Solar-Terrestrial Relations: From Solar Activity to Heliobiology 3031225473, 9783031225475

Table of contents :
Preface
Contents
Acronyms
Chapter 1: Introduction: The Problem of Solar-Terrestrial Relations
1.1 The Nature of Helio-Geophysical Disturbances
1.2 Observational Data and Main Lines of Research
Chapter 2: Main Characteristics of the Sun
2.1 The Sun as a Star
2.2 The Structure of the Sun
2.3 Age, Chemical Composition, Temperature and Density
2.4 Energy Source
2.5 The Concept of the Heliosphere
2.6 Methods for Studying the Sun and Heliosphere
Chapter 3: Solar Activity
3.1 The Structure of the Solar Atmosphere
3.2 Solar Wind
3.3 Solar Flares
3.4 Coronal Mass Ejections
3.5 Cyclicity of Solar Activity
3.6 Forecast of Future Solar Cycles
Chapter 4: Structure and Dynamics of the Interplanetary Environment
4.1 Corona Expansion and Solar Wind
4.2 The Global Magnetic Field of the Sun
4.3 Interplanetary Magnetic Field
4.4 Sector Structure of Interplanetary Magnetic Field
4.5 Modern Model of the Polar Magnetic Field
4.6 Fluctuations of the Interplanetary Magnetic Field
Chapter 5: Anomalous Component of Cosmic Rays
5.1 Discovery and Origin of ACR
5.2 The Original Acceleration Paradigm
5.3 Modern Models
5.4 Account for the Geometry of the Heliosphere
5.5 Interplanetary Acceleration
Chapter 6: Transport of Particles in the Heliosphere
6.1 Energetic Particles in the Heliosphere
6.2 Basic Concepts of Transport Theory
6.3 Energy Density and Transport of Energetic Particles
6.4 The Theory of Solar Cosmic Ray Transport
6.5 Shock Waves and Transport of Solar Particles
6.6 Energetic Particles and Wave Generation in Interplanetary Plasma
6.7 Particle Transport in Large-Scale Magnetic Structures
6.8 Solar Particles at Large Distances from the Sun
Chapter 7: Acceleration of Particles on the Sun
7.1 Solar Particle Acceleration Scenarios
7.2 Fermi Model Development
7.3 Acceleration in Solar Flares
7.4 Basic Acceleration Mechanisms
7.5 Acceleration of Particles and Magnetic Reconnection
7.6 Stochastic Acceleration
7.7 Shock Wave Acceleration
7.8 Combined SCR Acceleration
7.9 Flares, CMEs, and Two Classes of Solar Proton Events
Chapter 8: Accelerated Particles in the Solar Atmosphere
8.1 Nuclear Reactions in the Sun´s Atmosphere
8.2 Neutrons and Gamma Rays
8.3 Astrophysical Consequences and Applications
8.4 Localization of Sources of Acceleration
Chapter 9: Occurrence Rate of Extreme Solar Events
9.1 Concept of Extreme SCR Event
9.2 Past Extreme SCR Events
9.3 New Distribution Function for Extreme SEP Events
9.4 Flares on Stars Like the Sun
Chapter 10: Energetic Particles in the Geosphere
10.1 Earth´s Atmosphere and Cosmic Rays
10.2 Ionization and Conductivity of the Atmosphere
10.3 Production of Cosmogenic Isotopes
10.4 Formation of Nitrates
10.5 Formation and Dynamics of the Ozone Layer
10.6 Global Electrical Circuit
10.7 Cosmic Rays: A Trigger for Tropospheric Processes?
10.8 Other Cosmic Ray Effects in the Atmosphere
Chapter 11: Hierarchy of Solar-Earth Relations
11.1 Extreme Solar Events and Magnetic Storms
11.2 Main Characteristics of Magnetic Storms
11.3 Energetics of the Magnetosphere
11.4 Dynamics of Trapped Radiation in the Earth´s Magnetosphere
11.5 Solar ``Signals´´ in the Atmosphere and Lithosphere
11.6 Solar-Terrestrial Relations an Space Weather
Chapter 12: Influence of the Sun on the Biosphere
12.1 Modern Concepts and Fundamental Problems
12.2 The Role of Geomagnetic Pulsations
12.3 Cosmic Rhythms in the Biosphere
12.4 Features of Heliobiological Rhythms
12.5 Cosmophysical Factors and Creative Activity
12.6 Economic ``Kondratyev Waves´´
Chapter 13: Future of Solar-Terrestrial Physics
13.1 Solar Activity and Accurate Physical Measurements
13.2 Heliobiology and Medicine
13.3 Magneto-Biological Effect (MBE)
13.4 Astronautics Prospects
13.5 Space Weather Forecasting
13.6 Spaceship ``Earth´´
13.7 Search for Alien Life
Instead of an Afterword
Appendices
Geocentric Solar Ecliptic System
Geocentric Solar Equatorial System
Geocentric Solar Magnetospheric System
References

Citation preview

Leonty Miroshnichenko

Solar-Terrestrial Relations From Solar Activity to Heliobiology

Solar-Terrestrial Relations

Leonty Miroshnichenko

Solar-Terrestrial Relations From Solar Activity to Heliobiology

Leonty Miroshnichenko Pushkov Institute of Terrestrial Magnetism Ionosphere and Radio Wave Propagation Russian Academy of Sciences (RAS) Troitsk, Russia

ISBN 978-3-031-22547-5 ISBN 978-3-031-22548-2 https://doi.org/10.1007/978-3-031-22548-2

(eBook)

English translation of the 1st original Russian edition published by Moscow University Press, Moscow, 2011 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

To the blessed memory of my wife Nina Viktorovna Miroshnichenko —DEDICATED

Preface

This book is written on the basis of a special course of lectures, which the author read in 2008–2018 to the students of the Department of Space Physics at the Physics Faculty of Moscow State University. The lectures were of a purposeful nature—to give students the introductory ideas of the Sun, the immediate space environment of the Earth, the impact of cosmic factors on terrestrial phenomena, and the interaction of the Earth and the Cosmos as a whole. In other words, the students were supposed to present only the fundamentals of physics of what later became known as “SolarTerrestrial Relations” (STR). In fact, it was about the foundations of solar-terrestrial physics (STP). Later, a part of this area of cosmophysics received the resounding name “Space Weather.” This goal assumed that students only had basic astronomical and modern physical ideas about the world around them. Further deeper study of the subject, its fundamental physical and applied aspects, fell to the lot of the graduates of the Department themselves. In 2011, Russia widely celebrated the 300th anniversary of the birth of M.V. Lomonosov—an outstanding Russian scientist-encyclopedist, poet, thinker, and educator; thanks to his all-round activity, he is rightfully considered the de facto founder of Moscow University. As part of the implementation of the national project “Formation of the system of innovative education at Moscow State University named after M.V. Lomonosov,” at the Physics Department of Moscow State University in 2011, in particular, the author’s textbook for students “Physics of the Sun and Solar-Terrestrial Relations” was created and published. Over the decade that has passed since then, new observational data have appeared in the field of solar-terrestrial physics, many new models have been proposed to describe various phenomena. At the same time, however, the basic concepts have remained largely unchanged, and many “old” (pre-existing) problems still await their resolution—on the basis of new data, new models, and new methodological approaches. The author does not claim to be a comprehensive analysis of the problems of the STP (and even STR). We are only trying to draw the reader’s attention to the most pressing issues of the “frontier” (“cutting edge”) of this science. At the same time, vii

viii

Preface

the author considers it important to emphasize some fundamental and applied aspects of the STR, including the problems of impact on the Earth’s biosphere, the prospects of cosmonautics, and the philosophical role of knowledge about the STP. The book may be of interest not only to undergraduate and graduate students, but also to physicists from related fields who are interested in climatology, ecology, humanities, and some applied areas. While working on the book, the author largely relied on his many years of personal experience in this area. About 20 years I was happy to study the STRs under guidance of the first director IZMIRAN Prof. N.V. Pushkov, and about 10 years from 20, I was a secretary of STR seminar in our institute. So, in a number of cases, the author did not hesitate to express his own point of view. For example, the Section “Instead of an Afterword” tells about a long-standing and very principled dispute with one of the outstanding specialists in the field of solar-terrestrial relations—B.M. Vladimirsky—about the nature of mysterious muon bursts, registered at the underground Baksan Observatory of the Institute for Nuclear Research of the Russian Academy of Sciences. The fact that the book was prepared and published is due to many of my colleagues and friends from IZMIRAN and a number of other institutes. Especially great help was kindly given to me by my colleagues A.A. Abunin and V.G. Yanke (IZMIRAN). IZMIRAN, Troitsk 22 November 2021

Leonty Miroshnichenko

Contents

1

Introduction: The Problem of Solar-Terrestrial Relations . . . . . . . . 1.1 The Nature of Helio-Geophysical Disturbances . . . . . . . . . . . . . 1.2 Observational Data and Main Lines of Research . . . . . . . . . . . .

1 1 3

2

Main Characteristics of the Sun . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 The Sun as a Star . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 The Structure of the Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Age, Chemical Composition, Temperature and Density . . . . . . 2.4 Energy Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 The Concept of the Heliosphere . . . . . . . . . . . . . . . . . . . . . . . 2.6 Methods for Studying the Sun and Heliosphere . . . . . . . . . . . .

. . . . . . .

7 7 8 10 12 14 16

3

Solar Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 The Structure of the Solar Atmosphere . . . . . . . . . . . . . . . . . . . 3.2 Solar Wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Solar Flares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Coronal Mass Ejections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Cyclicity of Solar Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Forecast of Future Solar Cycles . . . . . . . . . . . . . . . . . . . . . . . .

21 21 26 28 32 35 39

4

Structure and Dynamics of the Interplanetary Environment . . . . . . 4.1 Corona Expansion and Solar Wind . . . . . . . . . . . . . . . . . . . . . . 4.2 The Global Magnetic Field of the Sun . . . . . . . . . . . . . . . . . . . 4.3 Interplanetary Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Sector Structure of Interplanetary Magnetic Field . . . . . . . . . . . 4.5 Modern Model of the Polar Magnetic Field . . . . . . . . . . . . . . . . 4.6 Fluctuations of the Interplanetary Magnetic Field . . . . . . . . . . .

43 43 44 45 48 50 52

5

Anomalous Component of Cosmic Rays . . . . . . . . . . . . . . . . . . . . . 5.1 Discovery and Origin of ACR . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 The Original Acceleration Paradigm . . . . . . . . . . . . . . . . . . . . . 5.3 Modern Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57 57 58 59 ix

x

Contents

5.4 5.5

Account for the Geometry of the Heliosphere . . . . . . . . . . . . . . Interplanetary Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . .

60 61

Transport of Particles in the Heliosphere . . . . . . . . . . . . . . . . . . . . 6.1 Energetic Particles in the Heliosphere . . . . . . . . . . . . . . . . . . . . 6.2 Basic Concepts of Transport Theory . . . . . . . . . . . . . . . . . . . . . 6.3 Energy Density and Transport of Energetic Particles . . . . . . . . . 6.4 The Theory of Solar Cosmic Ray Transport . . . . . . . . . . . . . . . 6.5 Shock Waves and Transport of Solar Particles . . . . . . . . . . . . . 6.6 Energetic Particles and Wave Generation in Interplanetary Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7 Particle Transport in Large-Scale Magnetic Structures . . . . . . . . 6.8 Solar Particles at Large Distances from the Sun . . . . . . . . . . . . .

63 64 65 68 69 72

7

Acceleration of Particles on the Sun . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Solar Particle Acceleration Scenarios . . . . . . . . . . . . . . . . . . . . 7.2 Fermi Model Development . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Acceleration in Solar Flares . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Basic Acceleration Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Acceleration of Particles and Magnetic Reconnection . . . . . . . . 7.6 Stochastic Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.7 Shock Wave Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.8 Combined SCR Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . 7.9 Flares, CMEs, and Two Classes of Solar Proton Events . . . . . . .

83 83 85 86 87 89 92 94 98 99

8

Accelerated Particles in the Solar Atmosphere . . . . . . . . . . . . . . . 8.1 Nuclear Reactions in the Sun’s Atmosphere . . . . . . . . . . . . . . 8.2 Neutrons and Gamma Rays . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Astrophysical Consequences and Applications . . . . . . . . . . . . 8.4 Localization of Sources of Acceleration . . . . . . . . . . . . . . . . .

. . . . .

103 104 106 109 113

9

Occurrence Rate of Extreme Solar Events . . . . . . . . . . . . . . . . . . . . 9.1 Concept of Extreme SCR Event . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Past Extreme SCR Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3 New Distribution Function for Extreme SEP Events . . . . . . . . . 9.4 Flares on Stars Like the Sun . . . . . . . . . . . . . . . . . . . . . . . . . .

117 118 119 120 121

10

Energetic Particles in the Geosphere . . . . . . . . . . . . . . . . . . . . . . . . 10.1 Earth’s Atmosphere and Cosmic Rays . . . . . . . . . . . . . . . . . . . 10.2 Ionization and Conductivity of the Atmosphere . . . . . . . . . . . . . 10.3 Production of Cosmogenic Isotopes . . . . . . . . . . . . . . . . . . . . . 10.4 Formation of Nitrates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5 Formation and Dynamics of the Ozone Layer . . . . . . . . . . . . . . 10.6 Global Electrical Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.7 Cosmic Rays: A Trigger for Tropospheric Processes? . . . . . . . . 10.8 Other Cosmic Ray Effects in the Atmosphere . . . . . . . . . . . . . .

123 124 127 128 131 134 137 140 143

6

74 76 78

Contents

xi

Hierarchy of Solar-Earth Relations . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Extreme Solar Events and Magnetic Storms . . . . . . . . . . . . . . . 11.2 Main Characteristics of Magnetic Storms . . . . . . . . . . . . . . . . . 11.3 Energetics of the Magnetosphere . . . . . . . . . . . . . . . . . . . . . . . 11.4 Dynamics of Trapped Radiation in the Earth’s Magnetosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.5 Solar “Signals” in the Atmosphere and Lithosphere . . . . . . . . . . 11.6 Solar-Terrestrial Relations an Space Weather . . . . . . . . . . . . . .

149 150 152 157

12

Influence of the Sun on the Biosphere . . . . . . . . . . . . . . . . . . . . . . . 12.1 Modern Concepts and Fundamental Problems . . . . . . . . . . . . . . 12.2 The Role of Geomagnetic Pulsations . . . . . . . . . . . . . . . . . . . . 12.3 Cosmic Rhythms in the Biosphere . . . . . . . . . . . . . . . . . . . . . . 12.4 Features of Heliobiological Rhythms . . . . . . . . . . . . . . . . . . . . 12.5 Cosmophysical Factors and Creative Activity . . . . . . . . . . . . . . 12.6 Economic “Kondratyev Waves” . . . . . . . . . . . . . . . . . . . . . . . .

173 174 179 182 184 187 189

13

Future of Solar-Terrestrial Physics . . . . . . . . . . . . . . . . . . . . . . . . . 13.1 Solar Activity and Accurate Physical Measurements . . . . . . . . . 13.2 Heliobiology and Medicine . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.3 Magneto-Biological Effect (MBE) . . . . . . . . . . . . . . . . . . . . . . 13.4 Astronautics Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.5 Space Weather Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.6 Spaceship “Earth”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.7 Search for Alien Life. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

193 194 198 201 203 206 210 213

11

160 166 170

Instead of an Afterword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Geocentric Solar Ecliptic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . Geocentric Solar Equatorial System . . . . . . . . . . . . . . . . . . . . . . . . . . Geocentric Solar Magnetospheric System . . . . . . . . . . . . . . . . . . . . . .

219 219 219 219

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

Acronyms

АСЕ AES AU BAP BDE СМЕ CORONAS CIR CIS CLOUD CR CVS EAS ECG EMF EOS ESA ESE ESF EPE FIP GCR GEC GEAS GLE GLONASS GOES GOST GSE

Advanced Composition Explorer Artificial Earth Satellites Astronomical Unit (a distance from the Sun to the Earth) Biologically Active Points Bastille Day Event Coronal Mass Ejection Complex Orbital Near-Earth Observations of the Sun (Russian spacecraft) Co-rotating Interaction Region Commonwealth of Independent States (the former Soviet Union) Cosmics Leaving Outdoor Droplets (experiment in CERN) Cosmic Rays Cardiovascular System Extensive Air Shower Electrocardiogram Electromagnetic Field Equation Of State European Space Agency Extreme Solar Event Extreme Solar Flare Extreme Proton Event First Ionization Potential Galactic Cosmic Rays Global Electric Current General Evolutionary Adaptation Syndrome Ground Level Enhancement Global Navigation Satellite System (Russia) Geostationary Operational Environment Satellite State Standard (in the USSR) Geocentric Solar Ecliptic System xiii

xiv

GSEQ GPS GSM HCS HNS IC IGRF IMF IPS IR IRI ISO ISS IZMIRAN LIC LISM LT MBE MS NASA NES NM NOAA OSO PCA PFU QBO RAS RBE RHESSI SAA SA SC SCR SGMF SINP SMM SNT STP STR SSC SR

Acronyms

Geocentric Solar Equatorial System Global Positioning System Geocentric Solar Magnetospheric System Heliospheric Current Sheet Heliospheric (Heliomagnetic) Neutral Sheet Ionization Chamber International Geomagnetic Reference Field (model) Interplanetary Magnetic Field Interplanetary Shock Infrared Radiation International Reference Ionosphere (model) International Standard Organization International Space Station Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences (RAS) Local Interstellar Cloud Local Inter-Stellar Medium (Local Bubble) Local Time Magneto-Biological Effect Magnetic Storm National Aeronautics and Space Administration (USA) Near-Earth Space Neutron Monitor National Oceanic and Atmospheric Administration (USA) Orbiting Solar Observatory (spacecraft) Polar Cap Absorption Proton Flux Unit (1 pfu = 1 proton/cm2 s ster) Quasi-Biennial Oscillation Russian Academy of Sciences Radiation Belts of the Earth Reuven Ramaty High Energy Solar Spectroscopic Imager (spacecraft) South-Atlantic Anomaly Solar Activity Spacecraft Solar Cosmic Rays Solar Global Magnetic Field Skobeltsyn Institute of Nuclear Physics, Moscow State University Solar Maximum Mission (spacecraft) Solar Neutron Telescope Solar-Terrestrial Physics Solar-Terrestrial Relations Sudden Storm Commencement Schumann resonances

Acronyms

SW SEE SEP SEU SFF SOHO SPE SPO SRI SSC SSM STEP STEREO TSW TRACE ULF UT VLF WMAP

xv

Shock Wave Single Event Error Solar Energetic Particle Single Event Upset Space Flight Factor Solar and Heliospheric Observatory (spacecraft) Solar Proton Event Short-Period Oscillations Institute of Space Research, Russian Academy of Sciences (IKI RAN) Storm Sudden Commencement Standard Solar Model Solar Terrestrial Energy Program, 1990–1997 Solar TErrestrial RElations Observatory (spacecraft) Terminal Shock Wave Transition Region and Coronal Explorer (spacecraft) Ultra Low Frequency Universal Time Very Low Frequency Wilkinson Microwave Anisotropy Probe (spacecraft)

Chapter 1

Introduction: The Problem of Solar-Terrestrial Relations

The river of truth flows through the channels of delusion. R. Tagore

Among the modern directions of cosmophysics one of the most important places is occupied by the physics of the Sun. First of all, we are strongly interested in the characteristics of the Sun as a star (structure, chemical composition, energy source, structure and dynamics of its atmosphere, corona expansion and solar wind). Further, a number of energetic phenomena (disturbances) in the solar atmosphere (named Solar Activity, or SA) are of great interest: solar wind, spots, flares, filaments, prominences, coronal holes, coronal mass ejections (CMEs) and fluxes of accelerated particles (solar energetic particles, or SEPs, or solar cosmic raysSCR). The geophysical consequences of these phenomena (magnetic storms, radiation storms, auroras, disturbances of the ionosphere, etc.) constitute the essence of the problem of solar-terrestrial relations (connections), or the problem of “SunEarth” (Fig. 1.1). One can see that between the Sun and the Geosphere there are some certain relations that are characterized by multiplicity and superposition of different factors. Figure 1.1 was taken from the so-called STEP project (Solar Terrestrial Energy Program, 1990–1997). Together with the mechanisms of their impact on the Earth, these phenomena are the subject of the study of solar-terrestrial physics (STP).

1.1

The Nature of Helio-Geophysical Disturbances

Solar disturbances are accompanied by a powerful release of energy, primarily in the form of kinetic plasma movements (shock waves, coronal mass ejections), as well as in the form of enhanced fluxes of electromagnetic radiation, solar wind and accelerated particles, against the background of a disturbed interplanetary magnetic field (IMF). Each of these factors has a different effect on the near-Earth space

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 L. Miroshnichenko, Solar-Terrestrial Relations, https://doi.org/10.1007/978-3-031-22548-2_1

1

2

1

Introduction: The Problem of Solar-Terrestrial Relations

Fig. 1.1 The Sun and the Geosphere: channels of energy supply from the Sun to the Earth, the main processes and main links in the system of solar-terrestrial relations (STR)

(magnetosphere, ionosphere and neutral atmosphere). Their geoeffectiveness depends not only on the energy fluence (i.e., its total flux), but also on the rate of its arrival in the vicinity of the Earth. In other words, almost from the very beginning in solar-terrestrial physics, it became necessary to take into account not only the energetics of disturbances, but also the peculiarities of the influence of various factors (so-called “information relations”, or information aspects) in the chain of “Sun—interplanetary medium—Earth” on the origin and development of geophysical processes. In this case, a large role can be played by “small disturbances” from the outside (trigger mechanism). On the other hand, in space research as a whole, we are dealing with four groups of fundamental physical factors—fields, particles, waves in plasma and electromagnetic radiation of various frequencies. These factors are both objects of research and carriers of information about the phenomena under study. Let us show this briefly using the example of solar cosmic rays (SCR). Sometimes they are simply named

1.2

Observational Data and Main Lines of Research

3

Solar Energetic Particles (SEPs). By participating in various processes in the space between the Sun and the Earth, SEPs make a significant energy and information contribution to all four areas of research. In particular, they make it possible to probe the magnitude, structure, and dynamics of magnetic fields in the solar atmosphere and interplanetary space. Many results of studying of the SEPs (composition, charge state, maximum energy, and spectrum of accelerated particles) can be very useful for the theory of particle transport, acceleration and astrophysics of cosmic rays in the whole. Finally, recent advances in the study of particle acceleration by coronal and interplanetary shock waves are of great interest for plasma physics in astrophysical objects of various scales - from the heliosphere boundary to the envelopes of supernovae (Panasyuk and Miroshnichenko 2022). Thus, the physics of the Sun and solar-terrestrial relations paves the way for us to “Big Astrophysics”.

