation b = L/(4Sd2), the inverse-square law of light. archaeoastronomy: The study of the astronomical signi¿cance of ancient buildings and other structures. asterism: A grouping of stars that is not itself a full constellation but is part of a constellation. The Big Dipper is one example. asteroid: Chunk of rock, smaller than a planet, that generally orbits the Sun between Mars and Jupiter. astrometry: Measurement of the position and motion of the stars in the plane of the sky. astronomical unit (AU): The average distance between the Sun and the Earth (1.5 u 108 km).

Glossary

aurora: The northern or southern lights, caused by energetic particles from the Sun interacting with atoms and molecules in Earth’s upper atmosphere, making them glow. Baily’s Beads: During a solar eclipse, the effect of sparkling lights created by sunlight passing through valleys on the Moon’s surface.

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Big Bang: The birth of the Universe in a very hot, dense state 13.7 billion years ago, followed by the expansion of space. binary pulsar: A pulsar in a binary system. Often, this term is used for systems in which the pulsar’s companion is another neutron star. binary star: Two stars gravitationally bound to (and orbiting) each other. bipolar outÀow: A phenomenon in which streams of matter are ejected from the poles of a rotating object. black body: An object that absorbs all radiation that hits it; none is transmitted or reÀected. It emits radiation due to thermal (random) motions of its constituent particles, with a spectrum that depends only on the temperature of the object. black hole: A region of space-time in which the gravitational ¿eld is so strong that nothing, not even light, can escape. Predicted by Einstein’s general theory of relativity. brown dwarf: A gravitationally bound object that is insuf¿ciently massive to ever be a main-sequence star but too massive for a planet. Generally, the mass range is taken to be 1375 Jupiter masses. charge-coupled device (CCD): A solid-state imaging chip whose properties include high sensitivity, large dynamic range, and linearity. celestial equator: Projection of Earth’s equator onto the celestial sphere. celestial sphere: The enormous sphere, centered on the Earth, to which the stars appear to be ¿xed. centrifugal force: The outward force felt by an object in a rotating frame of reference. Cepheid variable: A type of pulsating star that varies in brightness with a period of 1 to 100 days. 497

Cerenkov radiation: Electromagnetic radiation emitted by a charged particle traveling at greater than the speed of light in a transparent medium. The blue light emitted is the electromagnetic equivalent of a sonic boom heard when an aircraft exceeds the speed of sound. Chandrasekhar limit: The maximum stable mass of a white dwarf or the iron core of a massive star, above which degeneracy pressure is unable to provide suf¿cient support; about 1.4 solar masses. chromosphere: Hot, thin layer of gas just below the Sun’s corona and above the photosphere. closed universe: A universe having ¿nite volume. cold dark matter: Nonluminous matter that moves slowly, such as neutron stars and exotic particles. collapsar model: Model proposed for some types of gamma-ray bursts, wherein a rotating, massive star collapses and forms two highly focused beams (jets) of particles and light. comet: An interplanetary chunk of ice and rock, often in a very eccentric (elongated) orbit, that produces a diffuse patch of light in the sky when relatively near the Sun as a result of evaporation of the ice. constellation: One of 88 regions into which the celestial sphere is divided. The pattern of bright stars within a constellation is often named in honor of a god, person, or animal.

Glossary

convection: Process by which bubbles of gas or liquid repeatedly heat and expand, rise and give off energy, and fall again; seen in the stars and in Earth’s core. core: In a main-sequence star, roughly the central 10% by mass. In an evolved star, usually refers to the degenerate central region.

498

corona: The very hot, tenuous, outermost region of the Sun, seen during a total solar eclipse. cosmic microwave background radiation: Radio electromagnetic radiation that was produced in the hot Big Bang. It now corresponds to T | 3 K because of the expansion and cooling of the Universe. cosmic rays: High-energy protons and other charged particles, probably formed by supernovae and other violent processes. cosmological constant: In Einstein’s general theory of relativity, a term (/) that produces cosmic repulsion that can counterbalance the attractive force of gravity. Recent evidence suggests that its value is nonzero and somewhat larger than originally postulated by Einstein, causing the observed acceleration of the Universe’s expansion. cosmological principle: The Universe is homogeneous and isotropic (that is, uniform) on the largest scales. cosmology: The study of the overall structure and evolution of the Universe. crepuscular rays: Beams of light shining through gaps in clouds, usually best seen near sunset or sunrise. critical density: The average density of the Universe if it were poised exactly between eternal expansion and ultimate collapse, if the cosmological constant is zero. dark energy: Energy with negative pressure, causing the expansion of the Universe to accelerate. dark matter: Invisible matter that dominates the mass of the Universe. degenerate gas: A peculiar state of matter at high densities in which, according to the laws of quantum physics, the particles move very rapidly in well-de¿ned energy levels and exert tremendous pressure.

499

deuterium: An isotope of hydrogen that contains one proton and one neutron. deuteron: A deuterium nucleus. diffraction: A phenomenon affecting light as it passes any obstacle, spreading it out. dipole ¿eld: The pattern of electric ¿eld lines produced by a pair of equal and opposite electric charges or of magnetic ¿eld lines surrounding a bar magnet. Doppler shift: The change in wavelength or frequency produced when a source of waves and the observer move relative to each other. Blueshifts (to shorter wavelengths) and redshifts (to longer wavelengths) are associated with approach and recession, respectively. E = mc2: Einstein’s famous formula for the equivalence of mass and energy. earthshine: Sunlight illuminating the Moon after having been reÀected from the Earth. eccentric: Deviating from a circle. Eccentricity is a measure of this. eclipse: The passage of one celestial body into the shadow of another or the obscuration of one celestial body by another body passing in front of it. ecliptic: The path followed by the Sun across the celestial sphere in the course of a year.

Glossary

electromagnetic force: One of the four fundamental forces of nature; it holds electrons in atoms. electromagnetic radiation: Self-propagating, oscillating electric and magnetic ¿elds. From shortest to longest wavelengths: gamma rays, X-rays, ultraviolet, optical (visible), infrared, and radio.

500

electron: Low-mass, negatively charged fundamental particle that normally “orbits” an atomic nucleus. electroweak force: The uni¿cation of the electromagnetic and weak nuclear forces. ellipse: A set of points (curve) such that the sum of the distances to two given points (foci) is constant. elliptical galaxy: One of the two major classes of galaxies de¿ned by Edwin Hubble; has a roughly spherical or elliptical distribution of generally older stars, less gas and dust, and less rotation than its spiral counterpart. emission line: A wavelength (or small range of wavelengths) at which the brightness of a spectrum is more than it is at neighboring wavelengths. equinox: One of two points of intersection between the ecliptic and the celestial equator, or the time of the year when the Sun is at this position. escape velocity: The minimum speed an object must have to escape the gravitational pull of another object. event horizon: The boundary of a black hole from within which nothing can escape. expansion age: The time estimated for the age of the Universe since the Big Bang, determined by measuring the rate at which galaxies are receding from one another; currently thought to be about 13.7 billion years. extinction: The obscuration of starlight by interstellar gas and dust. extrasolar planet: A planet orbiting a star other than the Sun; an exoplanet. eyepiece: A small tube containing a lens (or combination of lenses) at the eye end of a telescope, used to examine the image.

501

Àat (critical) universe: A universe in which the laws of Euclidean geometry hold. fusion: The formation of heavier nuclei from lighter nuclei. galactic cannibalism: The swallowing of one galaxy by another. galaxy: A large (typically 5000 to 200,000 light years in diameter), gravitationally bound system of hundreds of millions (and up to a trillion) stars. Galilean satellites: The four large moons of Jupiter (Io, Europa, Ganymede, Callisto). gamma rays: Electromagnetic radiation with wavelengths shorter than about 0.1 Å. gamma-ray burst (GRB): A brief burst of gamma rays in the sky, now known to generally come from exceedingly powerful, distant objects. general theory of relativity: Einstein’s comprehensive theory of mass (energy), space, and time; it states that mass and energy produce a curvature of space-time that we associate with the force of gravity. globular cluster: A bound, dense, spherically symmetric collection of stars formed at the same time. glory: A thin halo of light around the shadow of an object projected on a cloud; caused by the bending of light around and within water droplets.

Glossary

grand uni¿ed theory (GUT): A theory that uni¿es the strong nuclear (“color”) and electroweak forces into a single interaction. gravitational lens: In the gravitational lens phenomenon, a massive body changes the path of light passing near it so as to make a distorted image of the object.