1.2

Observational Data and Main Lines of Research

Along with the accumulation of data on sunspots, auroras and other phenomena, attempts were made to explain the physical essence of the processes that are taking place in the past. So, already at the turn of the nineteenth and twentieth centuries, the first hypotheses about the nature of auroras and theoretical prerequisites for describing trapped radiation in the Earth’s magnetosphere (the theory of radiation belts, RB) appeared. In 1910–1940 many aspects of the physics of the Sun were developed (composition and internal structure, energy sources, the nature of the radiation of its atmosphere, etc.). However, it took several decades for the formation of the basic concepts of solar-terrestrial physics and the creation of a world observational base for the study of the “Sun-Earth” problem in the whole. The pinnacle of these scientific efforts was the holding of the International Geophysical Year (1957–1958). With the beginning of the “space age” (October 4, 1957) and manned space flights (April 12, 1961), a radical change also occurred in solar-terrestrial physics. Over the next three to four decades, an essentially new concept of “Space Weather” was formed, based on the latest discoveries in solar-terrestrial physics (in particular, on direct observations of the solar wind, interplanetary magnetic field, and coronal mass ejections). Thanks to spacecraft (SC), such fields of heliophysics as solar gamma astronomy, helioseismology, etc. have emerged or have received intensive development. The expressions “coronal hole”, “solar storm”, “geomagnetic storm”, “radiation storm”, “magnetosphere tail” and many others became widely used in scientific use. The concept of the “heliosphere” also emerged as a special cavity in outer space formed by the solar wind during its interaction with the interstellar medium. To date, solar-terrestrial physics (STP) includes several important theoretical, observational and applied aspects. Among them, first of all, are the generation of flares and CMEs, the acceleration of charged particles at/near the Sun, their transport in the interplanetary medium, and the interaction of the solar wind with the Earth’s

4

1

Introduction: The Problem of Solar-Terrestrial Relations

magnetosphere should be mentioned. This is followed by observations and interpretation of various geophysical effects of solar activity (SA). An important place is occupied by the issues of forecasting SA phenomena, geomagnetic and ionospheric disturbances, as well as forecasting fluxes of energetic solar particles. Of particular interest are the most powerful disturbances of electromagnetic conditions on the Sun itself (the so-called solar extreme events, or SEEs). As a rule, such events are accompanied by strong changes in radiation conditions in the interplanetary medium (up to the orbits of Mars and Jupiter) and various perturbations of the near-Earth space (NES) and all the Earth’s shells (envelopes) that make up the outer geosphere (i.e. magnetosphere, ionosphere, ozonosphere, stratosphere and troposphere). In other words, the impact of a powerful solar burst extends from the edge of the geosphere to the surface of the Earth (see Fig. 1.1, also Fig. 1.2 below). Moreover, SEEs also affect the hydrosphere and solid shell of the Earth (lithosphere). The troposphere, hydrosphere and lithosphere, in turn, are the natural habitats for the Earth’s biosphere, so that the impact of helio-geophysical disturbances on the biosphere is not only expected, but also completely inevitable. In recent decades, the problem of solar-tropospheric and solar-climatic relations has been intensively developed. In this problem, apparently, like in no other area of helio-geophysics, it is important to take into account the interaction between solar influences and purely terrestrial processes and factors. It is here that the nonlinear nature of such interactions and, as a consequence, the ambiguous nature of the effects can be strongly affected, i.e. seeming instability of connections. Of particular interest is the direction called “heliobiology”. This area of research has come a long and difficult way—from purely speculative guesses and statistical results confirming the effect of solar activity on the Earth’s biosphere, to profound physical theories and serious laboratory experiments. This book briefly covers the whole range of the listed issues. Many important details, however, remained outside the scope of our presentation. The reader can make up for this deficiency on his own: the list of recommended basic literature contains the most up-to-date articles, reviews and books on the main problems of solar-terrestrial physics. Many issues in this area have already been studied in great detail, up to accurate quantitative estimates and/or unambiguous observational data. At the same time, the author would not like to create the illusion of complete clarity and completeness: a number of problems still await a final solution, especially in terms of developing the modern physical mechanisms of solar-terrestrial connections. Moreover, it is precisely the unresolved problems that serve as “points of growth” for new research. Let us emphasize once more one of important peculiarities of STR—their multifactorial nature and dependence of observed effects on existing “background” (“underlying surface”). Note also, that modern consideration of the STR problems is impossible without taking into account the existence of the heliosphere.

1.2 Observational Data and Main Lines of Research

5

Fig. 1.2 General picture of a large helio-geophysical disturbance on March 23–24, 1991 (Shea and Smart 1996). From top to bottom, the graphs sequentially show: the flux of soft X-ray radiation (a signature of a flare) according to observations on the GOES 7 spacecraft; list of flares; fluxes of accelerated solar protons; data on the northern (GOES 7) and horizontal (Fredericksburg, USA) components of the geomagnetic field; variations of cosmic rays on a neutron monitor (Deep River, Canada). Below is a summary of anomalies in the operation of solar batteries and electronics on some satellites, other effects near and on the Earth’s surface: modification of the Earth’s radiation belts (ERB), radio communication disruptions at various frequencies, sudden power surges in the power system of the province of Quebec (Canada), telluric currents, etc.

Chapter 2

Main Characteristics of the Sun

Sol lucet omnibus. Latin poverb

The Sun is the central body of our Solar System. It is a hot rotating gas sphere with a radius of RS = 6.96 × 1010 cm and a mass of MS = 1.99 × 1033 g. The Sun is 750 times the mass of all other bodies in the Solar System, taken together, and 330 thousand times more massive than the Earth. The average density of solar matter is close to ρS = 1.4 g/cm3 (which is about 0.256 of the average density of the Earth, ρE), in the center of the Sun the density reaches 160 g/cm3, i.e. more than two orders of magnitude higher than the average. On the solar diameter (DS = 1,390,600 km), a chain of 109 such planets as our Earth could be placed. The Sun is located at a distance of 149,680,000 km from the Earth (this distance is called an astronomical unit, AU). In angular units in the Earth’s sky, the Sun (its diameter) is only about 0.5 degrees. For comparison, note that the average distance from the Earth to the Moon is 384,000 km. With a diameter of the Moon 3476.4 km, its angular size is close to 0.52 degrees, which practically coincides with the angular size of the Sun. That is why total eclipse of both the Sun and the Moon can be observed on the Earth’s surface.

2.1

The Sun as a Star

The Sun is the closest star to the Earth; its light reaches us in eight and a third minutes. In the earthly firmament, the Sun is the only one of the stars whose visible disk is visible to the naked eye. All other stars located at great distances from us, even when viewed through the most powerful telescopes, we do not reveal any details of their surfaces. The Sun belongs to a type of star called “yellow dwarfs”. According to the absolute magnitude of the stellar luminosity, the Sun has a brightness of +4.83, spectral type G2V. Spectral class G2 means that the star has a surface temperature ТS ≈ 5780 °K. In the star family of the observed Universe, on the classical Hertzsprung-Russell diagram “temperature-luminosity”, the Sun is © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 L. Miroshnichenko, Solar-Terrestrial Relations, https://doi.org/10.1007/978-3-031-22548-2_2

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Main Characteristics of the Sun

Fig. 2.1 Typical images when observing a quiet Sun (left), during active processes in its atmosphere (center) and during a solar eclipse (right). In the left image, solar granules are clearly visible, in the middle one—the inhomogeneous structure and active processes in the solar atmosphere (flares, prominences, etc.) are clearly manifested. The Sun’s corona is clearly visible in the right image (Wikipedia)

located on the main sequence. The closest star to the Solar System is a 12thmagnitude “red dwarf”, Proxima Centauri. This star has a parallax of 0.762, i.e. the distance to it is 1.31 parsecs (4.3 light years). The Sun is located near the plane of our Galaxy, not far from the border of one of its spiral arms. In this case, the Sun is immersed inside a partially ionized local interstellar cloud (LIC), or Local Bubble, and moves in the interstellar medium towards the border of the constellations Lyra and Hercules at a speed of about 25 km/ s relative to stars visible to the naked eye. The speed of movement of the Sun around the center of our Galaxy (the “Milky Way”) is about 250 km/s. The Sun is nearly 30,000 light years distant from the center of the Galaxy. Approximately the same distance lies between the Sun and the outskirts of the Galaxy. The period of the Sun’s revolution around the center of the Galaxy (galactic year) is ~230 million years. Typical observational images of the Sun are shown in Fig. 2.1.

2.2

The Structure of the Sun

According to the so-called Standard Solar Model (SSM), the Sun consists of three zones (Fig. 2.2), differing in composition, temperature, density and energy transfer process. The central zone, or core (within no more than 0.25RS, where RS is the radius of the Sun), about 35% consists of hydrogen, 64%—of helium, the share of other elements (in particular, the nuclei of carbon C, nitrogen N and oxygen O) accounts for no more than 1% (by weight). This is the densest part of the star, where matter is at extremely high pressure and temperature. The core of a star (core) occupies only 2% of the volume of the Sun, but contains almost half of its mass. In the center of the star, the density of matter reaches 150–160 g/cm3 (which is about 15 times the density of lead), and its maximum temperature can exceed 15 million degrees (≥ 1.5 × 107 K). At this temperature, a

2.2

The Structure of the Sun

9

Fig. 2.2 The internal structure of the Sun and the structure of its atmosphere (Wikipedia). Credit: NASA/Jenny Mottar

thermonuclear fusion reaction takes place, in which the hydrogen (p-p) cycle plays the main role 1H + 1H → 2H + e+ + ν; 2H + 1H → 3He + γ; 3He + 3He → 4He + 21H. Thus, 4 hydrogen nuclei form a helium nucleus with the release of a large amount of energy (for more details, see Sect. 2.4). When hydrogen burns, gamma rays γ (high energy photons) and neutrinos ν (particles devoided of charge and having a very small mass) are released. The release of energy in this case is millions of times greater (per unit mass) than in the chemical reactions of combustion of oil and gas. The core of the Sun is surrounded by a zone of radiation (or radiation zone, radiative zone), from which radiation by slow diffusion goes out towards the surface of the Sun. Heat is transferred due to the process of multiple absorption and repeated emission of quanta of electromagnetic radiation by ions from surrounded plasma. The released heat passes through the entire star and is emitted in the form of a luminous flux. The temperature gradually decreases along the radius. As a result, already in the next, static radiation zone, the temperature drops from 1.5 × 107 K to 1.0 × 106 K that is already insufficient for nuclear fusion. A slow diffusion of the heat

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2 Main Characteristics of the Sun

flux occurs until it reaches the border of the radiation zone at a distance of ~0.75RS. In general, it takes photons millions of years to pass through the radiation zone as they gradually propagate outward. At the border of the zone, the mechanism of heat transfer by radiation changes to a more efficient convective transfer. The outer convective zone is filled with turbulent hot plasma escaping onto the Sun’s photosphere. In the center of the Sun, gamma quanta are born. Their energy is millions of times greater than that of visible light quanta, and their wavelength is very small. On the way to the surface of the Sun, quanta undergo amazing transformations. A separate quantum is first absorbed by some atom, but is then re-emitted again. Most often, in this case, not one previous quantum appears, but two or even several. According to the law of conservation of energy, their total energy is conserved, and therefore the energy of each of them decreases. This is how quanta of lower and lower energies appear. Powerful gamma quanta seem to be split into less energetic quanta of the electromagnetic range—first X-rays (X), then ultraviolet (UV), visible (or optical, O) and, finally, infrared (IR) radiation. As a result, the Sun emits the greatest amount of energy in visible light (optical range), and it is no coincidence that our eyes are sensitive to it. On its way through the inner layers of the Sun, the flow of energy encounters an area where the opacity of the gas greatly increases. This is the convective zone of the Sun. Here energy is no longer transferred by radiation, but by convection. The essence of convection is that flows of hot plasma rise upward, where they give up their heat to the environment, and the cooled solar gas goes down. The solar matter appears to boil and stir like “sticky rice porridge” on a fire. The convective zone begins at about 0.75 RS from the center and extends almost to the most visible surface of the Sun (photosphere). Here, the mass density of the substance and its temperature fall to values of ρ ≈ 10-7 g/cm3 and T = 6 × 103 K, respectively, and the transfer of the main energy flux again becomes radiant. However, due to inertia, hot flows from deeper convective layers still penetrate here. Well-known to observers, the picture of granulation on the surface of the Sun (Fig. 2.1, left) is a visible manifestation of convection. As we have already said, it takes a very long time for a quantum to seep out through the dense solar matter. So, if the “stove” inside the Sun were suddenly extinguished, then we would only know about it millions of years later . . .

2.3

Age, Chemical Composition, Temperature and Density

There is still no consensus among astronomers-specialists in planetary cosmogony on the problems associated with the origin of the Solar System. The first and most natural stage in this process is the formation of the proto-planetary disk of the Sun from the material of the primary gas and dust cloud (nebula). However, the further “scenario” and physical mechanisms of the formation of the Sun and planets are still the subject of controversy and research. Initially, the hypotheses of the formation of

2.3

Age, Chemical Composition, Temperature and Density

11

the Sun and the Solar System can be divided into two groups. The hypotheses of the first group are based on the assumption of the joint formation of the Sun and its planetary system from a single proto-solar nebula. The second group of hypotheses is based on the separate formation of the Sun and its proto-planetary disk. In both cases, however, the formation of the proto-planetary disk itself was directly related to the formation of the most important characteristics of the Sun as a star (age, chemical composition, etc.). The dating of the age of meteorites and lunar matter by the radiochemical methods (using a radioactive “clock”) makes it possible to determine the absolute age of the Solar System together with restrictions on the time scale of some stages of planet formation. Thus, the time of formation of large bodies in the asteroid belt turns out to be less than five million years, and the time of the final formation (solidification) of the Earth is about 100 million years. When radiochemical dating is applied to rocks on the Earth’s surface, the oldest rocks are 3.8 billion years old, and in the case of meteorites, the oldest rocks are 4.57 billion years old. This value is a “typical” observational estimate of the age of the Solar System. Note that the most recent estimates of the Earth’s age give a value of 4.54 (±1%) × 109 years. According to the theory of stellar evolution, the Sun is a relatively young star of the so-called third generation with a high metal content. It was formed from the remains of stars of the first and second generations, during the evolution of which the formation of heavy elements took place. The current age of the Sun (more precisely, the time of its existence on the main sequence, TS) can be estimated using computer models of stellar evolution. One of the recent estimates of this kind gave the value TS ≈ 4.57 billion years. The latest data from cosmochronology (the science of time milestones in our world) suggest that the total age of the Solar System (including the Sun) is TS = 4.7 ± 0.1 billion years. The age of the Universe itself, estimated quite recently from the data of observations of the relict microwave background of the Galaxy on the WMAP (Wilkinson Microwave Anisotropy Probe) spacecraft, turned out to be TG = 13.73 billion years with an accuracy of about ±0.12 billion. . . An earlier estimate of the age of the Galaxy is about 15 billion years—was obtained by the radiochemical method under a number of model assumptions. From a comparison of TS and TG, it can be seen that by the time the Sun was born, our Milky Way had already existed for about 9 billion years—a sufficient time for the evolution and explosion of massive stars that saturated the interstellar gas with an abundance of chemical elements. A star as massive as the Sun should have existed on the main sequence for a total of about 10 billion years. Thus, the Sun is now approximately in the middle of its life cycle. The outer layers of the Sun are composed primarily of hydrogen (≤72%) and helium (≤27%). There is also a small amount (≤1%) of other elements (for example, nuclei of C, N, O, Ne, Si, S), including the metals Fe, Ni, Mg, Ca and Cr, formed from hydrogen in nuclear fusion reactions. These ratios change over time (very slowly) in the course of nuclear reactions, as small, light atoms turn into more massive ones. In general, the composition of the Sun is determined by spectroscopic methods when studying the spectrum of its visible light. The element helium was named after the Sun (“Helios” in Greek) since it was first discovered at the Sun.

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2 Main Characteristics of the Sun

There is a lot of helium on the Sun, but little on Earth. This element was discovered more than 150 years ago, during the total solar eclipse of 1868. Its abundance in the solar atmosphere is of great interest not only for solar physics, but also for understanding the chemical evolution of our Galaxy (see Sect. 6.3). The temperature of the Sun at various depths is determined by theoretical calculations based on models of its internal structure. In the outer layers, temperature is usually determined by measuring the energy of the Sun’s radiation in the form of heat and light. The temperature in the interior of the Sun, according to various theoretical estimates, can range from 10 to 22.5 million degrees (in the units of T° K). Recent experiments on the registration of solar thermonuclear neutrinos have generally confirmed the correctness of the standard solar model (SSM), in which the most probable temperature for the center of the Sun is considered to be a temperature TS of about 15 million degrees (≥1.5 × 107 K). The temperature of the photosphere (“surface” of the Sun) is about 5800 K. The outer atmosphere of the Sun (corona), usually observed during a solar eclipse, again becomes incandescent to 1.5–two million degrees. In the center of large spots, the temperature is relatively low—about 4300 K.

2.4

Energy Source

For not very massive stars like the Sun (with a mass of M ≤ 1.2MS), the main source of energy is the so-called hydrogen cycle (proton-proton or pp-cycle)—a sequence (chain) of thermonuclear reactions leading to the conversion of hydrogen into helium without the participation of catalysts. For stars more massive than the Sun, the main source of energy is the so-called carbon cycle (or CNO cycle), which also leads to the formation of helium from hydrogen, but with the participation of carbon C, nitrogen N, oxygen O and fluorine F as catalysts. In the centers of such stars (at М ≥ 1.2MS), the temperature is high enough for the CNO cycle to be more efficient than the hydrogen cycle. The contribution of the CNO cycle to the total luminosity of the Sun is only ~1.5% in the standard solar model. Other nuclear reactions under solar conditions are also unimportant. The hydrogen cycle begins with the collision reaction of two protons p with the formation of a 2D deuterium nucleus, a positron e+, and an electron neutrino νe: p þ p → 2 D þ eþ þ ν e

ð2:1Þ

This reaction is the slowest from the other ones, since it goes through the weak interaction channel; its characteristic time is ~1010 years. In essence, it is this reaction that determines the rate of energy release (per gram of matter) and the lifetime of a star on the main sequence. The resulting neutrino leaves the Sun almost unhindered and irrevocably carries away energy up to 0.42 MeV. Another channel for neutrino and deuterium production is also possible with a probability 70 MeV on both spacecraft has been increasing on average. In other words, the cosmic ray flux is constantly growing

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Main Characteristics of the Sun

Fig. 2.6 Variations in ion fluxes with energies >70 MeV at the heliosphere boundary as measured by the Voyager 1 and Voyager 2 space probes (Kiraly 2009)

as the spacecraft moves away from the Solar System and the heliosphere as a whole. This first information about the GCR directly from the interstellar medium raises new questions about the sources and nature (generation mechanisms) of the anomalous component of cosmic rays (see Chap. 5).

Chapter 3

Solar Activity

We live in a solar corona. Sydney Chapman (1957)

Before proceeding to the description of the phenomena of solar activity (SA), it is necessary at least briefly to get acquainted with the structure and physical properties of the outermost layers of the Sun. It is there that the main events take place—spots and torches are born and disintegrate, granules, filaments, prominences and coronal holes are formed, solar flares and coronal mass ejections (CME) occur, the solar wind is formed, magnetic clouds, shock waves, etc. As a characteristic of the SA level, data on the number of spots in the photosphere are usually used. The spots contain the necessary supply of magnetic energy, and its changes over time give rise to the main SA phenomena. Not all of these active formations and phenomena are described below with the same completeness. Some additional details will be provided in subsequent chapters.

3.1

The Structure of the Solar Atmosphere

The source of energy and the main physical mechanisms for the development of the phenomena of solar activity actually remain invisible, since they are located under the surface of the Sun—in its so-called convective zone (see Fig. 2.2). According to the standard solar model (SSM), vortex mixing of the plasma occurs closer to the surface of the Sun, and the transfer of energy outward occurs mainly by the movements of the substance itself. This method of transferring energy is called convection, and the subsurface layer of the Sun, where it occurs, is called a convective zone. Its thickness is about 200,000 km, and the temperature drops with altitude from ~106 to ~6000 K. According to modern data, the role of the convective zone in the physics of solar processes is enormous, since it is in it that various motions of solar matter and magnetic fields originate. In particular, the role of the convective zone in maintaining the hydrostatic and thermodynamic equilibrium of the Sun is extremely important. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 L. Miroshnichenko, Solar-Terrestrial Relations, https://doi.org/10.1007/978-3-031-22548-2_3

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Fig. 3.1 Sunspot and photospheric granulation as observed on October 5, 1998. The image was taken with the Kitt Peak National Observatory, USA (https://apod.nasa.gov/apod/ ap981005.html). Credit: Vacuum Tower Telescope, NSO, NOAO

Thermal equilibrium means that the processes of energy release in the interior of the Sun, its heat removal (heat transfer) to the surface and radiation from the surface must be balanced. The theory of stellar evolution shows that luminosity weakly depends on the rate of energy release in the core of the Sun and is mainly determined by the law (mechanism) of heat removal. This is one of the paradoxes of the hydrostatic equilibrium of stars, and this also explains the relatively low temperature of the solar photosphere. The need to maintain a thermal balance leads to the fact that the star turns out to be a stable self-regulating system. The observed radiation of the Sun arises in its thin outer layer, which is called the photosphere. The actual atmosphere of the Sun just begins with the photosphere, the lower boundary of which can be conventionally considered the surface of the Sun. The visible surface of the Sun is determined by the depth in the atmosphere below which it is practically opaque. This surface is conventionally taken as the level at which, when viewed from above, the so-called optical thickness at a wavelength of λ = 500 nm (5000 Å) reaches unity. He is measured by the height h in the atmosphere. The Sun is a ball of gas with no clear boundaries. However, we see its sharply outlined edge (limb) precisely because practically all of the Sun’s radiation comes from the photosphere. The photosphere is the lower part of the Sun’s atmosphere, visible in the optical wavelength range. Its thickness is ≤500 km, the temperature is about 5800 K (≈6000 °C). The mass density of matter at the lower boundary of the photosphere is ρ ≈ 5 × 10-7 g/cm3, which corresponds to the concentration of plasma particles n ~ 3 × 1017 cm-3; at the upper boundary it is a thousand times less. On the surface of the Sun, one can see a cellular structure consisting of bright granules (granule) against the background of a darker inter-granular space (see, for example, Fig. 2.1, left). The sizes of the granules are small, 1000–2000 km (about 1″ arc), the distance between them is 300–600 km. On the Sun, about a million granules are observed simultaneously (Fig. 3.1). Each granule exists for several minutes.