502

gravitational redshift: A redshift of light caused by the presence of mass. gravitational waves: Waves thought to be a consequence of changing distributions of mass. gravity: The weakest of nature’s fundamental forces but the dominant force over large distances because it is cumulative; all matter and energy contribute, regardless of charge. great circle: The intersection of a sphere with a plane passing through the center of the sphere. The meridian and the celestial equator are both great circles. green Àash: A subtle green glow sometimes visible in very clear skies just as the last part of the Sun is setting (or the ¿rst part is rising). greenhouse effect: The effect by which the atmosphere of a planet heats up above its normal equilibrium temperature because it absorbs infrared radiation from the surface of the planet. halo (galactic): The region that extends far above and below the plane of the galaxy. halo (solar or lunar): A circle of light around the Sun or Moon, having a radius of about 22 degrees, formed by light passing through hexagonal ice crystals. Hawking radiation: According to Stephen Hawking, the thermal radiation emitted by black holes because of quantum effects. Heisenberg uncertainty principle: One form: In any measurement, the product of the uncertainties in energy and time is greater than or equal to Planck’s constant divided by 2S. Another form: In any measurement, the product of the uncertainties in position and momentum is greater than or equal to Planck’s constant divided by 2S.

503

Hertzsprung-Russell (H-R) diagram: A plot of the surface temperature (or color) versus luminosity (power, or absolute brightness) for a group of stars. Also known as a temperature-luminosity diagram. homogeneous: The same (density, temperature, and so on) at all locations. horizon: The great circle de¿ned by the intersection of the celestial sphere with the plane tangent to the Earth at the observer’s location; it is 90 degrees away from the zenith. hot dark matter: Nonluminous matter with great speeds, such as neutrinos. Hubble’s law: The linear relation between the current distance and recession speed of a distant object: v = H0d. The constant of proportionality, H0, is called Hubble’s constant. in¿nity: All numbers. A countable in¿nity can be put in one-to-one correspondence with the counting numbers, whereas an uncountable in¿nity cannot. inÀationary universe: A modi¿cation of the standard Big Bang theory. Very early in its history (e.g., t | 1037 seconds), when the Universe was exceedingly small, it began a period of rapidly accelerating expansion, making its ¿nal size truly enormous. Subsequently, the regular Big Bang expansion ensued. interference: The property of radiation, explainable by the wave theory, in which waves in phase can add (constructive interference) and waves out of phase can subtract (destructive interference).

Glossary

interferometer: Two or more telescopes used together to produce highresolution images. interstellar extinction: See extinction. interstellar medium: The space between the stars, ¿lled to some extent with gas and dust. 504

inverse-square law: Decreasing with the square of increasing distance. For example, the brightness of a star is proportional to the inverse-square of distance, as is the gravitational force between two objects. ionized: Having lost at least one electron. Atoms become ionized primarily by the absorption of energetic photons and by collisions with other particles. isotopes: Atomic nuclei having the same number of protons but different numbers of neutrons. isotropic: The same in all directions (that is, no preferred alignment). Kelvin: The size of 1 degree on the Kelvin (absolute) temperature scale, in which absolute zero is 0 K, water freezes at 273 K, and water boils at 373 K. To convert from the Kelvin scale to the Celsius (centigrade, C) scale, subtract 273 from the Kelvin-scale value. Degrees Fahrenheit (F) = (9/5)C + 32. Kepler’s third law: If one object orbits another, the square of its period of revolution is proportional to the cube of the semimajor axis (half of the long axis) of the elliptical orbit. Kuiper belt: A reservoir of perhaps millions of Solar-System objects, orbiting the Sun generally outside the orbit of Neptune. Eris and Pluto are the two largest known Kuiper-belt objects, though some astronomers consider them to be planets. Large Magellanic Cloud: A dwarf companion galaxy of our Milky Way Galaxy, about 170,000 light years away; best seen from Earth’s southern hemisphere. large-scale structure: The network of clusters, voids, and other shapes seen on the largest scales of the Universe. light curve: A plot of an object’s brightness as a function of time.