3.1

The Structure of the Solar Atmosphere

23

Granules are surrounded by dark gaps (“honeycombs”). In granules, matter rises, and around them—descends. Granulation is a manifestation of convection in deeper layers of the Sun. The granules create a general background against which incomparably larger formations can be observed—active regions (AR). The latter include a set of changing structures (spots, torches, flares, prominences, etc.) in a limited region of the solar atmosphere. Active regions (AR) are associated with an increase in the magnetic field in them from ~10–20 G to ~ (4–5) × 103 G. The most noticeable formations in the photosphere are sunspots, areas of a round or oval shape, usually 10–20 thousand km in size and with a brightness of only 1–15% of the brightness of the surrounding photosphere. Figure 3.1 shows a typical photograph of a sunspot, showing some details of its structure. Around the darkest part, the shadow of the spot, there is a lighter wide border—penumbra, consisting of dark and light penumbra fibers elongated approximately along the radius from the center of the spot. The sizes of the largest spots can reach 100,000 km. The lifetime of a spot depends on its size and varies from several hours or days for small spots (pores) to several months for the largest spots. The temperature in the shade is 2000 K lower than in the calm photosphere, which is why the spot appears dark. A decrease in temperature is usually explained by suppression of convection by a strong magnetic field, which is present in the spot. The larger the spot, the larger the magnetic field induction is. In the pores, it is about 1000 G, in large spots up to 4000 G. The photosphere is followed by the chromosphere—a reddish layer with temperatures from ~6000 °C (in the lower part) to ~50,000 °C (at high altitudes) and up to 7000 km thick. Its color is determined by the glow of excited hydrogen atoms in the red region of the spectrum (mainly in the line 656.3 nm = 6563 Å). The chromosphere of the Sun is clearly visible only at the moments of total solar eclipses (see Fig. 2.1, on the right). The Moon completely covers the photosphere, and the chromosphere flares up like a small ring of bright red, surrounded by a pearl-white crown (corona). The intermediate region between the photosphere and chromosphere (at an altitude of h ≈ 500 km) is known as the temperature minimum region. Further, the temperature in the chromosphere grows rapidly, reaching values of ~3 × 104 K and higher in its uppermost layers, up to a temperature of the solar corona of ~106 K. These areas already belong to the so-called transition layer between the chromosphere and the corona. The corona is the outermost, most rarefied and hottest part of the solar atmosphere, with temperatures up to ~2 × 106 K and with a concentration of plasma particles from 109 cm-3 at the bottom to 104 cm-3 at a distance of 10 RS. In general, the corona can be traced from the solar limb to distances of tens of solar radii (i.e., it is elongated for several million kilometers). The brightness of the corona is millions of times less than that of the photosphere, so the corona can be seen only during a total solar eclipse, or with the help of extra-eclipse coronagraphs installed high in the mountains or on board a spacecraft. An important feature of the crown is its radiant structure. Coronal rays have a wide variety of shapes. With the 11-year cycle of the Sun, the general appearance of the solar corona changes. In the epoch of the minimum, the main glow comes from

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Solar Activity

Fig. 3.2 Ultraviolet image of the coronal arc obtained from the TRACE spacecraft. For a comparison, the size of the Earth (dark ball) is shown in the center of the photo (Credit: LMSAL/ NASA/JAXA/NAOJ)

the equatorial regions; at the epoch of the maximum, the shape of the crown becomes close to spherical. Observations of the corona from the spacecraft in the X-ray range have revealed one more structural (and physical) feature—the so-called “coronal holes”. They represent regions with a relatively low temperature (about 0.8 × 106 K), a reduced plasma density (about 0.25 of the density of quiet regions of the corona), and a magnetic field radial with respect to the Sun, and its field lines are devoid of arched magneto-plasma structures (coronal arcs) (coronal arch) and freely go into interplanetary space. The photosphere is followed by the chromosphere—a reddish layer with temperatures from ~6000 °C (in the lower part) to ~50,000 °C (at high altitudes) and up to 7000 km thick. Its color is determined by the glow of excited hydrogen atoms in the red region of the spectrum (mainly in the line 656.3 nm = 6563 Å). The chromosphere of the Sun is clearly visible only at the moments of total solar eclipses (see Fig. 2.1, on the right). The Moon completely covers the photosphere, and the chromosphere flares up like a small ring of bright red, surrounded by a pearl-white crown (corona). The intermediate region between the photosphere and chromosphere (at an altitude of h ≈ 500 km) is known as the temperature minimum region. Further, the temperature in the chromosphere grows rapidly, reaching values of ~3 × 104 K and higher in its uppermost layers, up to a temperature of the solar corona of ~106 K. These areas already belong to the so-called transition layer between the chromosphere and the corona. As follows from the above, the Sun’s corona is about 300 times hotter than its visible surface (photosphere). For more than 70 years, scientists have been looking for a mysterious energy source that heats the gas of coronal arcs to millions of degrees (Fig. 3.2). Arcs are streams of gas that rise hundreds of thousands of kilometers above the sun’s surface before falling back into the solar photosphere at great speed. Millions of coronal arcs of various sizes make up the Sun’s corona. It is not difficult to show theoretically that the direct heat flux from the photosphere is insufficient to lead to such a high corona temperature. Therefore, it is generally assumed that the energy for heating the corona is supplied by turbulent motions from under the photosphere (from the convective zone). Two mechanisms

3.1

The Structure of the Solar Atmosphere

25

have been proposed to transfer this energy to the corona. First, this is heating due to sound and magnetohydrodynamic (MHD) waves that are generated in the convective zone. They propagate into the corona and scatter there, while their energy is converted into thermal energy of the coronal plasma. The second, alternative mechanism is magnetic heating, in which magnetic energy, continuously generated by photospheric movements, is released by reconnecting the magnetic field in the form of large solar flares or a large number of small flares (so-called “nanoflares”). Images taken more than 25 years ago by the SOHO spacecraft (launched in December 1995) showed that energy is released during the interaction of loops (loops)—magnetoplasma formations elongated along magnetic lines of force. Extremely strong electric currents flow through the loops; when the loops interact, these currents and magnetic fields reconnect. The resulting electrical discharges heat the corona. In this case, the energy released during the interaction of the loops is quite sufficient to heat the corona to temperatures above 106 K (http://sohowww. nascom.nasa.gov/). On the other hand, observations on board the TRACE spacecraft in 1998–2000 allowed to significantly clarify the picture. Previously, it was believed that heating is carried out more or less uniformly throughout the entire thickness of the corona and the highest temperature is reached at the highest point of the loop, where the low gas density reduces the radiation efficiency. However, the data from TRACE devices showed that the gas temperature changes little with height and, therefore, heating occurs only in the lowest part of it. It turned out that the source of energy that heats the corona is within 16,000 km of the visible surface of the Sun. Gas loops heat up and rise along the lines of the Sun’s magnetic field to an altitude of 480,000 km, then cool and fall on its surface at a speed of more than 100 km/s. However, the specific phenomena leading to the heating of the corona are still mysterious. Back in the early 1980s, it was shown that all waves, except for MHD Alfvén waves, are scattered or reflected before they reach the corona, while dissipation of Alfvén waves in the corona is hindered. Therefore, many researchers do not exclude an alternative, magnetic heating mechanism mentioned above, although the final clarity on this issue has not yet been achieved. At the end of 2006, data began to arrive from the new space observatory, the international spacecraft Hinode. Due to a significant improvement in the spatialtemporal resolution of the observation equipment, already at the beginning of 2007, information was obtained on the presence of Alfvén waves, at least at the level of the chromosphere. Moreover, it has been shown that their energy is more than enough to maintain the temperature of the corona and provide energy for the solar wind. Computer simulations have confirmed the possible presence of Alfvén waves in the chromosphere. However, scientists have so far refrained from definitive conclusions, since chromospheric data alone do not yet prove that Alfvén waves reach high altitudes and warm up the Sun’s atmosphere as a whole.

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3.2

3

Solar Activity

Solar Wind

In addition to high temperature, the Sun’s corona has another remarkable property: it is continuously expanding into interplanetary space, carrying away the solar matter (plasma) along with the magnetic fields frozen into it (i.e. solar magnetoplasma) at great distances from the Sun. The physical reason for the expansion is quite understandable: the temperature of the corona is so high that the gravitational attraction of the Sun cannot hold the plasma. In other words, at a temperature of about 2 × 106 K, the corona cannot be in hydrostatic equilibrium, and this expansion under the existing boundary conditions should lead to the acceleration of coronal matter to supersonic speeds. As a result, already at distances r ~ (3–4)RS in the expanding corona, a continuous and (on average) rather stable stream of particles is formed that leave the Sun forever (solar wind). The foundations of the theory and the first models of the solar wind were proposed back in the 50s of the last century, but the discussions on certain aspects of this fundamental astrophysical phenomenon are still ongoing. The radical idea of the outstanding British mathematician and geophysicist S. Chapman (1957) turned out to be very fruitful in the formation and development of the problem of solar-terrestrial relations: “interplanetary gas is simply an extension of the solar corona.” On the planets of the Solar System with magnetic fields (Earth, Jupiter, Saturn, and others), the solar wind generates such phenomena as, for example, magnetic storms and auroras; when their magnetospheres interact with the solar wind, the radiation belts of the planets are formed. The influence of the solar wind also explains the different shape of cometary tails, always directed from the Sun. The area of space occupied by the solar wind extends to distances ≥100 AU. Ultimately, the solar wind forms the heliosphere (heliomagnetosphere), which prevents interstellar gas from entering the Solar System (Fig. 2.4). The solar wind is a helium-hydrogen plasma, which consists mainly of electrons, protons and helium nuclei (alpha particles); nuclei of other elements and non-ionized (electrically neutral) particles are contained in very small quantities. Because of the solar wind, the Sun loses about one million tons of matter every second. Although the solar wind comes from the outer layer of the Sun, it does not reflect the real composition of elements in this layer: due to differentiation processes, the content of some elements increases, while others decrease. This is due to the FIP effect, i.e. the influence of the energy of a single ionization of an atom (“the first ionization potential”, or FIP in English) on the composition of elements. The intensity of the solar wind depends on changes in solar activity and its sources. Depending on the speed u, the solar wind fluxes near the Earth’s orbit are conventionally divided into two classes: slow (u ≈ 300–400 km/s) and fast (u ≈ 600–700 km/s). The slow solar wind is generated by the “calm” part of the solar corona during its gas-dynamic expansion. The streams of a recurrent fast solar wind are emitted by the Sun for several months and have a recurrence period for observations from the Earth of 27 days (the period of the Sun’s rotation). These streams are associated with coronal holes.

3.2

Solar Wind

27

Table 3.1 Solar wind parameters Parameter Density n, cm-3 Speed u, km/s Flux nu, cm-2 s-1 Protons, Tp, К Electrons, Te, К Ratio Te/Tp

Average value 8.7 468 3.8 × 108 7 × 104 1.4 × 105 1.9

Slow solar wind 11.9 327 3.9 × 108 3.4 × 104 1.3 × 105 4.4

Fast solar wind 3.9 702 2.7 × 108 2.3 × 105 1.0 × 105 0.45

Due to the strong variability (dynamism) of the interplanetary medium, spacecraft usually measure hourly average values of its parameters. Table 3.1 shows typical values of various solar wind parameters from observations in Earth’s orbit. The most important parameters of the interplanetary medium, undoubtedly, should also include the average value of the modulus B of the interplanetary magnetic field (IMF). Near the Earth’s orbit, i.e. at a distance of 1 AU from the Sun, this value is close to 5 × 10-5 G = 5 nT (see Sect. 4.3 for more details). There are also short-term sporadic high-speed (u ≥ 1200 km/s) flows. When moving in space filled with the plasma of the slow solar wind, sporadic flows compact the plasma ahead of their front, forming a shock wave (SW) moving with it. Previously it was assumed that such phenomena are caused by powerful solar flares. However, at present, the prevailing opinion is that sporadic fluxes are caused by coronal mass ejections (CME). At the same time, it should be noted that both solar flares and CME are associated with the same active regions on the Sun and there is a statistical relationship and an undoubted physical connection between them. One thing is clear: a solar flare is part of a large and very powerful non-stationary process (burst) associated with the CME ejection. An important role for the dynamics of the solar wind plasma is played by the relationship between the energy densities of directed plasma motion wu, chaotic (thermal) motion wT, and interplanetary magnetic field wB. With np = 5 cm-3 and u = 400 km/s, we have wu = npmpu2/2 = 7 × 10-9 erg/cm3. At the same time, the energy density of chaotic motions is wT = neTe + npTp ≈ 2 × 10-10 erg/cm3, if we take Te = 1.5 × 105 K, Tp = 5 × 104 K and assume that temperatures are isotropic (an energy of 1 eV corresponds to 1.6 × 10-12 erg/cm3 or temperature 7.733 × 103 ° K). The energy density of the magnetic field is wB = B2/8π = 10-10 erg/cm3 at B = 5 nT. Thus, the kinetic energy of the “calm” solar wind flow near the Earth’s orbit is several tens of times higher than the thermal energy of the plasma and the energy of the magnetic field, while the magnetic and thermal energy are comparable. In the case of strong disturbances of the interplanetary medium during large flares, coronal mass ejections (CMEs, see Sect. 3.4), and the generation of associated shock waves, the relationships between wu, wT, and wB change significantly (see Sect. 7.3). The total number of particles leaving the solar atmosphere in the form of the solar wind is about 1.3 × 1036 per 1 s. Hence, it is easy to estimate that the total loss of matter in 1 year is close to (2 ÷ 3) × 10-14 solar mass, or 6.7 billion tons per hour. This is equivalent to a loss of mass equal to that of the Earth every 150 million years.

28

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However, so far, due to the solar wind, the Sun has lost only about 0.01% of its total mass. More powerful stellar winds are observed in other stars, and this leads to significantly greater losses of their matter.

3.3

Solar Flares

Solar flares are extremely powerful explosions (bursts) in the solar atmosphere. They occur near sunspots, usually along the dividing line (neutral line) between regions with oppositely directed magnetic fields. Physically, a flare is the response of the solar atmosphere to a sudden, rapid release of energy, most likely of magnetic origin. The response mainly affects the chromosphere and corona. The release of energy leads, first of all, to localized temporary heating (thermal flare), as well as to the acceleration of particles (electrons, protons and heavier ions). In this case, the temperature in the chromosphere is ~104 K (chromospheric, or low-temperature, flare), and in the corona reaches ~107 K (high-temperature flare). The energies of accelerated particles registered in the Earth’s orbit range from ~20 keV (for electrons) to ≥10 GeV (for protons). The total energy released during the strongest flares is ~1025 J = 1032 erg. The flare generates short-term electromagnetic radiation in a wide range of wavelengths (Fig. 3.3)—from hard X-rays (wavelength λ ~ 10-9 cm) to kilometer radio waves (λ ~ 106 cm). By its nature, the emission from the flare is predominantly thermal. At very short wavelengths (hard X-rays, λ < 1 Å, and gamma radiation, λ < 0.01 Å), non-thermal impulsive bursts of radiation generated in the solar atmosphere by accelerated particles are observed. They are non-thermal bremsstrahlung and synchrotron radiation of electrons, gamma radiation from the interaction of accelerated ions with the surrounding nuclei of the atmosphere, etc. In the very long wavelength range (radio emission), such bursts are generated by shock waves in the coronal plasma and solar wind. Figure 3.3 scales of electromagnetic waves emitted by the Sun.

ultraviolet

gamma ray X-ray Shorter wavelength higher frequency higher energy

visible

infrared

radio microwave longer wavelength lower frequency lower energy

Fig. 3.3 Scale of electromagnetic waves emitted by the Sun: https://imagine.gsfc.nasa.gov/science/ toolbox/emspectrum1.html

3.3

Solar Flares

29

Fig. 3.4 A typical solar flare (left) in the Hα hydrogen line (photo from the archive of the Big Bear Solar Observatory, USA, http://solarscience.msfc.nasa.gov/flares.shtml). In the center is shown a similar image of a powerful flare on August 7, 1972 (3B/X4). An image of the Sun with a bright flare near the center of the disk (3B/X5.7) is given on the right, as observed with the EIT ultraviolet telescope (Fe XII 195 Å iron ion line) on board the SOHO spacecraft on July 14, 2000 (BDE flare, http://sohowww.nascom.nasa.gov/hotshots/2000_07_14/)

A thermal flare is best seen and best studied from ground-based optical observations in the red hydrogen line Hα (λ = 6563 Å = 656.3 nm). In recent years, flares have also been regularly recorded on spacecraft in the soft X-ray range with a wavelength λ = 1–8 Å = 0.1–0.8 nm, which approximately corresponds to the energies of quanta in the range of ~2–10 keV. Soft X-ray radiation (λ = 0.1–10 nm) is the thermal emission of plasma at a temperature of T = 104 K. Flares in the hydrogen line Hα (Fig. 3.4) and X-ray flares are the result of low- and hightemperature solar flares, respectively. They have a number of characteristics in common, so that the term “flare in Hα” can be used to refer to thermal or optical flare in general. The peculiarities of the flares themselves and the variety of observation methods gave rise to their specific classification in terms of power and duration. Until January 1, 1966, the brightness of flares in the Hα line was characterized on a 4-point scale: 1- (or subflare), 1, 2, and 3; the largest flares were assigned a score of 3+ (Illustrated Glossary for Solar and Solar-Terrestrial Physics 1977). In 1966 a 5-point scale was proposed: S (subflare), 1, 2, 3, and 4. In this case, flares with a score of ≥2 were considered already strong. With the beginning of extra-atmospheric (satellite) observations, flares were also assigned an X-ray score (class) of C, M, or X. The most powerful flares belong to class X, their brightness in the range of 1–8 Å is ≥10-1 erg/(cm2 s). An M-class flare is 10 times, and a C-class one 100 times weaker than an X-class flare. To indicate the exact value of the flare intensity, the following designations are used, for example: C7, M8, X5. An X5-class flare corresponds to a flare intensity of 5 × 10-1 erg/(cm2 s) in the range of 0.1–0.8 nm (soft X-ray radiation). Since 1977, solar flares are usually divided into impulsive and gradual, depending on the duration of the soft X-ray burst (1 h, respectively). The current classification of solar flares is shown in Table 3.2. It can be seen that it has a serious observational rationale. Continuous monitoring of X-ray flares is currently being carried out by the GOES satellite system (NOAA). Typical examples of flares are shown in Fig. 3.4. The flare

30 Table 3.2 Classification of solar flares (Kallenrode 2003)

3 Parameter Duration in soft X-rays (SHR) Decay constant in SHR Height in corona Volume (cm3) Energy density Size in Hα Duration in hard X-rays (SHR) Duration in microwaves Type of metric radioburst Coronal mass ejection

Impulsive 5 min II, (III), IV Always

of August 7, 1972 resembles a seahorse in its outline. It is an example of the so-called “two-ribbon flare”, when the glow area looks like two bright lines (ribbons) penetrating the area between sunspots in the sunspot’s group. This flare in terms of radiation level could pose a danger to astronauts if at that time a flight to the Moon was carried out. Another flare (July 14, 2000), which occurred on the day of the French national holiday (Bastille Day Event, BDE), turned out to be interesting for a similar reason: in particular, it generated a rapid flux of SEPs that reached Earth’s orbit about half an hour after flare. This “radiation storm” caused “snow” in the images taken aboard the SOHO by the EIT telescope camera, due to the bombardment of the electronic detectors of the camera with high-energy particles (see also Chaps. 8 and 9). The flare was also accompanied by a powerful CME, which ejected billions of tons of solar plasma into interplanetary space. The ejection was moving towards the Earth at a speed of almost 1800 km/s, i.e. 2 times faster than usual. The duration of a flare in the optical range of the spectrum can be from several minutes to several hours. The period of rapid brightening and growth of the flare area to its maximum is called the flash phase of the flare. This period usually takes up to 15 min. In the flash phase, an explosive (burst) or impulsive phase is often observed, i.e., a sudden rapid increase in brightness (within ~1 min) in a small area of the flare (impulsive flare). Pulsed bursts of microwave radio emission and hard X-rays usually coincide with the impulsive phase. Microwaves with a frequency in the GHz range are synchrotron radiation of electrons (10–100 keV) in a magnetic field (20–100 G), and hard X-rays (E ≥ 20 keV) are the result of bremsstrahlung of accelerated electrons. During the flash phase, it is sometimes possible to observe small areas of the flare in white light (“white flares”) for about 10 min. The maximum brightness of such a flare is about 50% higher than the brightness of the photosphere. According to historical data, an increase in the brightness of the photosphere in white light (“white flare”) was first observed on September 1, 1859. The flare was accompanied by a strong geomagnetic storm, auroras up to geomagnetic latitudes of ±23°, high fluxes of energetic (accelerated) solar particles, disturbances (sparking) in the work of telegraph devices and other clear signs of disturbances in “Space Weather”.

3.3

Solar Flares

31

Fig. 3.5 An outburst (flare) on the star EV Lacertae on April 25, 2008, as observed by the Swift satellite (NASA)

Particles accelerated at/near the Sun are of interest for many reasons. Currently, accelerated solar particles with energies of ~10–100 MeV are usually called “solar energetic particles” (SEPs), but in the relativistic range (Ep ≥ 500 MeV for protons), the traditional (historical) name is “solar cosmic rays” (SCR). In addition to electrons with energies up to 10 MeV and protons up to tens of GeV and above, neutrons with energies up to 400 MeV and flare neutrinos are generated on the Sun. The movement of accelerated electrons in the magnetic fields of the solar atmosphere is accompanied by the generation of microwave radio emission. The interaction of accelerated ions with matter leads to the excitation of nuclei C, N, O, Fe, etc., the generation of gamma radiation in lines, the formation and decay of pions and other nuclear processes (see Sect. 8.6). Solar flares remain events of intense scientific interest. Solar flares are one of the most important sources of disastrous space weather events, leading to negative effects on spacecrafts and living organisms. It is not possible here to cover in any detail other aspects of the physics of solar flares. While solar flares are undoubtedly one of the most remarkable phenomena in astrophysics, they are by no means unique. Flares on other stars, at least on variable dwarf stars like UV Ceti, are fairly common. They are widely studied, and the physical nature of the activity of such stars is identical to the nature of solar activity. From the closest star to us, Proxima Centauri, for example, a flare was recorded equivalent to a 2X solar flare. More recently, on April 25, 2008, a small, faint star EV Lizard, 16 light-years away from us, experienced the brightest flare ever observed on an ordinary star, with the exception of the Sun (Fig. 3.5). The first flare was recorded by the Russian-made “Cone” detector on the American Wind satellite. Two minutes later, the radiation from the flare was captured by the X-ray telescope of the Swift satellite (NASA). In the X-ray range, the star remained bright for 8 h. If the star was located more successfully, the flash in the constellation Lizard would be visible to the naked eye. The unprecedented power of the flare is most likely due to the youth of the star. This star is an ordinary red dwarf,

32

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its mass is 3 times less than the mass of the Sun. It is 15 times younger than the Sun and rotates about seven times faster (one revolution in 4 terrestrial days). The faster rotation creates stronger magnetic fields, which are responsible for the flares.

3.4

Coronal Mass Ejections

During a flare, its substance can be heated to temperatures of ~107 K. Such heating leads to the emission of large fluxes of ultraviolet and X-ray radiation, as well as visible light. In addition, flares tend to eject large amounts of plasma outward at speeds of the order of 1000 km/s or higher (sometimes higher than 3000 km/s). These events are called coronal mass ejections (CMEs). Some researchers believe that the CMEs should be called coronal mass ejections of substance (CMES). As is often the case, behind this terminological discussion, there is a dispute about the physical nature of CME. The point is that the mass of CME (see below), according to modern estimates, can make up a noticeable fraction of the total mass of the corona. This means that CME is not only a coronal phenomenon, but can also affect other layers of the Sun’s atmosphere. Be that as it may, coronal ejections are, first of all, large-scale perturbations in the corona (Fig. 3.6), as a result of which a large mass of solar matter is ejected into interplanetary space. They cause strong disturbances in the solar wind, which largely determine the “space weather” in the Solar System. Under terrestrial conditions, due to the scattering of bright radiation from the photosphere in the atmosphere, it is practically impossible to observe the corona, except for rare moments of total solar eclipses. It became possible to monitor the state of the corona thanks to special coronagraph telescopes installed on board space observatories such as the European satellite SOHO and the Russian CORONAS-F. For the first time, CME was discovered on December 14, 1971 in observations on board the OSO-7 (7th Orbiting Solar Observatory) spacecraft. Launched in December 1995, the Solar Heliophysical Observatory (SOHO) includes two main instruments: the Large Angle Spectrometric Coronagraph Experiment (LASCO).

Fig. 3.6 Ejections of coronal matter during strong disturbances of the solar atmosphere on July 9, 1996 (left), July 14, 2000 (center), and November 4, 2003 (right) as observed from the SOHO spacecraft

3.4

Coronal Mass Ejections

33

These instruments provide white light images of the Sun’s corona up to 30 solar radii. The Extreme Ultraviolet Imaging Telescope (EIT) captures images of the solar disk and the lower corona above the limb in ultraviolet light. Each ejection carries away ~2 × 1014 ÷ 4 × 1016 g of solar matter. According to the maximum estimates, the CME mass can reach 2.0 × 1017 g (e.g., event on October 28, 2003). According to modern semi-empirical models of the corona, up to 10RS, it contains 1018–1019 g of matter. Thus, the mass of CME can reach ~1–10% of the mass of the entire corona, and the overwhelming part of this mass is usually drawn from the lower corona or even from lower levels (Hudson et al. 2006). The speed of movement of the CME can be different, usually in the range from 50 to 2000 km/s. In exceptional cases, much higher CME velocities are also observed: for example, on November 2, 2003, the CME velocity reached almost 3000 km/s, and on January 20, 2005, it also exceeded this value (see also Sect. 4.5). In some cases, the leading edge of the disturbance moves with acceleration or deceleration up to 250 m/s, although typical values are 20–30 m/s. Often, the CME velocity remains practically constant. The total CME energy spent on overcoming the gravitational attraction and imparting the appropriate velocity to the ejection is ~1031–1032 erg. Note, by the way, that this value is comparable to the energy of a large solar flare (see above), and empirical estimates show that in both cases, up to 10% of the total disturbance energy (flare or CME) is transferred to accelerated SEPs (solar cosmic rays). These estimates give additional arguments in the favour of the concept that both phenomena are two sides of the powerful burst—energy release on the solar atmosphere (see cover of this book). The form of CME emissions is very diverse, depending on the circumstances of a particular phenomenon and the characteristics of its projection onto the plane of the sky. When the direction of motion is close to the direction of the line of sight (towards or away from the observer), a disturbance appears around the eclipsing disk of the coronagraph in the form of an expanding diffuse ring. When the direction of movement is across the line of sight, the internal structure of the ejection is more clearly visible. Most often, CME consists of three main elements: the frontal part, which looks like a loop with ends fixed to the Sun, a darker region inside the loop, called a cavity, and a bright central core of the ejection. The core is the remnants of the eruptive prominence that initiated the coronal ejection. In addition to radial movement, the entire system expands while maintaining some semblance. As a result, the speed of the frontal part can be almost twice the speed of the central core. Coronal mass ejections are highly dynamic events in which plasma, initially confined in closed coronal magnetic structures, is suddenly ejected into interplanetary space. In the epoch of minimum solar activity (SA), coronal ejections occur in a day or two (at least once a week). At the maximum of the cycle, two to five CMEs are observed per day. When averaged over the entire solar cycle (≈11 years), the frequency of their occurrence is approximately 1 event per day. The separation from the Sun of such a structure, which seems to be very stable and magnetically closed, poses a number of fundamental questions for researchers from the field of plasma physics and magnetohydrodynamics (MHD). It is noteworthy that in about 90% of flares of all classes, coronal ejections are not observed, while only 60% of

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Solar Activity

Fig. 3.7 Model of a magnetic cloud at a distance of 1 AU. Shown is the bidirectional motion of trapped energetic electrons in the magnetic field of the cloud (Lepping et al. 1990)

CMEs occur without flares. Therefore, it is no coincidence that there is still no unanimity among scientists in understanding both the CME and flare origin (or the origin of “flare-CME” system, see a cover of this book). Also, in the assessment of the CME relative role (in comparison with flares) in the “Sun-Earth” problem (in the problem of solar-terrestrial connections) points of view are very different. All known connections of CME with other manifestations of activity on the solar disk are statistical (probabilistic), but not physical; the physical connections between these phenomena have not yet been unambiguously established and are the subject of intensive research. A separate class of interplanetary disturbances is represented by “magnetic clouds”—magneto-plasma structures with an enhanced magnetic field and increased values of the main plasma parameters (velocity, density and temperature). The clouds were first identified in the early 1980s from solar wind observations on the Helios 1 and SMM spacecraft. Magnetic clouds can be considered a manifestation of CMEs. CME observations near the Earth are usually carried out by only one spacecraft; therefore, it is not always possible to detect their connection with the clouds. A typical structure that can be observed for a fast CME from an ACE spacecraft is a shock wave (fast mode), which is accompanied by a dense sheath of hot plasma (downstream of the solar wind) and a magnetic cloud. The main characteristic of a cloud is an enhanced magnetic field, the vector of which rotates smoothly. Over time (as the cloud moves away from the Sun), there is a gradual decrease in the field, velocity, density, and temperature of the plasma. Magnetic clouds behave like a magnetosphere moving in the solar wind. They are distinguished by a very low dynamic pressure to magnetic pressure ratio and a high magnetic field modulus. As a result, the plasma in the cloud remains relatively isolated during propagation. The cloud gradually expands and its density decreases accordingly. One of the most important properties of magnetic clouds is the capture of SEPs in a magnetic trap (Fig. 3.7). In general, this is a very complex interplanetary

3.5

Cyclicity of Solar Activity

35

Fig. 3.8 Coronal hole observed by NASA’s Solar Dynamics Observatory, or SDO, on October 8, 2014. “Sun’s smile”. Credit: NASA/SDO

object, interesting from various points of view, in particular, for understanding the capture and transfer of SEPs from the Sun to the Earth. At the Sun there is also one very specific type of activity—so-called coronal holes. Figure 3.8 shows active regions on the Sun combined to look something like a jack-o-lantern’s face on October 8, 2014. The image was captured by NASA’s Solar Dynamics Observatory, or SDO, which watches the Sun at all times from its orbit in space. The active regions in this image appear brighter because those are areas that emit more light and energy. They are markers of an intense and complex set of magnetic fields hovering in the Sun’s atmosphere and corona. This image blends together two sets of extreme ultraviolet wavelengths at 171 and 193 Å, typically colorized in gold and yellow, to create a particularly Halloween-like appearance. This photo was called “the smile of the Sun”.

3.5

Cyclicity of Solar Activity

It is customary to refer to the totality of the observed phenomena in the atmosphere of the Sun as solar activity, causing changes in its radiation in different ranges of electromagnetic waves and fluxes of particles of different energies: spots, filaments, flares, prominences, CMEs, coronal holes etc. The SA state is characterized by several observational indices, among which the longest series has the relative number of sunspots (Wolf number W ). The Wolf number is a combined index.

36

3

W = 10 g þ f ,

Solar Activity

ð3:1Þ

including the number of sunspot groups g and the total number of sunspots f in the visible hemisphere of the Sun. This index was first introduced into scientific circulation by the Swiss astronomer R. Wolf in 1849. In fact, it was from this year, when scientific observations of the Sun began, that a reliable W series was obtained. In addition, Wolf, based on fragmentary data from individual European observers restored the monthly average W values since 1749 and the annual average W values since 1700. According to historical data on sunspots, as well as some indirect (proxy) geophysical data (for example, the content of the cosmogenic isotope 10Be in annual deposits of Greenland ice), modern researchers have approximately extended this series up to 1610. Thus, at present we have a time series of Wolf numbers about 400 years long. Every about 11 years, the number of sunspots simultaneously observed on the disk reaches its maximum value (Fig. 3.8). This phenomenon is called the “solar cycle” or “11-year cycle”. The 11-year period, however, is inaccurate and in the twentieth century was closer to 10 years, and over the past 300 years it has varied from 7 to 17 years. For example, the solar cycle that began in May 1996 peaked in April 2000; the secondary (somewhat smaller) maximum was noted in November 2001, and by analogy with the previous cycles, one should expect that in 2007–2008. a new cycle will begin. However, only in January 2009 the first spots of the new cycle began to appear. Nevertheless, it is the traditional 11-year cycle that still serves as the basis for numerous hypotheses about the causes of solar cyclicity and even for SA forecasts for the coming years (Fig. 3.8). The growth phase of the cycle can last from 2 to 5 years, and the decline phase can last from 5 to 12 years. The amplitudes of successive cycles vary smoothly from W ~ 50 (low cycle) to W ~ 200 (high cycle) (Fig. 3.9). Following the scheme proposed by R. Wolf, the cycle 1755–1766, began to be called cycle number 1 (its maximum was reached in 1761). In the year 2000, a maximum of the 23rd solar activity cycle was observed. There are almost no spots at all in the SA minima. Of particular interest was the behavior of the Sun in the 24th cycle of activity (see below Sect. 3.6 and Fig. 3.11). During the cycle, the sequence of the magnetic polarity of the main sunspots in the groups is preserved, but the opposite is true in both hemispheres. In the next cycle, the polarity is reversed. The spotting zone during the cycle shifts from middle latitudes (±30–35°) to ±5° at the end of the cycle. There is evidence of the existence of longer cycles: 35-year, “secular” (or the so-called “Gleisberg cycle” ~ 80–130 years) and even longer. At the end of the twentieth century, it became clear that the solar activity indices contain a very important quasi-biennial oscillation (QBO) period, which is also typical for a number of geophysical phenomena. The nature and hierarchy of SA cycles have not yet received a proper explanation, although their physical basis is beyond doubt: this is the structure and dynamics of magnetic fields in the convective zone of the Sun (see also Chap. 13).

3.5

Cyclicity of Solar Activity

37

Fig. 3.9 Changes in the average number of sunspots W on the disk from 1700 to 2005 (http://www. kosmofizika.ru/ucheba/sun_ act.htm). The values of Wolf numbers before 1749 were reconstructed from indirect geophysical data

200 150 100 50 0 1700 1710 1720 1730 1740 1750 1760 1770 1780 1790 1800 1810 200 150 100 50

(http://sidc.oma.be, Mar 1, 2005)

0 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1990 1910 200 150 100 50 0 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

In addition to quasiperiodic variations in the number of sunspots with a period of ~11 years, there are also SA variations of longer duration. Thus, in the second half of the seventeenth century (1645–1715), solar activity and, in particular, its 11-year cycle were greatly weakened (this era is known as the “Maunder minimum”). In the same era in Europe, there was a decrease in average annual temperatures (the so-called “Little Ice Age”), which is possibly caused by the impact of solar activity on the Earth’s climate. There is also a point of view that global warming is to some extent caused by an increase in the total SA level in the second half of the twentieth century. Indeed, not only sunspots are subject to 11-year variations, but also the total solar irradiance—the main source of energy for the Atmosphere heat engine. Figure 3.10 shows the variations in the SA parameters in the last three cycles: total radiation flux (irradiation); number of sunspots; index of solar flare activity and radio emission flux at a wavelength of 10.7 cm. Total radiation flux, i.e. direct solar flux at the top of the Earth’s atmosphere, shown as daily values and moving annual averages. All other data are rolling averages. Despite the undoubted correlation between the total solar radiation flux and various SA indices, the mechanisms of its effect on the Earth’s climate are not yet clear enough. Some possible mechanisms of the influence of cosmophysical factors on meteorological and climatic processes are discussed in Chaps. 10 and 11.

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Fig. 3.10 Variations in solar activity parameters over a period of about 30 years (1975–2007). A close correlation (http://en. wikipedia.org/wiki/Solar_ variation) is seen between sunspots, flare activity, radio flux at a wavelength of 10.7 cm and the total flux of solar radiation. The most important feature of SA cycles is the change in the magnetic polarity of the spots

Fig. 3.11 Dependence of the latitude of the appearance of sunspots on time (diagram of “butterflies” Maunder). Credit: NASA, Marshall Space Flight Center

The strongest magnetic fields are concentrated in the spots. Since the field is generated inside the Sun (deep below the photosphere) as a result of the dynamo mechanism, the lines of force of the emerging magnetic flux must begin and end in the photosphere. Therefore, spots appear either in pairs of opposite polarities, or one of the polarities may not be compact enough and is represented not by a spot, but by a flare area. The dipole moment of a group of sunspots is oriented predominantly in the latitudinal direction. It has a result that a spot of one polarity going in front in the direction of the Sun’s rotation is considered to be leading or head, and a spot (or torch) of opposite polarity is considered to be driven or tail. In the northern and southern hemispheres, the polarities of the head sunspots are opposite, so that the dipole moments of the groups are almost antiparallel. Long-term observations have shown that the global picture of the distribution of the magnetic field on the Sun changes quasi-periodically with an average period of about 22 years. In the second half of the complete “magnetic cycle” (or in the next 11-year sunspot cycle), the polarities of the head and tail sunspots in each hemisphere change. In each 11-year cycle, sunspots appear initially at latitudes of about ±30°, and then the sunspot-forming zone shifts to the equator. The diagram of the dependence of the latitude of the appearance of new spots on time has a characteristic form and is called the Maunder “butterfly” diagram (Fig. 3.11).

3.6

Forecast of Future Solar Cycles

39

During each 11-year cycle, all leading sunspots in the bipolar groups have some of the same polarity in the northern hemisphere and the opposite in the southern hemisphere. The same is true for tail sunspots, in which the polarity is always opposite to the polarity of the leading sunspot. In the next 11-year cycle, the polarity of the leading and tail sunspots is reversed. At the same time, the polarity of the general magnetic field of the Sun also changes, the poles of which are located near the poles of rotation (see Sect. 4.1). Therefore, it is more correct to speak not about the 11-year, but about the 22-year, “magnetic” cycle of solar activity (it is also called the “Hale cycle”). Moreover, in contrast to the traditional 11-year cycle of the number of sunspots, their 22-year periodicity can be called a “truly physical” cycle.

3.6

Forecast of Future Solar Cycles

Figure 3.11 shows prognostic estimates from the NASA archive for 2006, and shows a picture of the development of two neighboring SA cycles (1995–2015)—No. 23 (observations) and No. 24 (forecast). It can be seen that American experts predicted for the 24th cycle the maximum amplitude W of about 150 units, while at the maximum of the 23rd cycle the average observed value of the W number was about 120. But 3 years later, NASA experts significantly changed their forecast, and now their the curves for W look different: the height of the expected maximum of the 24th cycle will barely reach 90 units. Figure 3.11 shows both of these forecasts (the latest estimate is from October 2009). It is characteristic that in the new version of the forecast the maximum of the cycle from 2010–2011 shifted to about the beginning of 2014, and its end is likely to drag on until 2020 (Fig. 3.12). Judging by the data of numerous observations, solar cycle 23, indeed, differed in certain features. If we evaluate its development on the basis of the formal procedure of the method of moving monthly mean values of Wolf numbers W, then one would expect that a new cycle 24 should begin as early as January 1, 2009. However, according to a number of other parameters (radio emission flux at 10.7 cm, dipole, opening angle of the heliospheric current sheet, etc.) in 2009, either a decline or a prolonged “bottom of the minimum” was still observed. Nevertheless, the minimum of the 23rd cycle for sunspots was reached in December 2008, and since January 2009 the Sun “lives” already in the 24th cycle. The transition time was about 1.5 years. At the same time, although the minimum for sunspots was passed, the level of magnetic activity, for example, during 2009 was still falling, in part, possibly due to its characteristic delay in comparison with the number of sunspots or the flux of radio emission at a wavelength of 10.7 cm. Anomalies in the behavior of solar magnetic fields in the 23rd cycle make it more difficult to predict the height of the 24th cycle. Forecasters cannot come to any firm conclusion today. Discussion, held in June 2008 at NOAA Space Weather Prediction Center-SWPC (http://www.swpc.noaa.gov/SolarCycle?SC24/), showed that there are two alternative points of view: the cycle will be either high (140 units) or below average (90 units). The choice between these two possibilities has not yet

40

3

Solar Activity

S uns pot number P rediction made in 2006 by NAS A expert P res ent prediction

O ctober 2009

Fig. 3.12 Solar cycles 1995–2020 (2009, credit: David Hathaway/NASA/MSFC): No.23 (observations, broken curve) and 24 (forecast, smooth curve). The dotted line shows the confidence intervals (uncertainty limits) of the forecast

been made. The data on the polar field rather indicate a low cycle (the maximum value of the W number is about 80). On the other hand, according to the characteristics of the large-scale field and geomagnetic activity for the maximum of cycle 24 in IZMIRAN, moderate W values were obtained—128 and 113 units, respectively. According to various observational data on solar activity parameters, geomagnetic disturbances, variations in cosmic rays and other heliospheric phenomena, a lot of evidence has accumulated to date, indicating the beginning of an era of low solar activity cycles. A more serious failure of the 11-year cyclicity, such as the Maunder minimum (1645–1715), or at least such a decrease in the SA level, which was observed at the turn and at the very beginning of the twentieth century (Hale minimum), cannot be ruled out. In the context of the problem of solar-terrestrial relations, further study of these trends is extremely important, for example, to resolve the issue of the reality, causes and mechanisms of the so-called “global warming” of the climate. In particular, it is necessary to find out, at least, the sign of the main trend in the change in the average temperature on Earth in the coming decades: should we expect an increase in the rate of warming, its slowdown, or, on the contrary, should we prepare for a “global cooling”. . . It is important here to imagine that we are now experiencing a special period in the life of the Sun, a special era in the history of solar activity (Ishkov 2018). As for information about current situation, one can find them on special site https:// wwwbis.sidc.be/silso/datafiles. It contains all Wolf numbers in the new (“Belgian”) version (for details see below). There are daily, monthly, and annual, observed and

3.6

Forecast of Future Solar Cycles

41

smoothed data, in the forms of figures and plots. Note that current 25th cycle began in January 2020. According to the cyclical scenario of a reliable series of relative sunspot numbers, the 24th cycle opens the second epoch of decreased solar activity (SA). Cycles from the middle of the 9th to the 24th SA cycle, approximately 1849–2017, are considered reliable (Ishkov and Shibaev 2008). The main feature of this epoch (5 cycles) is the prohibition on the implementation of high solar cycles and the indispensable fulfillment of the basic observational rules in the development of individual cycles. By the end of the 23rd cycle, in particular, the background values of the total magnetic field of the Sun decreased by more than two times. This led to a complete restructuring of the physical conditions both on the Sun and in the inner heliosphere, which affected the state of the entire near-Earth space (NES). The past 24th solar cycle after 9.2 years of development has demonstrated that it was a cycle of low magnitude (W = 81.9), with a reduced flare activity (Ishkov 2018), with a lower geoeffectiveness of solar active phenomena, with a practical absence of the most powerful solar flare phenomena, as well as solar proton events (SPEs), especially GLEs, as well as manifestations of geomagnetic activity and ionospheric disturbances. Since July 1st 2015, the original Sunspot number data have been replaced by a new entirely revised data series (SILSO data/image, Royal Observatory of Belgium, Brussels) (for further details see, e.g., Veronig et al. (2021)).

Chapter 4

Structure and Dynamics of the Interplanetary Environment

Many theories have not survived their confrontation with observations. Margaret (Peggy) Shea and D.F. Smart, 2003

Chapter 3 summarized the current understanding of the global structure and basic properties of the heliosphere. Now it is necessary to consider in more detail its internal structure, the main physical factors, as well as the electrodynamic processes that determine the solar-terrestrial connections. One of the main factors of interplanetary space is undoubtedly the interplanetary magnetic field (IMF). The IMF owes its existence to the solar magnetic field, and its structure and dynamics, even in detail, are determined by the behavior of the solar wind.

4.1

Corona Expansion and Solar Wind

Remote observations from the Earth and numerous direct measurements on spacecraft and satellites over many decades have convincingly shown that interplanetary space is constantly filled with plasma moving from the Sun. Plasma streams directed from the Sun and magnetic fields in them were detected indirectly much earlier from observations of geomagnetic disturbances caused by them, deviations of comet tails and variations of cosmic rays. These streams exist always and everywhere around the Sun at sufficiently large distances, exceeding several solar radii outside the outer corona. They acquire an almost radial direction there. It is pertinent to emphasize that their speed is several times higher than the speed of sound and the Alfvén speed, so that the solar wind is supersonic in nature. This character of the flow is almost always preserved up to very large distances of ~100 AU (i.e., almost to the border of the heliosphere). The solar wind is formed in the solar atmosphere because there is no complete thermodynamic and mechanical equilibrium. According to modern concepts, the excess free energy of self-consistent plasma and electrodynamic transport processes in the Sun’s atmosphere is supported by energy flows from its interior.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 L. Miroshnichenko, Solar-Terrestrial Relations, https://doi.org/10.1007/978-3-031-22548-2_4

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4 Structure and Dynamics of the Interplanetary Environment

Free energy manifests itself, in particular, in the heating of the solar atmosphere up to coronal temperatures ≥106 K (see Sect. 3.1). Solar wind streams arise in the Sun’s atmosphere along with its heating. This is a single and complex dissipative process, which is based on the transformation of some types of free energy (thermal, electromagnetic and gravitational) into other types. On the other hand, it can be argued that the processes of formation of a regular flow of the solar wind are of a gradual, evolutionary in their nature. They are reduced, ultimately, to the transformation of the energy of powerful ordered and disordered movements and electromagnetic fields into the energy of a directed radial flow. The energy density of directed plasma motion in the formed solar wind is one to two orders of magnitude higher than the density of other types of energy, except for visible light. Optical radiation from the Sun is a much more powerful flow of energy, but it is weakly “adhered” to the plasma due to its extreme rarefaction and almost complete transparency in the upper atmosphere of the Sun and the heliosphere. The emission of the solar wind remains an important factor in the evolution of the solar system as a whole. The energy carried away into interplanetary space by solar wind particles is ~1027–1029 erg/s. This can be comparable to the power of a large flare, but 4–6 orders of magnitude less than the energy of the solar electromagnetic radiation ~4 × 1033 erg/s. During the year, the Sun loses ~2 × 10-14 of its mass with the solar wind. Similar phenomena—astrospheres and stellar winds—have been found in many other astrophysical objects.

4.2

The Global Magnetic Field of the Sun

In Sect. 2.5, we have already briefly described the properties of a vast region around the Sun occupied by the solar wind and magnetic fields up to contact with the local interstellar medium. This region received its name—the heliosphere—in the 50s of the last century, primarily in connection with studies of modulation of galactic cosmic rays. Two decades later, with the help of spacecraft, it was possible to establish that the heliosphere is actually the heliomagnetosphere (or the Sun’s magnetosphere). This discovery became possible only when the Pioneer 11 spacecraft on its way to Saturn, under the influence of Jupiter’s gravitational field, deviated from the ecliptic plane and in February 1976 reached the northern heliolatitude of 16° (Fig. 4.1). The magnetic fields observed in the solar photosphere are usually divided into two types, in accordance with their scale. A large-scale (general or global) magnetic field with characteristic dimensions comparable to the dimensions of the Sun has an average intensity at the level of the photosphere of the order of several gauss. At the minimum of the solar activity cycle, it has an approximately dipole structure, while its intensity at the poles of the Sun is maximum. Then, as the maximum of the cycle approaches, the field strengths at the poles gradually decrease and in 1–2 years after the maximum of the cycle they become equal to zero, i.e., the so-called “polarity

4.3

Interplanetary Magnetic Field

45

Fig. 4.1 Left: Diagram of the three-dimensional structure of the heliomagnetosphere (the solar global magnetic field, or SGMF) with a neutral current sheet near the equator (shaded). The tilt of the solar magnetic dipole M relative to the solar rotation axis Ω and the origin of open IMF lines of force at high heliolatitudes are also shown (Smith et al., 1978). Right: “Wavy” structure of the heliospheric current sheet near the Earth’s orbit (http://wso.stanford.edu/gifs/helio.gif)

reversal” of the solar magnetic field occurs. At this phase, the solar global magnetic field (SGMF) of the Sun does not completely disappear, but its structure is no longer dipole, but quadrupole. Further, the strength of the solar dipole increases again, but at the same time it has a different polarity. Thus, the full cycle of change in the SGMF, taking into account the change in sign, is equal to twice the duration of the 11-year cycle of solar activity—approximately 22 years (“Hale’s law”). Along the plane of the Sun’s magnetic equator, oppositely directed open field lines are parallel to each other and separated by a thin current sheet known as the interplanetary current sheet or heliospheric current sheet (HCS, see Fig. 4.1 on the left). The current sheet has a certain tilt, due to the difference between the tilt of the Sun’s rotation axis and its magnetic axis. It is also curved (due to the quadrupole moment of the solar magnetic field), and, therefore, has a wavy structure (like a “ballerina’s skirt”) as it stretches into interplanetary space (Fig. 4.2 on the right). Since the Earth is located sometimes above and sometimes below the rotating current sheet, this leads to regular, periodic changes in the IMF polarity (when measured near the Earth’s orbit). These periods of alternating positive (from the Sun) and negative (toward the Sun) polarity are known as the magnetic sectors (“sector structure”) of the IMF (see below Sect. 4.4). Such a structure plays very important role in solar-terrestrial relations. In particular, this structure seems to affect the Earth’s rotations (see Sect. 11.5).