505

light year: The distance light travels through a vacuum in 1 year; about 10 trillion kilometers, or about 6 trillion miles. lighthouse model: The explanation of a pulsar as a spinning neutron star whose beam we see as it comes around and points toward us. Local Group: The roughly three dozen galaxies, including the Milky Way, that form a small cluster. lookback time: The duration over which light from an object has been traveling to reach us. luminosity: Power; the total energy emitted by an object per unit of time; intrinsic brightness. magnetar: Spinning neutron star with an extraordinarily powerful magnetic ¿eld that occasionally releases a burst of gamma rays when the crust of the star undergoes a sudden restructuring (a “star quake”). magnitude: A logarithmic measure of apparent brightness; a difference of 5 magnitudes corresponds to a brightness ratio of 100. Typical very bright stars have mag 1; the faintest naked-eye stars have mag 6. main sequence: The phase of stellar evolution, lasting about 90% of a star’s life, during which the star fuses hydrogen to helium in its core. massive compact halo objects (MACHOs): Brown dwarfs, white dwarfs, and similar objects that could account for some of the dark matter of the Universe.

Glossary

merging: The interaction of two galaxies in space, with a single galaxy as a result. meridian: A great circle passing through the celestial poles and the zenith; the highest point in the sky reached by a star during each day-night cycle.

506

meteor: The streak of light in the sky produced when an interplanetary rock enters Earth’s atmosphere and burns up as a result of friction. If the rock reaches Earth’s surface, it is called a meteorite. meteoroid: An interplanetary rock that is not in the asteroid belt. Milky Way: The band of light across the sky coming from the stars and gas in the plane of the Milky Way Galaxy (our Galaxy). minor planets: Asteroids. Some astronomers now reserve this term for the largest asteroids and Kuiper belt objects. mirage: An image of an object, often inverted, formed by light passing through layers of air having different temperatures. multiverse: The set of parallel universes that may exist, with our observable Universe as only one part. nebula: A region containing an above-average density of interstellar gas and dust. nebular hypothesis: Theory of the formation of the Solar System, asserting that spinning clouds of interstellar matter gradually contracted and allowed for the formation of the Sun and the planets. neutrino: A nearly massless, uncharged fundamental particle that interacts exceedingly weakly with matter. There are three types: electron, muon, and tau neutrinos. neutron: Massive, uncharged particle that is normally part of an atomic nucleus. neutron star: The compact endpoint in stellar evolution in which typically 1.4 solar masses of material is compressed into a small (diameter = 2030 km) sphere supported by neutron degeneracy pressure.

507

nova: A star that suddenly brightens, then fades back to its original intensity; caused by the accretion of stellar matter from a companion star. nuclear fusion: Reactions in which low-mass atomic nuclei combine to form a more massive nucleus. nucleosynthesis: The creation of elements through nuclear reactions, generally nuclear fusion. Olbers’s paradox: The dark night sky; simple arguments suggest that it should be very bright. open cluster: A loosely bound cluster of stars, usually consisting of young stars that eventually break away from the cluster. open universe: A universe whose volume is in¿nite. parallax: Apparent movement of an object due to a change in the position of the observer. The parallax of a star is de¿ned as the angular distance subtended by 1 AU, the distance between the Earth and the Sun, as seen from the star. parsec: A unit of distance equal to about 3.26 light years (3.086 u 1013 km). particle physics: The study of the elementary constituents of nature. Pauli exclusion principle: Wolfgang Pauli’s explanation for the arrangement of electrons in an atom. The quantum mechanical principle states that no two electrons can be in the same “quantum state” (same con¿guration) in an atom at the same time.

Glossary

phase transition: The transformation of matter from one phase (e.g., liquid) to another (e.g., solid). photon: A quantum, or package, of electromagnetic radiation that travels at the speed of light. From highest to lowest energies: gamma rays, X-rays, ultraviolet, optical (visible), infrared, and radio. 508

photon sphere: A region of space surrounding a black hole at which the curvature of space is so great that it causes light to orbit in circles. photosphere: The visible surface of the Sun (or another star) from which light escapes into space. pinhole camera: A hole in an opaque sheet used to project an image of the Sun. Planck curve: The mathematical formula describing the spectrum of light produced by a perfect thermal emitter. Planck’s constant: The fundamental constant of quantum physics, h; a very small quantity. planet: A body that primarily orbits a star (so that moons don’t count), is large enough to be roughly spherical (typically, larger than about 600 km in diameter), gravitationally dominates its region of space (that is, has largely cleared away other debris), and has never undergone nuclear fusion. planetary nebula: A shell of gas, expelled by a red-giant star near the end of its life (but before the white-dwarf stage), that glows because it is ionized by ultraviolet radiation from the star’s remaining core. planetary system: A collection of planets and smaller bodies orbiting a star (e.g., our Solar System). planetary transit: The passage of a planet directly along a star’s line of sight, causing a momentary dimming of the star’s light; can be used to detect planets in other solar systems. planetesimals: Small bodies, such as meteoroids and comets, into which the solar nebula condensed and from which the planets subsequently formed. pole star: A star approximately at a celestial pole (Polaris, in the north). positron: The antiparticle of an electron. 509

precession: A conical motion undergone by spinning objects pulled by an external force not directed along the axis. The Earth’s precession causes the direction of the north celestial pole to shift gradually with time. progenitor: In the case of a supernova, the star that will eventually explode. prograde motion: The apparent motion of the planets when they appear to gradually move from west to east among the stars; retrograde motion is the opposite direction. prominences: Hot plumes of gas streaming from the Sun’s photosphere along the lines of the Sun’s magnetic ¿elds. proteins: Molecules consisting of long chains of amino acids. proton: Massive, positively charged particle that is normally part of an atomic nucleus. The number of protons in the nucleus determines the chemical element. proton-proton chain: A set of nuclear reactions by which four hydrogen nuclei (protons) combine to form one helium nucleus, with a resulting release of energy. protoplanetary disks: Also called proplyds; concentrations of matter around newly formed or still forming stars out of which planets may form. protostar: A star still in the process of forming in a cloud of gas and dust, collapsing nearly in free fall.

Glossary

pulsar: An astronomical object detected through pulses of radiation (usually radio waves) having a short, extremely well-de¿ned period; thought to be a rotating neutron star with a very strong magnetic ¿eld. quantum Àuctuations: The spontaneous (but short-lived) quantum creation of particles out of nothing.

510

quantum mechanics: A 20th-century theory that successfully describes the behavior of matter on very small scales (such as atoms) and radiation. quark: A fundamental particle with fractional charge; protons and neutrons consist of quarks. quasar (QSO): A star-like, extremely luminous object, typically billions of light years away. Now thought to be the nucleus of a galaxy with a supermassive black hole that is accreting matter from its vicinity. quintessence: A new particle or ¿eld in physics that can lead to repulsive dark energy. radial velocity: The speed of an object along the line of sight to the observer. recombination: Process by which electrons combine with protons and other atomic nuclei to form neutral atoms; believed to have ¿rst occurred about 380,000 years after the Big Bang. red giant: The evolutionary phase following the main sequence of a relatively low-mass star, such as the Sun; the star grows in size and luminosity but has a cooler surface. redshift: De¿ned to be z = (O  O0)/O0, where O0 is the rest wavelength of a given spectral line and O is its (longer) observed wavelength. The wavelength shift may be caused by recession of the source from the observer or by the propagation of light out of a gravitational ¿eld. reÀecting telescope: Telescope that uses a mirror instead of a lens to collect light; unlike the refracting telescope, it brings all colors into focus together. refracting telescope: Telescope that uses a lens to collect light and bring it to a focus. refraction: The bending of light as it passes from one medium to another having different properties. 511

relativistic: Having a speed that is such a large fraction of the speed of light that the special theory of relativity must be applied. resolution: The clarity of detail produced by a given optical system (such as a telescope). rest mass: The mass of an object that is at rest with respect to the observer. The effective mass increases with speed. rest wavelength: The wavelength radiation would have if its emitter were not moving with respect to the observer. retrograde motion: The apparent backward (east-to-west) motion among the stars that planets undergo for a short time each year. Roche limit: The distance from the center of a planet at which the planet’s tidal forces prevent particles from forming a moon through their mutual gravitational attraction. rotation curve: A graph of the speed of rotation versus distance from the center of a rotating object, such as a galaxy. Schwarzschild radius: The radius to which a given mass must be compressed to form a nonrotating black hole. Also, the radius of the event horizon of a nonrotating black hole. second law of thermodynamics: In any closed system, entropy (the amount of disorder) never decreases; it always increases or remains constant.