4.3

Interplanetary Magnetic Field

The interplanetary magnetic field (IMF) is part of the solar magnetic field, which is carried into interplanetary space by the solar wind. On the other hand, the solar wind is an almost perfectly conducting fluid (plasma) moving in a magnetic field. When

46

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Structure and Dynamics of the Interplanetary Environment

Fig. 4.2 Formation of a spiral structure of lines of force of interplanetary magnetic field (IMF) during the rotation of the Sun (Image credit: NASA)

the plasma moves relative to a magnetic field or a magnetic field relative to the plasma, an EMF of induction should appear in the latter. This EMF would cause an infinitely large current in an ideally conducting plasma, which is impossible. This limitation leads to the fact that the magnetic field cannot move relative to the plasma; therefore, it must move with the plasma as if it were “glued” or “frozen in.” If the liquid (plasma) expands, then the induction of the “frozen in” magnetic field decreases. If the liquid is compressed, then the magnetic field is enhanced. In other words, the IMF lines of force are “frozen” into the solar wind plasma, the magnetic field unites the plasma into a continuous medium in a collisionless region (r ≥ 10RS). Due to the rotation of the Sun, solar wind particles leaving the corona at successive times t0, t1, t2, t3, etc., are “glued” to the same magnetic field line (Fig. 4.2, top). As a result, the permafrost is pulled outward in the form of Archimedean spirals, which are often compared to water jets from a rotating sprinkler on a lawn (Fig. 4.2). The interplanetary magnetic field originates in areas on the Sun where the magnetic field is not closed, i.e., where lines of force emerging from one area do not return to a conjugate point, but stretch virtually to infinity into space. The direction (polarity, sign) of the field in the northern hemisphere of the Sun is opposite to the direction of the field in the southern hemisphere. The polarities of this SGMF

4.3

Interplanetary Magnetic Field

47

of the Sun change their sign to the opposite in each solar cycle. The interplanetary magnetic field is weak, its value near the Earth’s orbit varies from 1 to 37 nT, with an average value of ~5–6 nT. Note that the heliospheric current sheet is a threedimensional spiral that appears under the influence of the rotation of the global magnetic field of the Sun. Instead of the term “IMF”, its synonym “heliospheric magnetic field” has been widely used in recent years. This field is created mainly by electric currents in the heliosphere itself, and not only on the Sun. The electrical conductivity of the plasma is high; therefore, electric currents are easily excited everywhere on the Sun and in the heliosphere. The reasons for the excitation of currents are the induction mechanism in a moving plasma with its variable velocities, as well as the partial separation of charges in it while maintaining quasineutrality in general in large volumes. To describe the IMF as a whole and its specific structural and physical features, various methods and reference systems are used. In a heliocentric frame of reference that does not rotate with the Sun, the magnetic field outside a certain initial sphere of radius r0 can be described by simple formulas: Br = B0

r0 r

2

, Bθ = 0, Bϕ = - Br

Ωr sin θ: u

ð4:1Þ

where r, φ, θ are spherical coordinates, u is the solar wind speed, B0 is the value of the radial component of the magnetic field Br on some initial sphere of radius r = r0, and the value Ω = 2.7 × 10-6 radian/s is the angular speed of rotation of the Sun. In the plane of the helioequator, the radial component Br is inversely proportional to the square of the distance to the Sun, and the azimuthal (heliolongitudinal) component Bφ is inversely proportional to the first power of r. In the simplest axially symmetric case В0(θ) = В0sgn(θ-π/2) is taken, so that in the plane of the helioequator the heliolatitude component В0(θ) = 0 by definition. If the average field in the photosphere (i.e. on the “surface” of the Sun, at r0 = 7 × 1010 cm) is taken equal to ~2 G, then at the Earth’s orbit (r = 1 AU) we obtain B ≈ 5 × 10–5 G, which is in good agreement with the observed value. Such a model describes only in the most general terms a certain highly averaged IMF pattern in years of low solar activity. In a stationary coordinate system near the solar equator, the magnetic field lines (4.1) have the form of Archimedes spirals, twisted against the rotation of the Sun: r = r0 -

u ðϕ - ϕ0 Þ: Ω

ð4:2Þ

As noted above (Fig. 4.2), they are lines formed by macroscopic plasma elements emitted at successive times from a specific location on the surface of the Sun. Due to the “frozen-in” field, these plasma elements are connected by a single line of force. In the plane of the helioequator (θ = π/2), the spiral is flat; for other values of the latitudinal angle θ, the spiral turns are located on the surface of the cone θ = const. Due to the decrease in the component Bφ the magnetic field at high heliolatitudes

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4 Structure and Dynamics of the Interplanetary Environment

(θ → 0, π) becomes more and more radial. The angle Ψ between the radius and line of force is given by the formula Ψ = arctgfðrΩ=uÞsinθg

ð4:3Þ

At u = 400 km/s and sinθ = 1, we obtain Ψ = 45° near the Earth’s orbit, which also agrees with observations. In the Cartesian coordinate system, the interplanetary magnetic field can be represented in vector form B with three components in directions: В = B Bx , By , Bz :

ð4:4Þ

Two of them (Bx and By) are oriented parallel to the ecliptic, and the third one, Bz, is perpendicular to the ecliptic, and it is created by waves and other disturbances in the solar wind. When the IMF and geomagnetic field lines are opposite to each other, they can “reconnect”. This leads to the transfer of energy, mass and momentum from the solar wind into the magnetosphere. The strongest relationship between the IMF and the geomagnetic field and, accordingly, the most dramatic magnetospheric effects occur when the Bz component is directed south of the ecliptic (see Sect. 10.2). The spiral pattern of corpuscular flows from the rotating Sun like a jet of water from a rotating hose (Fig. 4.2) was indicated by S. Chapman (1929) and then described in his classic book “Geomagnetism”, written in collaboration with J. Bartels (1940). Subsequently, E. Parker (1958) theoretically substantiated the general character of the quasi-stationary IMF in the form of Archimedes spirals. The model of the solar wind with a spiral IMF was developed by Parker (1958, 1963) for the region near the plane of the ecliptic on the basis of a kinematic analysis of the equations of electrodynamics using the “frozen-in” approximation. In fact, the picture of the heliomagnetospheric field turned out to be much more complex than predicted by Parker’s theory. Further important steps in the development of the theory of the interplanetary magnetic field, were associated with the development of more realistic models of the three-dimensional structure of the heliospheric magnetic field. They were made by other researchers, and the main achievement was the awareness of the role of the heliospheric current sheet, its shape and location in space. The sector structure and especially dynamics of IMF over the Sun’s poles are of particular interest.

4.4

Sector Structure of Interplanetary Magnetic Field

As already mentioned many times, the interplanetary circumsolar space is filled with particles of the solar wind and the interplanetary magnetic field (IMF). The IMF is associated with the Sun and rotates with it, so that in interplanetary space a certain sector magnetic structure is formed (Fig. 4.1), which rotates at the speed of the Sun’s

4.4

Sector Structure of Interplanetary Magnetic Field

49

Fig. 4.3 The distribution of the velosity and density of the solar wind inside the IMF sector. Zero day is the day the Earth crosses the sector boundary (Dubov 1982)

rotation—one revolution in 27 days (when observed from Earth). The passage of the sector boundary past the Earth is recorded as the changes in the IMF sign and density and velocity of the solar wind (Fig. 4.3). The lines of force of the solar magnetic field are carried away from the Sun by the expanding solar wind (Fig. 4.2). This interplanetary magnetic field (IMF) is characterized by large-scale ordering (Illustrated Glossary. . . 1977). Observations carried out near the equatorial plane of the Sun show that the magnetic field consists of several (usually four) sectors or regions. The magnetic field in the sectors is directed mainly towards the Sun or away from the Sun along the Archimedean (Parker) spiral, which, in turn, is formed as a result of the rotation of the Sun. The sectoral boundary separating the fields of opposite polarity is usually very thin and sweeps past the observer (past the Earth) in a time of the order of minutes. The time corresponding to the width of a typical sector is about a week. Indirect evidence leads to the concept of the Heliomagnetic Neutral Sheet (HNS) (Fig. 4.1, left). The layer separates the regions in which the plasma moves from two different hemispheres of the Sun, usually with oppositely directed magnetic fields. Two plasma regions (northern and southern) are separated on the Sun by a wide equatorial belt of closed magnetic lines of force, from which the solar wind either escapes in very small quantities, or does not expire at all. Each time the observer (Earth) crosses the neutral layer, he marks the passage through the sector boundary. Large-scale azimuthal ordering of the photospheric magnetic field is the reason for the corrugation of the equatorial heliomagnetic neutral sheet (HNS) in interplanetary space. The layer deviates alternately north and south of the equator (corrugated current sheet). Thus, an observer who is near the solar equatorial plane, during the solar rotation, detects plasma alternately from one side of the neutral layer, then the other. As a consequence, a sector structure with a changing magnetic field polarity is observed. Shortly after the maximum of the solar cycle, when polar magnetic fields are weakened, the heliomagnetic current sheet can be highly

50

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Structure and Dynamics of the Interplanetary Environment

corrugated and irregular in shape. But during most of the solar cycle, the neutral layer is well pronounced and the corrugation that obscures the photospheric sector structure is small. When the Earth, in its orbit, reaches its maximum deviation from the solar equatorial plane (slightly more than 7°), then the magnetic polarity of the nearest polar field prevails. This phenomenon is known as the predominant polarity effect, or the Rosenberg-Coleman effect. Near the minimum of the solar cycle, when the strengths of the polar magnetic fields are high, the corrugation can be so small that a unipolar interplanetary magnetic field can be observed on Earth for several months. The three-dimensional structure of the heliomagnetic neutral layer is shown in Fig. 4.1.

4.5

Modern Model of the Polar Magnetic Field

Currently, the most developed model of the magnetic field for the polar regions of the Sun is L. Fisk’s model (Fig. 4.4). Observations show that slow solar winds are formed in large coronal loops. Fast solar wind streams begin in coronal holes. An

Fig. 4.4 An illustration of the movements of open lines of force of the solar magnetic field in the polar regions of the solar corona (Fisk et al. 1999). The drawing is made in a frame of reference rotating at the speed of rotation of the equatorial regions of the Sun. The M-axis is the axis of symmetry as the magnetic field expands from the polar hole. The Ω axis is the axis of rotation of the Sun. The green lines are open lines of force, and p is the line of force associated with the heliographic pole. The red lines are the trajectories of the lines of force, the movement of which is set by the differential rotation of the photosphere

4.5

Modern Model of the Polar Magnetic Field

51

obvious question arises: how is the magnetic flux distributed with open lines of force (open magnetic flux) outside the coronal holes? The sun rotates differentially, but coronal hole regions show no sign of such rotation. Hence it follows that if coronal holes are not asymmetric with respect to the axis of rotation of the Sun, then the open magnetic flux presumably must cross the boundaries of coronal holes. The solution to this dilemma is possible on the assumption that the open field lines on the Sun reconnect so often that the open magnetic flux turns out to be “uncoupled” from the differential rotation of the photosphere. Due to the known properties of the global distribution of coronal loops, the open magnetic flux is concentrated in coronal holes. At the same time, it does not remain static, but moves all the time under the joint action of differential rotation and diffusion of the magnetic field caused by the reconnection of the magnetic loops. As a result, the bases of open field lines are continuously moving inward and outward from coronal holes, while they are concentrated inside coronal holes due to the predominance of small loops in these regions. The described concept is presented in detail in schematic Fig. 4.3, which shows an idealized polar coronal hole, an open magnetic flux emanating from it, and the motion of the bases of field lines from the region of the coronal hole to the region of large coronal loops. The figure is built in a frame of reference that rotates at the same speed as the equatorial region of the Sun. The open lines of force from the polar coronal hole in Fig. 4.3 make large-scale motions: they travel from coronal-hole regions to large coronal-loop regions on one side of the Sun, and then move back into coronal-hole regions on the opposite side of the Sun. Such dynamics of the magnetic field in the polar regions is of interest not only for studying the physics of the Sun, but also turns out to be important, for example, for the interpretation of some effects of modulation of galactic cosmic rays in the heliosphere. As measurements on the Ulysses space probe have shown, during the epochs of SA minima from regions of large heliolatitudes, the solar wind blows at a speed twice as high (750–800 km/s) than from the region of the helioequator. Because of the interaction of fast SW fluxes from coronal holes with slow SW from the helioequator regions, so-called co-rotating interaction regions (CIRs) arise, which lead to the appearance of recurrent changes in the GCR flux. At the SA maximum, most coronal holes disappear, and coronal regions with closed magnetic field lines prevent the free outflow of solar matter. During such periods, a more symmetric solar wind blows with an average speed of about 400 km/s. Other features of the large-scale dynamics and structure of the heliosphere in space and time are also observed. Thus, analysis of the data shows that at the maximum of solar activity, coronal mass ejections (CMEs) with a frozen-in magnetic field appear, which create the so-called merged interacting regions (MIR). These regions then merge and create global merged interacting regions (GMIR). These formations (MIR and GMIR) can be considered as global phenomena that disrupt the stable structure of the outer heliosphere. With increasing distance from the Sun, the braking effect of the interstellar medium on the solar wind speed increases. For example, in 2002, the Voyager 2 probe, which was located at a distance of about 65 AU, recorded the solar wind

52

4 Structure and Dynamics of the Interplanetary Environment

velocity approximately 60 km/s lower than in the inner heliosphere. Finally, on December 16, 2004, the Voyager 1 spacecraft at a distance of 94 AU and at latitude 350°N crossed the terminal (boundary) shock wave (TSW) and entered the “heliosheath” (see Fig. 2.4). Direct observations on board the Voyager 1 spacecraft showed a decrease in solar wind velocity, an increase in temperature and density during interaction with the interstellar medium, and a strong increase in the intensity of low-energy ions in the TUV region. The magnetic field increased approximately 3–4 times, there was also an increase in field fluctuations due to its compression in the shock wave region, and this was decisive evidence of the passage of the Voyager 1 spacecraft through the terminal shock wave.

4.6

Fluctuations of the Interplanetary Magnetic Field

Perturbations are superimposed on the averaged topology of the zero-order IMF (4.4)—inhomogeneities of the IMF of various scales. Usually IMF is represented as the sum of the regular and random components: B = B0 + δB, where = B0; = 0; ǀδB/Bǀ 105 s ≈ 1 day) should be considered as a given regular field that does not

4.6

Fluctuations of the Interplanetary Magnetic Field

53

change during the observation time of this increase in the SCR flux at Earth. For the processes, the time of which is longer than the period of the Sun’s revolution, the interval τ can be chosen equal to 27 days. This approach is applicable, in particular, to the analysis of 11-year GCR modulation. Then, a regular field can be understood as a large-scale and, accordingly, a low-frequency part of the total field, and a random field—its small-scale fluctuations. The values of the scale L0 or the characteristic period T0, distinguishing the regular and random fields, can be different in different problems. On the other hand, as we will see in Chap. 11, large-scale IMF formations (background fluctuations) are very important for generating geomagnetic disturbances such as magnetic storms. It is convenient to consider fluctuations of density, velocity, and magnetic field in the solar wind within the framework of the theory of turbulence. It has been established by direct and indirect measurements that in the interplanetary medium there is a wide range of magnetic inhomogeneities, typical of developed turbulence. The spectrum has a continuous distribution over scales (frequencies or wavelengths). The observed spectrum (spectral density, or power spectrum) of IMF fluctuations can be represented as: PðkÞ = dh2 =dk = A=ðk0 þ kÞq = A=ðf þ f 0 Þq

ð4:5Þ

where h is a random field, k is a wave vector, f is a frequency of fluctuations; the quantities k0 and f0 correspond to the so-called basic turbulence scale L0. Its meaning, in addition to what was said above, is that within the region L0 the values of the field components are noticeably correlated, i.e. are not independent. The quantity A is a normalization constant depending on the level of turbulence, and the exponent q determines the slope (shape) of the spectrum at different wavelengths. So, if k « k0, then the spectrum (4.5) becomes flat, and for k » k0 they satisfy the power law k-q. Thus, formula (4.5) has a simple physical meaning: it approximately describes the energy density distribution between IMF fluctuations of various scales (see Fig. 4.5). Relation (4.5) was obtained by synthesizing a large number of observations near the Earth’s orbit. Naturally, it does not reflect all the details of the spectrum and its dynamics. In particular, the spectrum index q can vary significantly depending on the frequency interval under consideration, the level of turbulence, the phase of the solar cycle, and the type of inhomogeneities. For example, Fig. 4.5 shows the power spectrum of fluctuations for the total IMF vector. The spectrum was constructed according to the 1998 measurements on board the ACE (Advanced Composition Explorer) spacecraft at the Lagrange point L1 at a distance of 1.5 million kilometers from the Earth towards the Sun. Figure 4.6 shows the power spectra for three IMF components in a reference frame with the minimum variance, i.e., in a reference frame in which one of the axes is elongated along the direction of the field with the smallest fluctuations. This method of analysis provides information on the spatial distribution of fluctuations

Fig. 4.5 Power spectrum of fluctuations of the total IMF vector as measured in 1998 aboard the ACE spacecraft. One can clearly see a significant change in the slope of the spectrum (q = 1.6–3.0) in the region of high fluctuation frequencies (i.e., small sizes of inhomogeneities), with a break near the proton cyclotron frequency νpc

4

Structure and Dynamics of the Interplanetary Environment

103 Power Spectral Density [nT2/Hz]

54

ACE/MAG 1998/084 0800-1100 UT

102 f−1.60±0.02

101 100 10−1

f−2.98±0.02

10−2 10

VPc

−3

10−4 10−3

10−2

10−1

100

101

Spacecraft-Frame Frequency [Hz]

Fig. 4.6 Power spectra of fluctuations for various IMF components in a minimum variance reference frame (from Bruno and Carbone 2005). The graphs are based on measurements on the Helios 2 spacecraft in 1976 in the distance range of 0.3–1.0 AU

of a given vector. The component with the lowest variance is shown in Fig. 4.6 by the black (bottom) curve, the blue (top) curve is the component with the highest variance, and the red (middle) curve is the component with the intermediate variance. It is easy to see that the maximum and intermediate components are much more powerful than the component with the minimum variance. Thus, most of the fluctuation power is associated with the quasi-transverse IMF components. In general, this anisotropy characterizes Alfvén-type turbulence inherent in highspeed solar wind streams. The use of a well-developed theory of hydrodynamics to describe and understand the properties of “magnetized” solar wind plasma has a long history. Back in 1941 a Soviet academician A.N. Kolmogorov predicted that the spectrum of hydrodynamic turbulence should have the form of a power law with an exponent q = -5/3. Such a spectrum is formed due to a peculiar process of energy conservation in the system

4.6

Fluctuations of the Interplanetary Magnetic Field

55

through its cascade transfer from large to small scales. This state lasts until dissipative mechanisms arise, that remove energy from the system. This, apparently, turned out to be true for the spectrum of IMF fluctuations with frequencies in the range from 10-4 to ~0.5 Hz, which is called the inertial region. Many years of testing have confirmed that the spectrum of IMF fluctuations inevitably softens near the proton cyclotron frequency νpc. This break in the spectrum means the onset of dissipation mechanisms, and the region of higher frequencies is precisely called the dissipation region. This remarkable feature was observed in all IMF measurements on spacecraft—from Helios to Voyager. The kink is usually considered to be evidence of cyclotron deceleration of Alfvén waves, although a complete understanding of the dissipation processes has not yet been achieved.

Chapter 5

Anomalous Component of Cosmic Rays

All things are difficult before they are easy/are done. English proverb

The anomalous component of cosmic rays (ACR) in the heliosphere (Fig. 5.1) was discovered in the early 1970s from spacecraft measurements. The ACR contains light hydrogen ions 1H, as well as heavier ions 4He, C, N, O, Ne, Ar and, possibly, S, Si, and Fe with energies up to ~50 MeV/nucleon, which are found in interplanetary space and in the Earth’s magnetosphere. The chemical composition of this component differs from the solar and galactic content of elements, for example, sometimes there is a certain excess in the content of carbon C in relation to oxygen O.

5.1

Discovery and Origin of ACR

Figure 5.1 shows typical energy spectra of oxygen nuclei as measured by various detectors on board the ACE spacecraft (see, e.g., review by Klecker 2008 and references therein). Other ions tend to have similar spectra. The bold curves correspond to particle fluxes for a “stable” state of the interplanetary medium; light dotted line refers to transient (transient) components; the bold dotted line denotes the postulated “calm” background of suprathermal solar particles. Due to the rotation of the Sun around the galactic center, the interstellar environment at the border of the heliosphere changes. This leads to changes in the structure and expansion of the heliosphere, as well as in the intensity of CR and neutral gas fluxes. On the other hand, in the local interstellar medium (LISM), the inflow of the neutral component of the interstellar gas into the heliosphere occurs almost unhindered and, in the case of sufficiently large flows, can change the chemistry of planetary atmospheres. As known, the interplanetary space probes Voyager 1 (hereinafter V1) and Voyager 2 (hereinafter V2), launched in 1977, played a special role in the study of the ACR. Both probes are already had long gone beyond the Solar System. Thus, the first of these spacecraft crossed the border of the heliosphere in December 2004, the second—in August 2007. This happened, respectively, at distances of about 94 AU © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 L. Miroshnichenko, Solar-Terrestrial Relations, https://doi.org/10.1007/978-3-031-22548-2_5

57

58

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Anomalous Component of Cosmic Rays

Fig. 5.1 Typical energy spectra of oxygen ions representing different populations of particles in the heliosphere (adapted from the review by Klecker 2008)

and 84 AU from the Sun, respectively. Since then, both vehicles appear to be moving in the interstellar dust cloud (LISM) in which the solar system is submerged (the so-called “Local Bubble”).

5.2

The Original Acceleration Paradigm

According to many direct observations, ACR began to appear (be detected) about 40 years ago (for further details see, e.g., recent review by Panasyuk and Miroshichenko 2022). Over the years, a paradigm has been developed to explain their origins. They were supposed to begin life as interstellar neutral atoms drifting into the heliosphere. Then these atoms become singly ionized. This happens either through a charge exchange with the ions of the solar wind, or through photoionization. Further, the formed ions are “picked up” by the expanding solar wind and then

5.3

Modern Models

59

are accelerated to the observed energies by the DSA (Diffusive Shock Acceleration) mechanism (for more details see below, Sect. 8.3) on the terminal shock wave (SW) of the solar wind (it is also called the boundary shock wave); hereinafter, for brevity, we will refer to it simply as TW. This first paradigm of ACR particle acceleration gained wide acceptance and withstood tests during further observations until December 16, 2004, when V1 crossed the terminal wave (TW) and did not find the ACR source. In August 2007, V2 crossed the TW at a different location, but also failed to find the location of the ACR source. It became clear that the location of the ACR source had nothing to do with TW, which was crossed by both spacecraft. Alternative models were proposed, in which the acceleration in other places of TW and/or other accelerating processes in heliosheath was assumed.