Glossary

singularity: A mathematical point of zero volume associated with in¿nite values for physical parameters, such as density. solar mass: The mass of the Sun, 1.99 u 1033 grams, about 330,000 times the mass of the Earth. solstice: The northernmost or southernmost point on the celestial sphere that the Sun reaches, or the time of the year when the Sun reaches this point. 512

space-time: The four-dimensional fabric of the Universe whose points are events having speci¿c locations in space (three dimensions) and time (one dimension). special theory of relativity: Einstein’s 1905 theory of relative motion, gravity excluded. spectroscopic binary stars: Binary stars detected by examining the periodically varying Doppler shift in their absorption lines. spectrum: A plot of the brightness of electromagnetic radiation from an object as a function of wavelength or frequency. spiral galaxy: One of the two major classes of galaxies de¿ned by Edwin Hubble; made up of a roughly spherical central “bulge” containing older stars, surrounded by a thin disk in which spiral arms are present. star cluster: A gravitationally bound group of stars that formed from the same nebula. steady-state theory: A model of the expanding Universe based on the assumption that the properties of the Universe do not change with time. Matter must be continually created to maintain constant density. Stefan-Boltzmann law: Law stating that, per unit of surface area, an opaque object emits energy at a rate proportional to the fourth power of its surface temperature. string (superstring) theory: A possible uni¿cation of quantum theory and general relativity in which fundamental particles are different vibration modes of tiny, one-dimensional “strings,” instead of being localized at single points. stripped massive stars: Stars that have lost their hydrogen and helium envelopes, either through stellar winds or through transfer of gas to a companion star; thought to be the progenitors for gamma-ray bursts.

513

strong nuclear force: The strongest force, it binds protons and neutrons together in a nucleus. Actually, it is the residue of the even stronger color force that binds quarks together in a proton or neutron. sundog: A pair of bright spots on the outer edge of the solar halo at roughly the Sun’s altitude above the horizon. sun pillar: A faint pillar of light above the Sun in the sky, best visible after sunset. sunspots: Cooler regions on the Sun’s photosphere that appear as dark blotches. supercooled: The condition in which a substance is cooled below the point at which it would normally make a phase change. supergiant: The evolutionary phase following the main sequence of a massive star; the star becomes more luminous and larger. If its size increases by a very large factor, it becomes cool (red). supernova: The violent explosion of a star at the end of its life. Hydrogen is present or absent in the spectra of Type II or Type I supernovae, respectively. supernova remnant: The cloud of chemically enriched gases ejected into space by a supernova. symmetric: Forces that are symmetric act identically. They act differently when the symmetry is broken.

Glossary

synchronous rotation: The rotation of a body having the same period as its orbit. terminator: The line between night and day on a moon or planet; the edge of the part that is lighted by the Sun.

514

terrestrial planets: Rocky, earth-like planets. In our Solar System: Mercury, Venus, Earth, and Mars. tidal force: The difference between the gravitational force exerted by one body on the near and far sides of another body. time dilation: According to relativity theory, the slowing of time perceived by an observer watching another object moving rapidly or located in a strong gravitational ¿eld. transverse velocity: The speed of an object across the plane of the sky (perpendicular to the line of sight). Universe: All that there is within the space and time dimensions accessible to us, as well as regions beyond (but still physically connected to) those that we can see. variable star: A star whose apparent brightness changes with time. virtual particle: A particle that Àits into existence out of nothing and, shortly thereafter, disappears again. wavelength: The distance over which a wave goes through a complete oscillation; the distance between two consecutive crests or two consecutive troughs. weakly interacting massive particles (WIMPs): Theorized to make up the dark matter of the Universe. weak nuclear force: Governs the decay of a neutron into a proton, electron, and antineutrino. weight: The force of the gravitational pull on a mass. white dwarf: The evolutionary endpoint of stars that have initial mass less than about 8 solar masses. All that remains is the degenerate core of He or C–O (in some cases, ONeMg). 515

wormhole: A hypothetical connection between two universes or different parts of our Universe. Also: Einstein-Rosen bridge. year: The Earth’s orbital period around the Sun. zenith: The point on the celestial sphere that is directly above the observer. zodiac: The band of constellations through which the Sun moves during the course of a year.

Glossary

zodiacal light: A faint glow in the night sky around the ecliptic, stretching up from the horizon shortly after evening twilight and shortly before morning twilight, from sunlight reÀected by interplanetary dust.

516

Biographical Notes

Aristarchus of Samos (roughly 310230 B.C.). Greek astronomer; measured the Sun-Earth distance relative to the Earth-Moon distance. Realized that the Sun is much larger than the Earth and reasoned that the Sun (rather than the Earth) is at the center of the Universe, predating Copernicus by 1800 years. Aristotle (384322 B.C.). The most inÀuential early Greek philosopher. He lectured on a vast range of subjects; however, many or most of his beliefs in physics and astronomy turned out to be wrong. Developed a widely adopted geocentric (Earth-centered) model of the Universe consisting of 55 spheres. Correctly concluded that the Earth is spherical. Brahe, Tycho (15461601). Danish astronomer; measured the positions of planets with unprecedented accuracy, laying the foundations for Kepler’s work. Discovered and studied a bright supernova in 1572; thus, the “sphere of ¿xed stars” is not immutable, in contradiction to Aristotelian and Christian dogma. Cannon, Annie Jump (18631941). American astronomer; classi¿ed the photographic spectra of several hundred thousand stars, demonstrating that the spectra depend mostly on the stellar surface temperature. She arranged the spectral types into the sequence OBAFGKM. Chandrasekhar, Subrahmanyan (19101995). Indian-born American astrophysicist. Awarded the Nobel Prize in Physics in 1983 for his work on the physical understanding of stars, especially the upper mass limit of white dwarfs. Copernicus, Nicolaus (14731543). Polish astronomer; proposed the heliocentric (Sun-centered) model of the planetary system. He showed how the retrograde motion of planets could be explained with this hypothesis. His book De Revolutionibus was published the year of his death.

517

Eddington, Sir Arthur (1882–1944). British astrophysicist who studied the physical structure of stars and was an expert on Einstein’s general theory of relativity. Through his observations of a total solar eclipse in 1919, he helped to con¿rm this theory. Einstein, Albert (18791955). German-American physicist, the most important since Newton. Developed the special and general theories of relativity, proposed that light consists of photons, and worked out the theory of Brownian motion (the irregular, zigzag motion of particles suspended in a Àuid is due to collisions with molecules). Responsible for E = mc2, the world’s most famous equation. Eratosthenes (276194 B.C.). Greek geographer who estimated the circumference of the Earth to within 1% accuracy through measurements of the length of a stick’s shadow at different locations on Earth. Galileo Galilei (15641542). Italian mathematician, astronomer, and physicist; was the ¿rst to systematically study the heavens with a telescope. Discovered the phases of Venus and the four bright moons of Jupiter, providing strong evidence against the geocentric model for the Solar System. After being sentenced by the Inquisition to perpetual house arrest, he published his earlier studies of the motions of falling bodies, laying the experimental groundwork for Newton’s laws of motion.

Biographical Notes

Gamow, George (19041968). Russian-American physicist; he suggested that the Universe began in a hot, compressed state and predicted the existence of the cosmic background radiation that was later discovered by Arno Penzias and Robert Wilson. Also devised a theory of radioactive decay. Guth, Alan (1947 ). American physicist; proposed the inÀationary theory of the Universe to eliminate some glaring problems with the standard Big Bang model. His perspective was that of an elementary particle physicist, not an astronomer; he was most troubled by the absence of magnetic monopoles. Hawking, Stephen (1942 ). English physicist, best known for his remarkable theoretical work while physically incapacitated by Lou Gehrig’s disease (ALS). His prediction that black holes can evaporate through 518