5.3

Modern Models

According to further observations, the fluxes of the ACR in the range of medium and higher energies on board V2 as in 2013 exceeded the fluxes measured on board V1, but the spectra of V2 were more strongly modulated. This fact testifies in favor of theoretical models in which the ACR source is located along the flank or tail of the TW, since V2 is located farther from the “nose” of the heliosphere than V1 (see Fig. 5.2). The fact that the ACR energy spectra at V2 appear to be more modulated than at V1 may be due to the difference in the rigidity dependence of the diffusion coefficient between V2 (source in the south) and V1 (source in the north). Although the observations are in qualitative agreement with the ACR source along the flank or tail of the TW, other models are now being considered. They include acceleration in “hot spots” of turbulent TW, acceleration at the heliopause due to magnetic Fig. 5.2 Asymmetry of the heliomagnetosphere and generation of ACR (McComas and Schwadron 2006)

60

5 Anomalous Component of Cosmic Rays

reconnection, and also acceleration by the mechanism of magnetic pumping, which takes place mainly near the heliopause. Obviously, new observations are needed to clarify the nature and position of ACR sources.

5.4

Account for the Geometry of the Heliosphere

The difference in the distances where the above spacecraft crossed the boundary of the heliosphere indicates an asymmetry in its structure (Fig. 5.2). Asymmetry, in turn, is due to the movement of the Sun in interstellar space. Indeed, our Sun (together with the entire solar system) moves relative to the nearest stars at a speed of ~20 km/s. The movement takes place in interstellar gas. In this case, neutral interstellar atoms (interstellar wind) penetrate into the solar system and ultimately serve as a source of ACR. According to modern concepts, their generation occurs as a result of the processes of recharging of penetrating atoms with particles of the solar wind and acceleration by a terminal shock wave at the boundary of the heliosphere. In addition, it was found that ACR ions, penetrating into the Earth’s magnetosphere, create a belt of trapped particles, the formation mechanism of which is different from the traditional one. The theory of ACR acceleration, proposed in one of the early works (Fisk et al. 1974), asserts that ionized (neutral in the past) particles can indeed be accelerated from ~4 keV/nucleon to >10 MeV/nucleon just at the heliopause (at the terminal shock wave) if they are “picked up” by the solar wind. Another approach (alternative or complementary) is reduced to the assumption that the source of the ACR is the ionospheric plasma of “magnetic” planets, enriched with O+ ions. In addition, it is pertinent to recall (see Sect. 5.3) that interstellar matter is actually present inside the Earth’s magnetosphere (in the form of trapped Anomalous Cosmic Rays). In this case, the ERB, consisting of ACR particles, is located at a distance slightly more than 2RE (terrestrial radii) in the equatorial plane. GCR particles with energies E > 70 MeV (protons) showed that the terminal wave (TW) has been already passed several years ago, and both spacecraft (V1 and V2) have already been introduced into Local Inter-Stellar Medium—LISM. It should be noted that there are currently two more long-lived space probes in space—Pioneer 10 and Pioneer 11, launched back in the 1970s, but with different targets and in the “opposite” direction (compared to V1 and V2) . . . The last contact with Pioneer 10 took place on January 22–23, 2003. At this time, the spacecraft was at a distance of 82.19 AU from the Sun and moved away from it with a relative speed of 12.224 km/s. The further fate of Pioneer 10 is unknown, but it is assumed that it continues its flight and eventually leaves the solar system, heading towards the star Aldebaran. The last signal from Pioneer 11 was received on September 30, 1995. After that, the direction of its antenna to Earth was lost, and the device cannot maneuver to return it. It is not known whether Pioneer 11 continues to transmit signals, and no further tracking is planned. It is assumed that Pioneer 11 is heading

5.5

Interplanetary Acceleration

61

towards the constellation Eagle and will pass near one of its constituent stars, after about 4 million years.

5.5

Interplanetary Acceleration

In connection with the analysis of possible sources of ACR, it seems appropriate to consider the possibility of accelerating charged particles in the interplanetary medium itself. This is especially interesting during the passage of structures such as corotating regions of interaction (CIR) of two solar wind streams of different velocities. Such structures are regularly present in the interplanetary space. The data in Fig. 5.3 refer to the SEP event on March 22, 2000. On this day, a co-rotating region enriched with solar particles 4He, C, O, and Fe (e.g., Mason et al. 2008). The tendency towards the enrichment of the flux of accelerated particles with heavy ions (right panel) is clearly visible when considering the spectra in total energy. It would be very interesting to check on these data the acceleration model proposed by Fisk and Lee (1980) just for the conditions of interplanetary space, when co-rotating interacting regions (CIR) are present in the IMF. Note that in the interplanetary medium, by analogy with solar flares, there is a magnetic reconnection of oppositely directed magnetic fields. In this case, a combination of two mechanisms can work—DSA (see Chap. 8) and direct acceleration of particles by electric fields arising in the process of magnetic reconnection (e.g., Zank et al. 2015; Adhikari et al. 2019).

Fig. 5.3 Spectra of 4He, C, O, and Fe ions obtained by the ULEIS and SIS detectors aboard the ACE spacecraft during observations of the co-rotating region on March 22, 2000 (e.g., Mason et al. 2008 and review by Klecker 2008)

Chapter 6

Transport of Particles in the Heliosphere

Among the continuum of wacky theories, there are sure to be some whose predictions coincide with experiment. Niels Bor

To date, it is well established that the heliosphere is filled with charged particles of various origins (solar wind and solar cosmic rays, GCR, anomalous component of cosmic rays, etc.). In general, they occupy a huge range of energies (about 20 orders of magnitude). In particular, solar cosmic rays (SCR) occupy the range of kinetic energies from Еk ≥ 1 MeV to Еk ≥ 10 GeV, possibly up to ~100 GeV (for protons). Below we will present the basic information on the transfer of particles, mainly using the example of SCR. The same transport laws are valid for GCRs, for their anomalous components, for particles of a different origin in interplanetary space, but taking into account other temporal and spatial scales. If particles move in coronal, interplanetary and geomagnetic fields without interacting with each other, then their transfer can be considered within the framework of a simple trajectory approach. Such an approach is possible in the case when the particle energy density is significantly lower than the magnetic energy density, i.e., when the condition. mр np v2 =2 < < B2 =8π

ð6:1Þ

where mр, np and v are the mass, concentration and velocity of the proton, respectively, and B is the magnetic field strength. In the opposite case, it is necessary to take into account the collective interaction of the ensemble of particles with the surrounding magnetic field (self-consistent approach). As for the SCR itself, the kinetic energy Еk ~ 1 MeV/nucleon for most flares can be conventionally taken as the lower limit of their spectrum. However, we will not limit our consideration to the dominant SCR component (i.e., protons with energy Ep ≥ 1 MeV): the initial stage of particle acceleration from thermal velocities (see Chap. 6) is of fundamental interest, and the most acute problems of the formation of the SCR spectrum are just in the energy range Еk ≤ 1 MeV/nucleon. The transfer of energetic particles in the heliosphere implies various types of their motions and interactions: movement in © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 L. Miroshnichenko, Solar-Terrestrial Relations, https://doi.org/10.1007/978-3-031-22548-2_6

63

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Transport of Particles in the Heliosphere

large-scale magnetic structures, scattering by inhomogeneities of the interplanetary magnetic field, various kinds of drifts, wave-particle interactions, generation of disturbances in interplanetary plasma, etc. In addition, a particle may experience acceleration or deceleration, i.e. change your energy. In fact, we are talking about changes in the distribution function of particles f(r, p, t) in the process of transfer, while both the spatial coordinates (vector r) and the components of the particle velocity (its momentum p) can change.

6.1

Energetic Particles in the Heliosphere

Figure 6.1 shows the modern summary picture of corpuscular radiation in the heliosphere in the Earth’s orbit—from thermal ions and electrons of the solar wind to relativistic GCR particles. As can be seen from the left panel of Fig. 6.1, below ~10 MeV, the proton flux in interplanetary space can actually be a mixture of particles accelerated in flares, on shock waves, and in the Earth’s magnetosphere; above 10 MeV, apparently, flare protons predominate. The center shows similar observational data for electrons (for comparison, a typical spectrum of accelerated flare protons is also shown). Noteworthy is the sharp difference in the intensities of accelerated flare protons and electrons at the same energies, starting from Еk ~ 105 eV. This difference concerns one of the fundamental problems of the physics of flares and particle acceleration on the Sun, namely, the possible role of nonthermal protons as the main carrier of energy in the solar atmosphere at the preflare stage.

Fig. 6.1 Energy spectra of protons and some other ions (left panel) and electrons (middle panel) of various origins from observations in the Earth’s orbit (Lin 1980). For comparison, the right and middle panels, respectively, also show the typical spectra of accelerated flare protons and electrons. The right panel shows typical spectra of oxygen nuclei from different sources as measured by various instruments on board the ACE spacecraft (Garrard et al. 1997)

6.2

Basic Concepts of Transport Theory

65

Anomalous cosmic rays were first detected in the early 1970s in spacecraft measurements. Instead of the expected decrease in the flux of particles with energies below 100 MeV/nucleon, it turned out that an increase in their intensity is observed in the spectra of some nuclei. Subsequently, it was found that this effect takes place for nuclei H, He, C, N, O, Ne, Ar and, possibly, also for nuclei S, Si and Fe up to energies Еk ~ 50 MeV/nucleon. The emergence of ACR near the Earth is associated with the acceleration of particles at the boundary of the heliosphere, in the region of the terminal shock wave (see Sect. 2.5). On the one hand, neutral particles of interstellar gas and charged particles of the solar wind are involved in the generation of ACRs. Charge exchange occurs between these two populations of particles, then the newly formed “interstellar-heliospheric” ions are accelerated on the shock wave and slowly seep through diffusion to the Earth’s orbit. The speed of penetration deep into the solar system depends on the energy and charge of the ions. For “anomalous” hydrogen and helium ions, for example, the delay relative to the same “normal” GCR ions can be about 280–350 days. In this regard, it is appropriate to note that the problem of ACR formation is closely related to the theory of GCR modulation, the consideration of which is beyond the scope of this book. It is important, however, to emphasize that the foundations of the transport theory are common to both of these problems, as well as to describe the propagation of solar cosmic rays. It is timely to mention here a great contribution of many researchers to this a multifaceted problem, especially theorists like Parker (1958, 1963), Dolginov and Toptygin (1966), Jokipii (1971), Toptygin (1983) and many other theoreticians. On the other hand, it seems more reasonable first to give some general physical base (basic principles) of the problem. The author prefers this last approach. More detailed descriptions of different specific issues are beyond the scope of this text book and may be found in the special books (e.g., Toptygin 1983) and reviews (e.g., Jokipii 1971).

6.2

Basic Concepts of Transport Theory

In its most general form, the motion of a nonrelativistic particle with mass m and charge q in magnetic and electric fields is determined by Eq. (5.1), or, which is equivalent, by component Eqs. (5.5) and (5.6) in the case of a unidirectional magnetic field. In Chap. 5 we have already seen some consequences of Eq. (5.5) for motion along a magnetic field, so now it is appropriate to consider motion across the field. The simplest description of such a motion is given by the theory (approximation) of the leading center. Its main assumption is that the temporal and spatial variations of the electric and magnetic fields are considered sufficiently small compared to the rotation period and Larmor radius of the particle. Then the motion of the particles can be represented as a perturbation relative to the motion that the particle would perform in the case of uniform and stationary fields. The original equations are obtained by expanding the vector fields in a Taylor series, then the terms of the second and higher orders are discarded. This first-order

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6 Transport of Particles in the Heliosphere

approximation is valid if the gyroradius ρ and the rotation period τg are much smaller than the spatial and temporal scales for the field variations. The zero-order motions for a particle are: circular motion around the field line of force, electric drift in crossed electric and magnetic fields E × B, as well as motion under the action of any of the field components E parallel to B. Hence, the particle position vector x can be represented as x. x = r þ rg

ð6:2Þ

where r is the position vector of the leading center, i.e. the center of the orbit of rotation, and rg is a vector drawn from the leading center to the particle. Replacing x in the equations of motion, expanding the fields in series and then, averaging over the rotation period, we obtain the equation of motion for the leading center of the particle: d 2 r=dt 2 = ðe=mÞE þ ðe=mÞdr=dt × B–ðμm =mÞΔB

ð6:3Þ

where μm = mvg2/2B is the magnetic moment (or the first adiabatic invariant), and vg is the speed of the circular rotation of the particle (gyrospeed). The magnitude of the rotation speed and the Larmor radius are related by the relation vg = ωρ, where ω = eB/m is the Larmor or gyrofrequency, 2π/ω = τg is the rotation period (gyroperiod). A detailed solution to Eq. (6.3) for the leading center velocity dr/dt can be found in Priest and Forbes (2000). If the temporal variations are negligible, and the electric field E is weak enough, then the only effect of the electric field in Eq. (6.3) is reduced to the excitation of an electric drift in the field E × B, which does not lead to any change in the total energy of the particle. In addition to the concept of a leading center, one of the key concepts of the transport theory is the resonant scattering of particles by wave disturbances (inhomogeneities) of the medium. The expression for the wave vector k in the case of resonant scattering of particles has the form: k res ffi 1=ρ = ZeB=cp = B=R

ð6:4Þ

where ρ = v/ω is the Larmor radius of a particle with charge Ze, mass m and velocity v in a magnetic field B; ω = ZeВ/mc—its Larmor frequency, R = ρ/B = cp/Ze is magnetic rigidity, and the energy and rigidity of the particle are related by relations (6.4). The meaning of formula (6.4) is that scattering occurs most efficiently (to the maximum angle) when the Larmor radius of the particle is comparable to the size (radius) of the magnetic inhomogeneity (wavelength). Figure 6.2 shows examples of resonant scattering of particles by inhomogeneities of the interplanetary magnetic field (IMF). The nature of the motion of particles of a given energy in an interplanetary magnetic field substantially depends on the relationship between their Larmor radius ρ and the scales l of inhomogeneities of IMF. In such fields, the leading center of the particle in the first approximation moves along the line of force, experiencing a weak transverse drift. The energy of the particles changes slightly due to the electric field,

6.2

Basic Concepts of Transport Theory

67

Fig. 6.2 There are two types of scattering of solar particles by IMF inhomogeneities: (a) thickening of field lines; (b) bending of lines of force with their simultaneous thickening; 1—power lines of the IMF; 2—trajectories of solar particles; S—the Sun; E—the Earth

which in interplanetary space is small compared to the magnetic one. The change in the pitch angle of the particle is determined by the preservation of the adiabatic invariant р2 ┴=В ¼ const

ð6:5Þ

(р┴ is the transverse component of the particle momentum). The motion of particles under these conditions can be described in the approximation of the leading center, or on the basis of exact equations of motion. Motion in fields with a scale of irregularities (fluctuations) of the order of or less ρ is more complicated. In interplanetary space, fields of this scale for particles of not too high energies have the character of random inhomogeneities. They lead to a rapid and irregular change in the coordinates and pitch angle of the particle. Of particular interest is the case l ~ ρ considered above (resonant scattering, Fig. 6.2). If along with magnetic there are also electric fields (moving magnetic inhomogeneities), then the energy of the particle also changes. These changes are in the nature of diffusion in the phase space. Based on modern data on the characteristics of IMF, it is easy to show that for relativistic particles with Ek > 200 GeV, the entire interplanetary field is a set of small-scale inhomogeneities. In the energy range from hundreds to several GeV, large-scale IMF structures should be considered as a regular field, against the background of which there are random inhomogeneities (fluctuations) with dimensions l of several million kilometers or less. The Larmor radius of particles with energies below several GeV satisfies the condition ρ < lmax, where lmax is the maximum size of IMF inhomogeneities. The scattering intensity of such particles depends significantly on the form of the spectral function of magnetic fluctuations (4.5). With an incident spectrum of fluctuations, the scattering field, which includes magnetic structures with l ≤ ρ, is small compared to the large-scale field formed by structures with l >> ρ. This leads to the fact that particles are scattered at a small angle at each Larmor revolution and becomes possible to use the theory of perturbations. If the main contribution to the IMF perturbation is made by strong MHD discontinuities, especially shock waves and rotational discontinuities, then,

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apparently, scattering can be described using the model of magnetic “clouds” deflecting particles at a large angle. It is clear from what has been said that SCR particles (energy range from Ek ≥ 1 MeV to Ek ≥ 10–100 GeV) are affected by both large-scale magnetic formations and small-scale IMF inhomogeneities. Therefore, below we will focus on the theory of transport of particles moving in a large-scale field with small-scale inhomogeneities.

6.3

Energy Density and Transport of Energetic Particles

As already noted, electric and magnetic fields have a decisive influence on the motion of fast particles in interplanetary space. It is easy to verify this by assessing the impact of various factors, for example, on particles of solar origin. Thus, the gravitational energy of a proton on the surface of the Sun is about 2 keV; the kinetic energy of the solar wind protons has such an order of magnitude. Since SCRs have much higher energies, the influence of the gravitational field on them can be neglected. Coulomb collisions of fast particles with interplanetary plasma are also insignificant: the range relative to scattering through a large angle, even for thermal electrons and ions near the Earth’s orbit, is greater than 1 AU. With increasing energy, the range increases in proportion to its square at nonrelativistic energies. The range of accelerated particles relative to nuclear collisions is even greater. On the other hand, the range of protons with energies of ~1 MeV relative to collisions with magnetic inhomogeneities of the IMF in most cases exceeds 1 AU and often much less than this value. Therefore, when considering the motion of energetic particles in the heliosphere, with its characteristic size of ~100 AU (see Chap. 4), one can neglect the influence of the gravitational field, Coulomb and nuclear scattering and consider only the interaction of particles with interplanetary magnetic fields. The nature of the interaction of fast particles with IMF substantially depends on the ratio of their energy densities (6.1). If the energy density of the particles is low, then their reverse effect on the interplanetary medium can be neglected. In this case, the regular (4.1) and random (4.5) fields in the solar system can be considered given. In this case, the transfer of energetic particles is described by linear equations. Otherwise, the influence of fast particles (for example, SCR) on the IMF and, through it, on the solar wind leads to a nonlinear problem. In this case, it can be expected that increased fluxes of solar protons will generate additional turbulence in the interplanetary medium (see Sect. 6.5). The characteristic value of the magnetic energy density near the Earth’s orbit is wB ≈ 10–10 erg/cm3, which corresponds to В ≈ 5 × 10-5 G (1 eV = 1.6 × 10-12 erg). To estimate the energy density of cosmic particles, we use the GCR proton spectrum (GCR) shown in the left panel of Fig. 7.1. It is quite typical and characterizes the “background” of cosmic particles that constantly exists in interplanetary space. An estimate of the energy density gives wGCR ≈ 3 × 10-12 erg/cm3, which is much less than the IMF energy density. If this spectrum is continued with the same

6.4

The Theory of Solar Cosmic Ray Transport

69

differential exponent s = 3 up to Ep = 1 keV, then we obtain the energy density wGCR ≈ 3 × 10-12 erg/cm3 ≤ 2 eV/cm3, which is two orders of magnitude less than the energy density of the magnetic field in the orbit Earth. The accuracy of these estimates is low, since data on subcosmic ray particles are unreliable. However, in general, it is generally accepted that the total energy density of the GCR within our Galaxy is ~1 eV/cm3, and this value is comparable to the energy density of electromagnetic radiation of stars, the energy of motion of interstellar gas and the energy density of its turbulent motions, as well as the energy density of magnetic fields of the Galaxy. At the periphery of the heliosphere, the energy density of the interplanetary medium is rather low, so that the interstellar magnetic field, cosmic rays, neutral and ionized gas have a noticeable effect on it. For very powerful flares, the SCR energy density wp can be comparable to the IMF energy density. So, after the well-known outburst on August 4, 1972, the SCR energy density near the Earth’s orbit reached 6.44 × 10-9 erg/cm3 = 4 × 103 eV/cm3 (near 22:00 UT) in the proton energy range of 10–60 MeV with a differential proton spectrum exponent s = 2.5. According to the measurements on the Prognoz-2 spacecraft, the thermal energy of the solar wind plasma fluctuated in the range of 3 × (103 ÷ 104) eV/cm3 in the interval 22:00–22:40 UT, and the kinetic energy density of the plasma remained almost constant at a level of ~3 × 104 eV/cm3. The magnetic field strength by 22:40 UT reached ~50 nT = 5 × 10-4 G, and its energy density was wB ≈ 10-8 erg/cm3. If the spectrum of protons had the same exponent 2.5 up to energies Еp = 5 MeV, then we obtain their energy density wp ≈ 2 × 108 erg/cm3. With all the uncertainty and limitedness of these estimates, it can be seen from their comparison that in some periods the energy density of accelerated solar particles could exceed the IMF energy density. Finally, when strong MHD waves interact with fast particles, the effect of the latter on the front structure can also be significant.

6.4

The Theory of Solar Cosmic Ray Transport

The foregoing leaves no doubt that the trajectory of an individual particle in interplanetary space cannot be calculated due to the random nature of the smallscale magnetic field. The description of particle motion should be probabilistic: it is convenient to describe the system of particles by distribution functions f(r, p, t) that satisfy kinetic equations. The kinetic equations, however, are complex, and their solutions can be obtained in analytical form only for some simple cases. At the same time, for a wide class of problems it turns out to be possible to simplify these equations. If the size of the system is large enough and the particles have time to scatter strongly, so that their directional distribution becomes close to isotropic, then the diffusion approximation can be used. It is obtained by expanding the distribution function f(r, p, t) in a series in spherical harmonics of the angles of the vector p and confining ourselves to the first two terms of the expansion (Dolginov and Toptygin 1966):

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Transport of Particles in the Heliosphere

F ðr, p, t Þ = 1=4π N ðr, p, t Þ þ 3=v2 × v × J ðr, p, t Þ

ð6:6Þ

Here F(r, p, t) is the concentration (density), and J(r, p, t) is the flux density (intensity) of particles with a given value of the absolute value of the momentum. The transport equation for the particle density n has the form (Toptygin 1983): p ∂n ∂n ∇•u = ∇α κ αβ ∇β n - u • ∇n þ 3 ∂p ∂t

ð6:7Þ

The first term on the right-hand side describes the diffusion of particles (κ is the diffusion coefficient in coordinate space) in an anisotropic medium (indices α and β), the second term describes their convection due to the motion of scattering centers (magnetic inhomogeneities) with a velocity u. The last term is responsible for the change in the energy of particles interacting with a moving medium. The transfer equation, equivalent to (6.6), can be written in a different form, if instead of the density of particles in the phase space, we introduce their density per unit interval of kinetic energy E. Then we get: 1 ∂ ∂n ðaEnÞ∇  u = ∇α καβ ∇β n - ∇  ðunÞ þ 3 ∂E ∂t

ð6:8Þ

When particles propagate in a stationary inhomogeneous magnetic field (which can be considered the IMF), the kinetic equation takes the form (Toptygin 1983): ∂f ∂f ∂f ν ∂B ∂f 1 ∂ - κ ⊥ ðz, νÞ þ ν cos θ þ sin θ b ðz, θÞ sin θ sin θ ∂θ s ∂θ ∂t ∂z 2B ∂z ∂θ 2



2

∂ f ∂ f = δðz- z0 ÞδðxÞδðyÞSðt ÞQðθÞ þ ∂x2 ∂y2

ð6:9Þ

Here f is the distribution function averaged over possible realizations of the magnetic field (the need for averaging is due to the fact that the distribution function rapidly oscillates in space and time). The right-hand side of Eq. (6.9) contains the source of accelerated particles: the function S(t) describes the time dependence of the source, and Q(t) describes the time dependence. The z coordinate should be measured along the line of force of the regular magnetic field (i.e., along the Archimedean spiral), bs is the diffusion coefficient on the pitch-angle θ, and κ is the transverse diffusion coefficient. Equation (6.9) also contains the term (v/2B) × (∂B/∂z)sinθ(∂f/∂θ), which takes into account the focusing effect of a decreasing magnetic field (a decrease in the pitch angle of a particle with distance from the Sun). This effect is important, in particular, for the analysis of the arrival times of the first SCR particles to the Earth. In this case, the focusing length L characterizes the spatial variations of the average (smoothed) magnetic field. Over the length L, the modulus B of the IMF decreases by a factor of e:

6.4

The Theory of Solar Cosmic Ray Transport

71

ð1=LÞ = ð- 1=BÞð∂B=∂zÞ

ð6:10Þ

The scattering efficiency can be characterized by the diffusion coefficient κ in the coordinate space. In this context, it should be noted that the diffusion phenomenon, which is central to the particle transport problem, was first discovered heuristically in the mid-1950s as a result of the analysis of a number of large SCR events. Only in the mid-1960s was the diffusion equation derived theoretically from the equation of motion of particles in an inhomogeneous magnetic field (e.g., Toptygin 1983). About 10 years later, it was shown that diffusion solutions are the lowest-order solutions of the general kinetic equation of particle transport in the Fokker-Planck approximation. If solutions of higher orders are taken into account, a number of non-diffusion effects become significant (coherent propagation, particle velocity dispersion, exponential decay of the particle intensity during focused diffusion, etc.). Let us consider the interplanetary medium as a homogeneous and scattering SCR particles with a transport range Λ, and the Sun as an instantaneous point source of N accelerated particles with a power f(t), then the concentration of particles n(r, t) at a distance r from the Sun is determined by the equation: ∂n = κ ðE ÞΔn þ f ðt Þ ∂t

ð6:11Þ

where κ(Е) = (1/3)vΛ(E) is the diffusion coefficient for particles with velocity v and energy E. For f(E, t) = N(E)δ(t) we obtain the simplest solution of the diffusion equation (see, e.g., Dorman and Miroshnichenko 1968): nðr, t, EÞ =

N ðE Þ 8½πκðEÞt 3=2

exp - r 2 =4κðE Þt

ð6:12Þ

From formula (6.12) it can be seen that the time profile of the SCR intensity in the Earth’s orbit has the form of a diffusion “wave”, asymmetric with respect to t, with a maximum at tmax = r2/6κ = r2/2vΛ. Due to the exponential factor in (6.12), the concentration of particles decreases rapidly with distance and depends on time in a complex manner. For t ≥ r2/4κ, the exponential factor in (6.12) does not play a special role, and the particle concentration begins to decrease approximately according to the law n ~ t-3/2 (see Fig. 6.3). This time course is the most essential sign of the realization of three-dimensional diffusion in an isotropic unbounded medium. The real picture of the transport of fast charged particles in interplanetary space can be very different from the idealized diffusion approximation. Nevertheless, by the mid-1960s, the simplest diffusion model made it possible to reveal such an important feature as the dependence of the transport path on the particle energy. The first estimates were obtained for the number of accelerated protons N in the source, the energy spectrum, the possible duration of their generation, and a number of other key characteristics of SCRs. As it turned out later, in a more sophisticated analysis, it

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Fig. 6.3 Time profiles of the intensity of relativistic SCR (protons) from observations on the Earth’s surface: Left—observational 15-min data at the Mexico City station on February 23, 1956 (I—ionization chamber, N—neutron monitor); on the right—5 min data from the IceTop muon detector at the South Pole station on December 13, 2006 (e.g., Miroshnichenko 2014a, b)

is also necessary to take into account convection, focusing, and adiabatic change in the energy of fast particles. These non-diffusion effects already require a kinetic approach, which is currently being successfully implemented not only in the relativistic region, but also in the range of moderate and low energies (up to Ep ~ 1 MeV, for protons).

6.5

Shock Waves and Transport of Solar Particles

As noted in Sect. 5.7, energetic solar particles can have different sources on or near the Sun, and their absolute fluxes, intensity time profiles, spectra, and angular characteristics will vary from event to event. In part, these variations will be determined by the relative position of the particle source and the observation point. If the source is a shock wave associated with the CME, then a distinct asymmetry in the form of time profiles will be observed in the Earth’s orbit (Fig. 6.4), depending on whether the source is located in the western or eastern heliolongitude with respect to the CME and the shock wave. Such a picture was obtained from the data accumulated over about 20 years of observations for 235 proton events with an intensity above 10-2 (cm2 sr s MeV)-1 in the energy range 1–23 MeV (for protons). Suppose an observer sees CME from a western source (W53°). At this moment, the observation point is well connected with the bow of the shock wave, which is still near the Sun. By the time the shock wave reaches the Earth’s orbit (1.0 AU), the observer will be 53° from its bow towards the eastern flank of the wave. As a result, it hits the flux tubes, which eventually become associated with a weaker source of particles, so that their intensity decreases steadily. This decrease inevitably follows from the very geometry of the process, even if the speed and degree of compression of all parts of the shock wave do not change with time. The point of magnetic connection of the observer with the wave front is shifted eastward.

6.5

Shock Waves and Transport of Solar Particles

73

Fig. 6.4 Typical time profiles of the intensity of energetic solar particles in Earth’s orbit for three proton events observed at different heliolongitudes with respect to the position of the CME and the shock wave (Reames 1995). One can see the asymmetry of the profiles depending on the position of the source: on the left—west longitude W53°, on the right—east longitude E45°, in the center of the figure—the source is located at longitude E01° (near the center of the solar disk)

An observer near the center (E01°) can see the slow initial phase of the event, since during this period he is associated with the western flank of the wave. However, if the CME has a large length in longitude, then a flat time profile will be seen at the observation point, corresponding to an almost constant acceleration. Immediately behind the front, the intensities fall by an order of magnitude or more as the observer plunges into the CME proper, where many lines of force can still remain connected to the Sun at both ends. Finally, consider the case when the observer is on the western flank of the wave (E45°). In this case, the intensities may start to rise slowly as the wave approaches the base of the observer’s field line in the corona, far to the west of the particle source. The intensities increase as the junction point moves eastward towards the bow of the wave. However, peak intensities will only be reached after the observer crosses the front, 45 degrees west of the bow of the wave, and when he ultimately finds himself on the lines of force that will connect him to the bow of the shock front from behind. Of course, both CME and the wave front can have irregular shape distortions. However, it seems quite obvious that the particles will be most efficiently accelerated near the central (“nose”) part of the wave, where it is the strongest, and the speed, most likely, is the highest.

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Transport of Particles in the Heliosphere

Energetic Particles and Wave Generation in Interplanetary Plasma

As shown above (Sect. 6.3), in some proton events, the SCR energy density in the Earth’s orbit can be comparable or even exceed the IMF energy density. In such cases, in accordance with formula (6.1), it is necessary to take into account the collective interaction of an ensemble of energetic particles with the surrounding magnetic field. These circumstances served as the basis for the hypothesis that large fluxes of solar protons can generate additional disturbances in the interplanetary medium (i.e., their own turbulence, for example, Alfvén waves). Such disturbances are called self-generating waves (SGW). Since the “wave-particle” interaction is considered to be the cause of particle scattering, the newly formed waves, in turn, will change the conditions for the transfer of solar particles. An important consequence of this fact, from a theoretical point of view, may be the dependence of the SCR transport path on time. Further, the pitch-angle diffusion coefficient, as well as the temporal profiles of the intensity and anisotropy of solar protons, will undergo significant changes. Thus, in principle, it becomes possible to find signs of the influence of GWS in the observational data themselves. The time profiles of proton events, however, are influenced by many other factors. They are, for example, the duration of emission and focusing of accelerated particles, adiabatic changes in their energy in the interplanetary medium, the dependence of the diffusion coefficient on the energy of particles and the distance to the Sun, etc. Therefore, it is an extremely difficult task to distinguish the contribution of the SGW against this background. Another way to confirm the generation of additional turbulence is a direct search for SGW using data on fluctuations in the parameters of the interplanetary plasma. From formula (6.11) it follows that the search for waves generated by accelerated protons should be carried out closer to the Sun, where their flux should be maximum. Attempts to find SGW during proton events were undertaken by a number of researchers, in particular, based on the data of observations on the Helios 1 and Helios 2 spacecraft in the range of distances from the Sun of ~0.31–0.93 AU. However, unambiguous results were not obtained. Perhaps, at the indicated distances, the effect of SGW generation is masked by other phenomena and factors of the interplanetary medium. For example, it remained unclear how the dependence of the IMF modulus (4.1) on the distance to the Sun affects the assumed effect. In addition, it should be noted that the investigated cases did not belong to the most powerful proton events. Meanwhile, if SGW generation takes place, then another quite observable effect should exist, namely, self-limitation, or self-saturation of the SCR flux (streaminglimited saturation) due to additional scattering of protons on Alfvén-type waves. A visible manifestation of this effect will be a plateau in the region of the maximum of the time profile. Figure 6.5 shows the profiles of the intensity of protons with energies of 8.7–14.5 MeV, 39–82 MeV and 110–500 MeV according to the data of observations on the GOES spacecraft in 1989–1992 for six large proton events.

6.6

Energetic Particles and Wave Generation in Interplanetary Plasma

75

Fig. 6.5 Time profiles of proton intensity for six large SPEs (September-October 1989, June 1991, and October–November 1992) according to measurements on board the GOES spacecraft in 1989–1992 (Reames and Ng 2004). The dashed lines show the limiting flux intensities in three energy channels from 8.7 to 500 MeV

The dashed horizontal lines show the expected limit values of the intensity of selfsaturation. The data for the first two energy intervals indicate that these events are practically reaching the nominal saturation limits. For the 110–500 MeV interval, the limiting intensity values were reached (or exceeded) only in four events in September– October 1989. In this case, the profiles for the event of October 19–22, 1989 turned out to be very similar at all energies, even in the region > 100 MeV. This behavior of the intensity may indicate a connection between the self-limiting effect and the acceleration of particles on shock waves generated by CME. As the velocity of the shock wave increases, high-energy particles begin to behave like lower-energy particles. It is important to note that the concept of flux limitation (saturation) does not apply to the intensity of particles near the shock front itself. The shock wave is a source of accelerated particles, which then must move along the IMF lines of force and, with sufficient intensity, additionally turbulize the interplanetary plasma, thereby creating the preconditions for the emergence of the effect of selflimiting flow.

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Transport of Particles in the Heliosphere

Particle Transport in Large-Scale Magnetic Structures

In contrast to immediate vicinity of the Sun, at distances of ~1 AU, in the inner heliosphere, valuable information on the physics and dynamics of the heliospheric plasma can be obtained from the study of the so-called Forbush decreases in the GCR intensity, CME properties, and SCR propagation in the interplanetary magnetic field. The possible acceleration of particles on inhomogeneities of the interplanetary plasma (plasma turbulence) and shock waves is also of great interest, especially in the case of so-called “super-events” with huge fluxes of accelerated particles. Sometimes they are called “abnormal” proton events, by analogy with solitary ocean waves, “hermits”, which are formed extremely rarely, but have gigantic amplitudes (tens of meters). The description of such events on the basis of a rigorous theory of particle transport becomes impossible, so that the only method for their investigation is numerical simulation. Proton super-events in interplanetary space are usually associated with coronal mass ejections and multiple shock fronts. In particular, in August 1972, two converging shock waves were observed in the Earth’s orbit, which were accompanied by a very intense and prolonged increase in the flux of energetic particles. To explain this unusual phenomenon, a first-order Fermi mechanism has been proposed to accelerate particles between converging interplanetary shock waves (Filippov and Chirkov 1977). Estimates have shown that such a mechanism has a sufficient rate and high acceleration efficiency. Subsequently, other similar periods with very high particle intensity were identified, when multiple shock waves generated by coronal mass ejections were observed, as well as other proton events with high particle intensity between pairs of shock waves. Well-known super-events were observed near the Earth on July 14, 1959, August 4, 1972, October 19, 1989, and July 14, 2000 (e.g., Miroshnichenko, 2018). Solitary proton events were recorded in the inner heliosphere and at other distances from the Sun: November 4, 1980 on the Helios 1 spacecraft (0.5 AU) and in March 1991 on the Ulysses spacecraft (2.5 AU). These unusual proton events cannot be the result of a simple compression of the medium between two converging shock waves: although the distance between the converging waves will decrease ~ r as the waves move away from the Sun, the cross section of the stream tube will increase as ~ r2, which will ultimately lead to an increase in volume between waves. Figure 6.6 shows possible geometric configurations for shock pairs and IMF. On the left in Fig. 6.6, the simplest case is shown: two converging waves and the nominal Archimedean spiral of the IMF (the Sun is on the left). Particles arriving at the wave from the region upstream of the solar wind flow are partially reflected, since the compression of the magnetic field perpendicular to the shock front creates a magnetic “mirror”. Therefore, the particles can be “swept away” by the wave. However, it is impossible to imagine the reflection of particles approaching the front from the downstream region, since then they are exposed to the effect of the diverging field. Thus, although the shock waves will “rake” the particles, their

6.7

Particle Transport in Large-Scale Magnetic Structures

77

Fig. 6.6 Possible magnetic configurations for accelerating energetic particles in the interplanetary medium between two converging shock waves generated by the Sun (Kallenrode and Cliver 2001a, b)

accumulation in the volume between the fronts will not occur; first-order Fermi acceleration is not realized. To avoid this problem, a mechanism has been proposed related to the magnetic Gold bottle (middle part of Fig. 6.6): a large magnetic loop stretches ahead of the front, and some particles in the upstream medium have a chance (depending on their pitch-angles) to be reflected back and forth along the line of force. As the wave expands, the length of the field line in the upstream region decreases and the particles are accelerated in the first-order Fermi process. Although sometimes, indeed, large loops were observed extending beyond 1 AU, this configuration, apparently, is not the only possible explanation of super-events, especially after a typical super-event was observed on the Ulysses spacecraft at distance of 2.5 AU from the Sun. Numerical modeling (simulation) of processes related to the problem of separating two populations of particles in regions upstream and downstream in a magnetic cloud is a difficult task. However, after analyzing all the features of super-events, we can suggest the scenario depicted on the right side of Fig. 6.6. In this scenario, the particles are repeatedly reflected between the lagging wave (particles with small pitch angles passing the front near the cloud) and the magnetic cloud behind the leading shock front. The corresponding numerical model (Kallenrode and Cliver 2001a, b) for a given magnetic configuration allows simulating the effect of the CME/front pair on two populations of particles. The results of such simulations allow us to draw several important conclusions: (1) the magnetic cloud following the leading front is extremely important for generating high particle intensities; (2) shock fronts must converge (converge) in order to create an increase in intensity; (3) the presence of a trailing cloud is necessary to reduce the intensity of the particles after the passage of a pair of shock waves.

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Solar Particles at Large Distances from the Sun

As follows from Sect. 5.7, the acceleration of solar particles by shock waves in interplanetary space greatly complicates the interpretation of proton events in the framework of the rigorous particle transport theory outlined above. Indeed, in contrast to the idealized case with a point instantaneous source on the Sun (6.11), in the presence of a shock wave, the source of accelerated particles becomes distributed along the shock front. Moreover, its power changes over time. It is especially difficult to predict the behavior of particle fluxes with energies of ~10–30 MeV at significant distances from the Sun (outside the Earth’s orbit). Below, we briefly consider the radial dependence of SCR fluxes and their relationship with the position of the source on the Sun and the spiral structure of the IMF. When extrapolating proton fluxes to other heliocentric distances r, one proceeds from the assumption that diffusion across the IMF can be neglected. At the same time, the volume of the magnetic field tube decreases with distance from the Sun according to the laws of classical geometry. In this case, a power function like ~r-3 can be used to extrapolate. Estimates based on the allowance for transverse diffusion give a dependence of ~r-3.3. A similar radial gradient for solar proton fluxes is obtained from a comparison of data from the Voyager spacecraft and near-Earth satellites. The available data on the radial gradient are rather limited, but in general it can be assumed that outside the Earth’s orbit (at r ≥ 1 AU) the intensity of solar protons changes according to a power law from ~r-3 to ~r-4. For distances r < 1 AU, respectively, a gradient can be taken in the range from ~r-3 to ~r-2. From the point of view of space weather, the time profiles of proton fluxes with Ek ~ 10–30 MeV, unfortunately, are often distorted due to many factors, especially due to the influence of interplanetary shock waves. In particular, the region of particle capture around the shock front can turn out to be the region of the highest intensity of accelerated particles if the acceleration on the shock wave continues as it moves away from the Sun. If the wave decays with distance, then this effect should not be expected. In addition, at distances >1 AU interaction or merging of various “transient” waves can occur, and co-rotating shock waves begin to play a role, which further accelerate some solar particles left over from the transient waves. Usually, for simplicity, it is assumed that the maximum possible flux of solar protons should be observed at a point that is “well connected” by the IMF magnetic field line with the location of the particle source on the solar disk. In other words, energetic solar particles at a certain point of observation at a distance r from the Sun will have maximum intensity when their source is located at the western heliolongitude Φ = Ωr=u = 51:4r

ð6:13Þ

Here, the average solar wind speed u is taken equal to 450 km/s, the angular rotation speed of the Sun is Ω = 360/27°/day, and the heliolongitude Φ is expressed in degrees. To reach the observation point, the particles must travel a distance L

6.8

Solar Particles at Large Distances from the Sun

Table 6.1 Connection parameters of some planets with the Sun (Kahler 2001)

Planet Venus Earth Mars Asteroids Jupiter

L=

r (AU) 0.72 1.00 1.52 2.77 5.20

79 Φ (°) 37 51 78 142 268

1 þ r2 Ω2 =u2 dr

L (AU) 0.77 1.32 1.91 4.63 13.67

T (min) 15 26 37 90 265

B/B0 1.69 1.00 0.55 0.264 0.134

ð6:14Þ

For the above values of u and Ω, we obtain L = 1.32 AU for the Earth’s orbit. If the observer (spacecraft) is near the Earth, then the most favorably located source will have a heliolongitude of the conjunction Φ = 51° to the west of the “Sun-Earth” line. With a radial distance from the Earth’s orbit, the angle of twist of the IMF Archimedean spiral will increase. Therefore, at other points of observation (for example, in the orbit of Mars) the region of favorable longitudes will be located already near Φ = 78°, and so on. During spacecraft flights to other planets (Venus, Jupiter, etc.), the corresponding values of L and Φ will be very different (Table 6.1). When an interplanetary spacecraft with cosmonauts (astronauts) moves away from the Earth’s orbit towards the outer planets, the longitude of the magnetic connection on the Sun’s disk moves to the west. But even for a Martian observer, the conjunction region still remains on the visible part of the disk near the western limb, i.e. there is an analogy with the situation for a terrestrial observer. However, already in the asteroid belt and beyond, the only sign of explosive processes on the Sun for an observer on board the spacecraft will be only powerful CMEs behind the western limb, while manifestations of solar activity on the visible disk may be completely absent. Beyond the orbit of Mars, the length of the traversed path L and the time of movement of particles T also increase significantly due to the twisting of the IMF lines of force mainly in the azimuthal direction. The scattering of solar particles by IMF magnetic inhomogeneities leads to a significant decrease in their maximum intensity with distance from the Sun. An additional decrease in intensity occurs due to the divergence of the IMF lines of force. For a population of particles bounded by a tube of lines of force with a magnetic flux B × A (where B is the magnetic field strength, A is the cross-sectional area of the tube), the decrease in the particle intensity with distance should follow the law of variation of B. It has been empirically established that the value of B changes near the Sun approximately as r-2, and at distances of the order of several astronomical units, this dependence is close to r-1. It is with this radial dependence of the IMF taken into account that the B/B0 ratios were calculated (see the last column of Table 6.1). At a distance of Jupiter’s orbit, for example, the intensity of 100 MeV protons should decrease by 7–8 times compared to their intensity near the Earth’s orbit. As already mentioned in Sect. 2.6, for a comprehensive study of the Sun, planets, the interplanetary medium and the heliosphere as a whole, practical astronautics

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Fig. 6.7 Longitudinal distribution of possible SCR sources over the solar disk for 48 GLE events based on ground-based observations for the period 1956–1991 (Shea and Smart 1993)

makes extensive use of spacecraft gravitational maneuvers in the gravity field of various planets of the Solar System. Such maneuvers are planned to be applied, in particular, during the first manned flight to Mars (possibly already in the next decade). Since the radial distance to Mars is ~1.5 AU, the flux of solar particles near its orbit will be about 1/3 of their flux near the Earth. Hence, one might get the impression that the problem of predicting the radiation hazard for the orbit of Mars is not much different from a similar problem for the orbit of the Earth. However, it should be borne in mind that a full-fledged expedition to Mars will last more than 2 years (round trip). All this time, the interplanetary ship will move along a complex, winding trajectory, maneuvering between Venus, Earth and Mars, crossing various IMF flux tubes, and, accordingly, getting into different radiation conditions. In this case, the probability of a “surprise” (i.e., the appearance of an SPE in the absence of visible activity on the solar disk) in the orbit of Mars will be significantly greater than in the orbit of the Earth. Observations in the Earth’s orbit show that about 20% of all registered SPEs are not visually associated with the observed solar flares. This suggests that the origin of many SPEs that do not have flare sources in the visible part of the disk is associated with the Sun’s out-of-limb activity. To illustrate the effect, Fig. 6.7 shows the heliolongitudinal distribution of 48 so-called GLEs (or Ground Level Enhancements) observed on the Earth’s surface in 1956–1991. Of the 48 events with relativistic protons, 10 SPEs (GLEs) apparently had as their source flares behind the western limb of the Sun. If we consider the entire series of GLEs (70 events for the period 1942–2006), then there will be at least 12 such outof-limb sources. The distribution of non-relativistic SPEs has approximately the same form. There is, however, information that the sources of SPEs from shock waves are distributed differently, with a maximum distribution at heliolongitude of about 30°W (e.g., Miroshnichenko 2014a, b). By analogy with this, one should expect that in Mars orbit about half of the detected events will be associated with sources on the

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Solar Particles at Large Distances from the Sun

81

invisible side of the Sun. Let us estimate the region of “favorable heliolongitudes” for Mars. When Mars is removed by 1.5 AU from the Sun, the time of movement of the solar wind at a speed of 400 km/s will be about 6 terrestrial days. During this time, the Sun will turn westward by ~86°, which essentially corresponds to the western limb of the Sun as viewed from Mars. Assuming that the distribution of solar proton flares is symmetric in heliolongitude, we can conclude that about half of the SPE source flares will be invisible to a Martian observer. This circumstance requires special measures to be taken to monitor and predict the radiation situation along the trajectory of the interplanetary spacecraft (see Sect. 14.3).

Chapter 7

Acceleration of Particles on the Sun

The truth is always simpler than one might think. Richard Feynman

One of the most important physical processes on the Sun and/or near it is the acceleration of charged particles (electrons and ions) to high (relativistic) energies. This process is closely related, first of all, to the large-scale structure and dynamics of the atmosphere as a whole (macroscopic effects of magnetohydrodynamic nature). At another, microscopic level of consideration, acceleration is closely related to the intimate properties of solar magnetoplasma (microphysical processes of generation, for example, of local electric fields). It can even be argued that the acceleration process at the initial stage (from thermal velocities) is mainly determined by microscopic processes in the plasma, while the final stage (acceleration to the maximum possible energies) requires the presence of extended (large-scale) magnetic formations in the solar corona.