quantum tunneling is an important step in attempts to unify quantum physics and gravity (general relativity). He is Lucasian Professor of Mathematics at Cambridge University, as was Newton. Hipparchus (c. 160–c. 127 B.C.). Greek astronomer who made the ¿rst accurate star catalogue. Re¿ned the methods of Aristarchus of Samos. Determined the length of the year to within six minutes and noticed that the direction of the north celestial pole changes with time. Hoyle, Fred (19152001). English astronomer; proposed the steady-state theory of the Universe, which stimulated much important work in cosmology. Also made fundamental contributions to the understanding of the origin of the chemical elements. Coined the term Big Bang. Hubble, Edwin (18891953). American astronomer, after whom the Hubble Space Telescope is named. He proved that “spiral nebulae” are galaxies far outside our own Milky Way and discovered the expansion of the Universe (Hubble’s law) by recognizing that the redshift of a galaxy is proportional to its distance. He also proposed a widely used morphological classi¿cation scheme for galaxies. Kepler, Johannes (15711630). German mathematician and astronomer; was Tycho Brahe’s assistant and gained access to Brahe’s data after his death. Developed three empirical laws of planetary motion that represent a signi¿cant revision of the Copernican model. Studied a very bright supernova in 1604. Leavitt, Henrietta (18681921). American astronomer; demonstrated a relationship between the period and luminosity of Cepheid variable stars. This was done by analysis of Cepheids clustered together and, therefore, at the same distance, so that differences in brightness indicate luminosity differences. Maxwell, James (18311879). Scottish physicist; showed that visible light is only one form of electromagnetic radiation, whose speed can be derived from a set of four equations that describe all of electricity and magnetism. Also investigated heat and the kinetic theory of gases. 519

Newton, Isaac (16421727). English mathematician and physicist; developed three laws of motion and the law of universal gravitation, all published in The Principia (1687). Invented the reÀecting telescope, determined that white light consists of all colors of the rainbow, and invented calculus. At age 27, became Lucasian Professor of Mathematics at Cambridge University. Became Warden of the Mint in 1696; knighted in 1705. Ptolemy, Claudius (85165). Greek astronomer who developed an elaborate model for planetary motions, based on Aristotle’s geocentric Universe, that endured for more than 1400 years. Compiled the Almagest, a set of 13 volumes that provides most of our knowledge of early Greek astronomy. Rubin, Vera (1928 ). American astronomer; was the ¿rst to observationally show that the rotation curves of most spiral galaxies imply the presence of considerable amounts of dark matter. She also obtained early evidence for large-scale peculiar motions of galaxies relative to the smooth expansion of the Universe. Sagan, Carl (19341996). American astronomer and the 20th century’s most well known popularizer of science, especially astronomy. Among his scienti¿c accomplishments, he demonstrated that Venus suffers from an enormous greenhouse effect. Cosmos, his 13-episode public-television astronomy series, has been seen by more than 500 million people. He was an eloquent proponent of unmanned Solar System exploration.

Biographical Notes

Sandage, Allan (1926 ). American astronomer and disciple of Edwin Hubble, he has made fundamental contributions to the determination of globular cluster ages, the distances of galaxies, the Hubble constant, the age of the Universe, and the rate at which the expansion of the Universe is changing. Shapley, Harlow (18851972). American astronomer; correctly deduced that the Sun is not at the center of the Milky Way Galaxy and that the Galaxy is larger than previously believed. Incorrectly concluded that the “spiral nebulae” are within the Milky Way, but most of his reasoning was logically sound.

520

Zwicky, Fritz (18981974). Swiss-American astronomer; proposed that supernovae result from the collapse of the cores of massive stars, producing neutron stars and energetic particles (cosmic rays). Compiled an extensive atlas of galaxy clusters and showed that many such clusters must contain dark matter in order to be gravitationally bound.

521

Bibliography

Essential Reading: Adams, Fred, and Greg Laughlin. The Five Ages of the Universe: Inside the Physics of Eternity. New York: Free Press, 2006. Alvarez, Walter. T-Rex and the Crater of Doom. London: Vintage, 1998. Beebe, R. Jupiter: The Giant Planet, 2nd ed. Washington, DC: Smithsonian Institution Press, 1996. Begelman, Mitchell, and Martin Rees. Gravity’s Fatal Attraction: Black Holes in the Universe. New York: W.H. Freeman, 1998. Carroll, Bradley W., and Dale A. Ostlie. An Introduction to Modern Astrophysics, 2nd ed. New York: Addison Wesley, 2006. Chaikin, Andrew. A Man on the Moon. New York: Time-Life Books, 2001. Christianson, Gale E. Isaac Newton and the Scienti¿c Revolution. New York: Oxford University Press, 1998. Cristensen, Lars L., Robert A. Fosbury, and M. Kornmesser, Hubble: 15 Years of Discovery. Berlin/New York: Springer, 2006.

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