7.1

Solar Particle Acceleration Scenarios

Energetic particles are present everywhere in the Universe, and, as it turned out from the very beginning, on the whole they are not in thermodynamic equilibrium. They manifest themselves, for example, in the form of cosmic rays, mainly protons of galactic and solar origin, falling on the earth’s atmosphere. Relativistic electrons generate synchrotron radiation from distant radio galaxies. Energetic (accelerated) particles are also found in the solar wind near the shock fronts before coronal ejections (CME) and at the boundary of the Earth’s magnetosphere. Moreover, even inside the magnetosphere there are vast regions filled with captured fast particles (the Earth’s radiation belts). The main reason that nature avoids a uniform distribution for such particles is that they rarely occur with other particles. For example, during, say, a million years, while a GCR particle wanders around the disk of our Galaxy, it has a probability of colliding with another particle only ~10-8.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 L. Miroshnichenko, Solar-Terrestrial Relations, https://doi.org/10.1007/978-3-031-22548-2_7

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On the other hand, charged particles in space are subject to complex electromagnetic fields. In the simplest case, the equation of motion for a nonrelativistic particle with constant mass m, velocity v, and charge Ze in electric E and magnetic B fields has the form: m

dv = ZeðE þ v × BÞ dt

ð7:1Þ

At the same time, large-scale electric fields are extremely rare in the plasma of the Universe, so that during most of their lifetime, particles move in magnetic fields B in circular orbits under the action of only the Lorentz force F = Zev × B

ð7:2Þ

This force acts in the direction perpendicular to the velocity vector and therefore does not act on the particle, thereby allowing it to keep its energy unchanged. In other words, the magnetic field does no work on the particles. On the other hand, this property makes it difficult for the particle to acquire energy, so that in the absence of collisions, the particle can increase its energy only under the action of an electric field. We describe here only the basics of classical processes; therefore, we confine ourselves to a brief consideration of the simplest case, when a particle moves along a uniform magnetic field under the action of an electric field. In fact, there are many more subtle aspects and more complex cases when non-longitudinal electric fields, shock waves, current sheets, etc. arise. In the nonrelativistic case, the behavior of a particle is characterized by several main parameters—the Larmor radius ρ and the Larmor (cyclotron) frequency (gyrofrequency) of rotation ωB in a magnetic field ρ = v=ω; ωB = ZeB=mc

ð7:3Þ

as well as magnetic rigidity R, rest energy E0 and kinetic energy Ek: R = cp=Ze = ρ=B; Ek þ E0 = E2 0 þ ðZeRÞ2

1=2

; R = E2 k þ Ek E0

1=2

ð7:4Þ

All these parameters turned out to be very convenient for analyzing the motion of particles in various cosmophysical processes, in particular, in models of particle acceleration on the Sun (see below), the interaction of accelerated particles with the solar atmosphere (Chap. 8), transport in interplanetary space (Chap. 6), etc. The problem of particle acceleration in space has a rather long history. Back in 1933 W. Swann first proposed an acceleration mechanism in which particles can reach the energies of cosmic rays as a result of electromagnetic induction associated with alternating magnetic fields of stars. This mechanism later became known as the betatron mechanism. In 1949–1954 Enrico Fermi suggested that cosmic rays gain

7.2

Fermi Model Development

85

their energy by stochastic acceleration in the process of scattering of charged particles on randomly moving magnetic clouds (Fermi 1949, 1954). With regard to SCR, it is appropriate to mention here a number of pioneering works in which first attempts were made to combine plasma physics with the theory of acceleration and to duly interpret the numerous observations of SCR (e.g., Wentzel 1964a, b, 1965; Hayakawa et al. 1964; Syrovatsky 1966; Dorman and Miroshnichenko 1968; Perez-Peraza 1975).

7.2

Fermi Model Development

As is well known, Fermi’s hypothesis developed mainly in two directions (for detailed reviews and references, see, for example, the books Priest and Forbes 2000) and Dorman (2006). In a process called first-order Fermi acceleration, two magnetic mirrors (clouds) continuously converge, moving toward each other, so that the particles oscillate back and forth many times, regularly increasing their energy with each reflection. If U is the velocity of the cloud and v is the velocity of the particle, then its energy increases in proportion to the U/v ratio. Such a process is sometimes called simply shock wave acceleration (see, for example, Ellison and Ramaty 1985). The degree of compression of the plasma σ in the shock wave plays an important role (in Ellison and Ramaty (1985) this value was assumed to be in the range of ~1.6–3.0). In the case of a second-order Fermi acceleration (actually stochastic acceleration), the clouds move in random directions. In “counter” collisions, the particles gain energy, and in “catching up” they lose. However, due to the difference in the relative velocities U and v in the first and second cases, the probability of collisions is higher than the probability of catching up, so that in the end there is a net increase in energy, but already proportional to U2/v2, more precisely—/ (uA/v)2, where uA is the Alfven velocity in the plasma. The kinematics of the reflection of particles during Fermi-type acceleration [13, 14] in the modern view and the geometry of the corresponding magnetic configurations (magnetic clouds) are shown in Fig. 7.1. The initial “push” to start energizing the particle may take place at the curvilinear section of the force line and/or at the points of reflection. Fermi’s original idea of accelerating CR by interstellar clouds has changed greatly over time, but both first- and second-order mechanisms have developed considerably and continue to occupy a prominent place in astrophysics. The firstorder mechanism can operate, in particular, in the interplanetary medium (see Fig. 6.6, its description and corresponding comments), as well as between oppositely directed MHD pulses (Parker 1958) or accreting astrophysical currents (e.g., Cowsik and Lee 1982; Schneider and Bogdan 1989). However, the most efficient configuration in which it operates seems to be shock wave (SW).

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Fig. 7.1 Kinematics of particle reflection and geometry of the Fermi mechanism in the modern view (from the presentation of MI Panasyuk on May 22, 2019)

7.3

Acceleration in Solar Flares

As for the acceleration of particles on the Sun, in recent decades, a subtle connection between large-scale macroscopic magnetohydrodynamics of a solar flare and microscopic physics of plasma in accelerating processes has been revealed and studied in detail. There is no doubt that the global environment (medium), in which acceleration occurs, is created by MHD processes, which, in turn, are influenced by the processes of microscopic physics (for example, the occurrence of anomalous resistance and anomalous transport in plasma). Macrophysics and microphysics are also combined in the processes of fragmentation of coronal plasma, which were revealed, for example, during observations of hard X-rays, microwave radio bursts, the so-called spikes of radio emission, and other phenomena. To accelerate SCR, several macroscopic scenarios were proposed, which were based on real (observed) properties of the solar atmosphere and turned out to be applicable for more detailed calculations of microscopic processes. One scenario involves blowing up a magnetic arcade and closing it down by magnetic reconnection. In this case, flare loops and chromospheric ribbons appear, which are observed during a typical eruptive two-ribbon flare. The second scenario is related to the interaction (by reconnection) between individual flare loops, as assumed in the buoyant magnetic flux model. The third scenario is based on the fragmentation of energy release in a large number of small current sheets (microflares), although this process could also occur in each of the first two scenarios. In each of these scenarios, the following processes take place: (1) direct acceleration by the electric field associated with reconnection; (2) acceleration on shock waves (both near the reconnection point and on a fast shock wave that propagates outward from the region of primary energy release); (3) stochastic acceleration due to turbulence at the reconnection site (or sites) and in jets that accelerate away from the reconnection region. At the same time, for the development of quantitative models, it is important to solve such issues as the mechanisms of formation of

7.4

Basic Acceleration Mechanisms

87

current filaments, the nature and detailed properties of reverse currents; acceleration efficiency and the fraction of magnetic energy that is transferred to the accelerated particles.

7.4

Basic Acceleration Mechanisms

Since the magnetic field does not work on the particle, all acceleration occurs when it moves along the electric field. In this regard, we use the term “direct acceleration” in order to indicate processes in which acceleration is provided due to the averaged, or mean, electric field, and not due to the fluctuating field. For example, an auroral electron passing through a potential jump along a field line undergoes direct acceleration, while a CR particle scattered by magnetic fluctuations does not experience such acceleration. On the contrary, this last of the two processes is a classic example of indirect, stochastic acceleration. However, there are also processes that blur the distinction between the terms “direct” and “stochastic” acceleration. Below, for example, we will discuss diffusion acceleration on a shock wave, which is a direct process if we look at a single act of collision between a particle and a shock front. However, if we consider multiple collisions of particles with a shock wave and turbulent magnetic fluctuations upstream of the plasma flow, the process becomes stochastic. The nonrelativistic equation of motion of a particle (7.1) in the case of a unidirectional magnetic field can be divided into a component directed along the magnetic field m dvk =dt = qEk

ð7:5Þ

and the component perpendicular to the magnetic field m

dv⊥ = qðE⊥ = v⊥ × BÞ dt

ð7:6Þ

When the lines of force are not unidirectional, the longitudinal velocity component v|| is subjected to the action of the transverse component of the electric field, and v⊥—to the action of the longitudinal component E||. In the relativistic version of Eq. (7.1), the factor mdv/dt is replaced by the factor d/dt(γmv), where γ = 1/(1-v2/ c2)1/2 is the Lorentz factor. Let us first consider the simplest case, when a particle moves along a uniform magnetic field under the action of an electric field. According to Eq. (5.5), the electric field will accelerate the particles unrestrictedly along the magnetic field, and ions and electrons will move in opposite directions. This process can continue until the electrical force is balanced by the force of collisional friction. For ions with mass mi and charge qi, moving with an average drift velocity ud relative to the electrons, this will happen when the condition is satisfied

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mi ðud =τÞ ≈ qi E

ð7:7Þ

where τ is the characteristic time of deceleration of ions due to interaction with electrons. Parallel electrical conductivity σ || is then defined as the ratio σ || = j/E, where the electric current is j ≈ qiniud ≈ eneud at charge neutrality. Now from (7.7) we find that the parallel electrical conductivity, in terms of the frequency of electronion collisions, ν = mini/(menet), has the form σ + = ε0 ω2 pi τ =

ε0 ω2 pe ν

ð7:8Þ

where ωpe = [(e2ne)/(ε0me)]1/2 and ωpi = [(q2ini)/(ε0mi)]1/2 are the electron and ion plasma frequencies, respectively. Let us now take into account that the drift velocity ud is much less than the thermal velocity of the electrons vTe = (kBTe/me)1/2. As a result, the collision frequency ν and, consequently, the collision friction grows linearly with the velocity ud, and the final formula for the electrical conductivity has the form σ+ =

6ð2π Þ3=2 me v3 Te ε0 2 T 3=2 ≈ 0:0152 e sim m - 1 2 ln Λ e ln Λ

ð7:9Þ

where lnΛ is the known Coulomb logarithm. It can be seen that the conductivity increases as Te3/2, so, a hotter plasma is a better conductor. The corresponding drift velocity from Eq. (5.7) can now be estimated from the relation π E 2 ED

ð7:10Þ

qi ln Λ 4πε0 λ2 D

ð7:11Þ

ud =3 vTe where the value ED =

is known as the Dreiser’s field, and λD = ½ε0 kB T=ðne e2 Þ is the Debye length. These relationships are important for understanding the very initial stage of acceleration, which is obviously completely determined by microprocesses in the plasma. It is at this stage that the generation of local electric fields takes place, the generation of plasma instabilities in the interaction of the “wave-particle” type begins, and the so-called runaway particles appear. Indeed, as the relative drift velocity ud of ions and electrons approaches the thermal velocity of electrons vTe, the linear relationship between E and j is broken. Equilibrium between the electric force and the friction force due to collisions becomes no longer possible, and the particles begin to accelerate indefinitely until the generation of “wave-particle” instabilities begins. This particle runaway

7.5

Acceleration of Particles and Magnetic Reconnection

89

phenomenon was first analyzed by Dreicer (1959). He considered the equation of motion for an ion with a velocity ud relative to the surrounding background of electrons: ml where the ratio hud i =

pud , 2vTe

dud = eE - eE D Gðud Þ dt

function Gðhud iÞ =

erf ðhud iÞ 2ðhud iÞ2

ð7:12Þ -

2 di e - hup , hud i π

and the product

eEDG is the friction force (i.e., the ion is accelerated by the electric field E, but decelerated by the friction force eEDG). In this case, the distribution of electrons was assumed to be Maxwellian, and the electric field was assumed to be ≥ED. The most important property of thepfriction force is that it begins to fall when the drift velocity ud exceeds the value of 2vTe . In other words, as soon as ud reaches the range of values where this force begins to p decrease, particles escape. The critical value of the electric field Ec, at which ud = 2vTe, is equal to Ec = 0.214ED; this maximum field for the equilibrium state occurs at the maximum value of the function G(‹ud›). The appearance of runaway particles can be considered as the first stage in particle acceleration. Further development of the process requires more intense energization (heating) of the plasma at the tail of the Maxwell distribution.

7.5

Acceleration of Particles and Magnetic Reconnection

Particles are accelerated in many places and in different environments throughout space. In some cases, acceleration can be directly responsible for one of the main phenomena in plasma—the so-called magnetic reconnection. This phenomenon is essentially a restructuring of the topology of the magnetic field caused by a change in the connectivity of its field lines, violation of their frozen-in, etc. In this case, the accumulated magnetic energy is released, which in many situations is the predominant source of free energy in the plasma. Of course, in a plasma, in addition to reconnection, many other processes also take place. However, this fundamental process seems to be the most important for explaining large-scale dynamic transformations of magnetic energy. The most striking evidence of reconnection is found precisely on the Sun. Above we mentioned three main mechanisms of particle acceleration (forward acceleration, stochastic acceleration, and acceleration on shock waves). Below we provide illustrative examples of how these mechanisms work in solar conditions. First of all, we will consider the forward acceleration directly related to the magnetic reconnection in the solar atmosphere. In this problem, astrophysicists have long been confused by one fundamental difficulty. As we have already noted, cosmic plasma has a very high electrical conductivity. Therefore, it is difficult to imagine how a space charge could arise in such a plasma, sufficient for the appearance of a noticeable electric field: after all, this charge should be instantly destroyed.

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Acceleration of Particles on the Sun

Fig. 7.2 Formation of the zero line of the magnetic field and the neutral current sheet in the solar atmosphere. Left: The appearance of the zero line of the magnetic field (point A) in the area of contact of two sunspots with magnetic fields of opposite polarity (at point A, the line is perpendicular to the plane of the figure). Right: Current sheet (dots) and magnetic field (solid lines) above the developing bipolar sunspot group. The double shading shows the areas of dense plasma, which are observed as bright filaments against the background of the flare. The current flows perpendicular to the XY plane, the fibers are visible when viewed from above (Syrovatsky 1966)

However, already in the 60s of the last century, it was shown that in some special configurations of magnetic fields, an electric field can arise in small volumes and persist for a period of time sufficient to accelerate particles to relatively high energies. One such configuration is likely to arise in the Sun’s atmosphere at the interface between two sunspots of opposite polarity. In the area of contact of spots, where a solar flare usually begins to develop, the magnetic field becomes equal to zero—a “zero line” appears (Fig. 7.2, on the left). The magnetic field in this place “annihilates” or “dissipates”, and the process itself is called “magnetic reconnection”. The reconnection process is not limited to the formation of one neutral point, but leads over time to the formation of a neutral current sheet (Fig. 7.2, on the right). Indeed, as the spots move, the pattern of the lines of force will change over time. Instead of the zero line, a thin layer of electric current (“current sheet”) arises, which separates the regions of the oppositely directed magnetic field. In this case, two dense plasma fibers are formed along the edges of the current sheet, parallel to the zero line. Over time, the fibers move apart at the rate of expansion of the current sheet. It is this fibrous structure that is observed in powerful solar flares. The current sheet is an unstable formation, and its real structure and physical properties can be very different from those assumed. Thus, for a self-consistent description of the acceleration of particles in a layer, one has to introduce small magnetic fields along and across the layer, thereby violating its “neutrality”. At the same time, of fundamental importance is the fact that the “break” of the current can cause the appearance of a strong electric field, which, working in a relatively small volume, is capable of accelerating a huge number of particles in a short time. Thus,

7.5

Acceleration of Particles and Magnetic Reconnection

91

Fig. 7.3 Trajectories of particles in a current sheet with a thickness of 2 l, a two-component magnetic field Bx = - B0y/ l, By = λ┴B0, and an electric field Ez (Speiser 1965)

the energy of the magnetic field is converted into the energy of the electric field, and then into the energy of the accelerated particles. In some models of the current sheet, the electric field strength can reach very high values of ~10–30 V/cm. The real motion of particles in the region of the current sheet and in its vicinity during acceleration is also very complex. Figure 7.3 shows the trajectories of motion of protons (ions) and electrons of particles for the case when in a current sheet with a thickness of 2 l the magnetic field has two components Bx = -B0y/l, and By = λ┴B0, and the electric field Ez is directed perpendicular to the XY plane. In general case, a particle entering the current sheet is affected by three forces: the E × B force causes the particle to drift in the y direction; a parallel electric field accelerates the particle; a transverse magnetic field causes a circular rotation of the particle relative to the y direction. Of course, this schematic picture does not exhaust the entire complexity of particle acceleration in magnetic reconnection. However, there is now no doubt that this fundamental process plays a very important role in various acceleration scenarios (see, for example, Priest and Forbes 2000). Magnetic reconnection is responsible for the process of energy release during the generation of a solar flare. Moreover, the onset of energy release is likely to initiate another outstanding phenomenon of solar activity—coronal mass ejection (CME). Typical values of magnetic field in the corona B ffi 100 G and plasma density n ffi 1011 cm-3 resulted in the typical velocity of CME movement from the Sun, equal to the Alfvén velocity VA ffi 1000 km/s. Assuming that the velocity of plasma inflow into the current sheet is equal to u = 0.1VA (fast reconnection at high, but finite conductivity), it is possible to estimate the layer formation time tac = L/ u = 102–103 s, where L = 109–1010 cm is characteristic scale for the width and

92

7 Acceleration of Particles on the Sun

length of the layer. Assuming the presence of a confining transverse electric field outside the layer, we obtain the characteristic acceleration time tac ffi 0.03 (Ep/ 1 GeV) s. Hence, it follows that a proton can be accelerated to an energy of Ep ~ 100 GeV in just 3 s (Litvinenko and Somov 1995). As noted by Priest and Forbes (2000), magnetic reconnection provides an elegant and so far only explanation for the movements of chromospheric ribbons and flare loops during solar flares. Without involving reconnection, it is also impossible to explain the output of the solar magnetic flux during CME and eruptive prominences and a number of other solar phenomena. Most importantly, reconnection explains the tremendous energy released in solar flares. The first spatial observations of gamma radiation from flares onboard the RHESSI satellite (Lin et al. 2003) showed that accelerated electrons and ions invade the chromosphere in significantly different regions. This new fact generally agrees with the assumption of the primary acceleration of particles by an electric field (Somov 1992) in a high-temperature turbulent current sheet (HTTCS). Positively and negatively charged particles are accelerated by an electric field in opposite directions and, accordingly, fall out of the HTTCS into the chromosphere along various lines of the magnetic field. Unfortunately, there are no accurate calculations of the effect. In addition, there are still many unresolved issues related mainly to the estimation of the relative contribution of magnetic reconnection and shock waves to the formation of the spectrum of accelerated particles. At the same time, recent observations by the Hinode spacecraft (2008) for the first time brought virtually direct evidence of magnetic reconnection.

7.6

Stochastic Acceleration

When magnetic fields reconnect, many different types of waves are generated. In other words, a turbulent medium is created near the reconnection region, in which energy can be transferred to particles by stochastic acceleration. The forerunner of this idea was Fermi (1949), who suggested that galactic cosmic rays are accelerated by the scattering of charged particles by randomly moving interstellar magnetic clouds. Clouds act like magnetic mirrors, elastically reflecting particles. In a head-on collision, the particle acquires energy, while in an overtaking collision the particle’s energy decreases (Fig. 7.4). This hypothesis developed in two directions. In a process called first-order Fermi acceleration, two mirrors continuously move towards each other, so that the particles oscillate back and forth many times, increasing their energy with each reflection. If U is the speed of the cloud and v is the speed of the particle, then the energy increases in proportion to the ratio U/v. In this case, it is assumed that the speed of the particle is much greater than the speed of the cloud. In the case of second-order Fermi acceleration (truly stochastic acceleration), the clouds move in random directions. This means that in many collisions the particle is forced to lose energy rather than gain it. However, as can be shown, collisions with

7.6

Stochastic Acceleration

93

Fig. 7.4 Kinematic scheme of collision of particles (1) with a moving magnetic cloud (2). When the cloud moves, an electric field E arises, directed perpendicular to the vectors H and u. This field accelerates the particle in a head-on collision or slows it down if it catches up with the cloud

loss of energy are statistically (on average) less frequent than collisions with gain of energy. As a result, there is still a net increase in energy, albeit at a lower rate, ΔЕ ~ U2/v2. Therefore, this acceleration turns out to be much less efficient than the first-order Fermi acceleration. In this case, it is also necessary to fulfill the condition v >> U. Second-order Fermi acceleration can still work even if collisions with an increase in energy (opposite) and with a loss of energy (catching up) are equally probable, since there is momentum diffusion in the phase space. At high energies, the volume of phase space is much larger than at low energies, so it seems highly unlikely that the random walk of a particle in momentum space would cause its velocity to decrease to zero. The main problems when accelerating particles on the Sun (or near it) are associated with two necessary conditions: a well-developed wave turbulence must exist in the solar plasma, i.e., a sufficient level of turbulence (wave spectrum), and the particles being accelerated must first have a certain injection energy Еi. At the same time, stochastic acceleration has one remarkable property— the resonant nature of the “wave-particle” interaction. Resonance is described by the expression: x  ω - k‫ ׀׀‬v‫ ׀׀‬- nΩ=γ = 0

ð7:13Þ

where ω is the frequency of the wave, k‫ ׀׀‬is the component of its wave vector k along the magnetic field, Ω is the cyclotron frequency, γ is the Lorentz factor of the particle, n is the harmonic number, x is the parameter of frequency mismatch. The most effective resonance (i.e., energy selection-transfer from wave to particle) occurs at n = 0 (Landau damping). Although Fermi’s original idea for accelerating GCRs by interstellar clouds has undergone major changes, both mechanisms—first and second order—have been

94

7 Acceleration of Particles on the Sun

greatly developed and continue to occupy an outstanding place in astrophysics. The first-order mechanism can act between oppositely directed MHD pulses or accreting astrophysical currents. However, the most effective configuration in which it operates is a shock wave. The latter provides collisions for particles that cross the shock front and are scattered by magnetic inhomogeneities located upstream and downstream of the shock front. This mechanism, called diffusion acceleration at the shock front, is described below (Sect. 7.5).

7.7

Shock Wave Acceleration

Shock waves of various types naturally create favorable conditions for accelerating particles in two main ways. In the case of drift acceleration, the motion of individual particles in the electromagnetic field of the shock front is usually monitored, and their interaction with fluctuating electric and magnetic fields is neglected. Since particles can enter the shock front region at different pitch angles, they can appear at the exit with a whole set of energies. In the case of diffusion acceleration at the shock front (or DSA—diffusive shock acceleration) the particles move back and forth between inhomogeneities that exist upstream and downstream relative to the front. In this case, the particles repeatedly cross the shock front and each time increase their energy. Before considering the motion of a particle near the shock wave, it is necessary to find out which frame of reference is most convenient for analyzing the properties of the shock front. In this case, one should give preference to the reference frame moving with the shock front and follow the plasma approaching the front from the upstream direction and leaving the front in the downstream direction. Generally speaking, the magnetic field will have some slope with respect to the plasma velocity vector. Therefore, the flow will carry the magnetic lines of force to the front on one side and away from the front on the other, so that the point of intersection of the lines of force with the shock front will move along the front, say, with a velocity uI. Let us consider for simplicity the process of drift acceleration on a perpendicular shock front (Fig. 7.5). In a given configuration, the plasma approaches the shock front with a velocity uI much lower than the particle velocity v and amounts to ~0.1с. In this region, the upstream particle rotates in the magnetic field B1y, while its leading center drifts with the velocity E × B1/B22 = uIx. When a particle penetrates through the shock front into the region downstream, its orbit has a smaller radius of curvature, because the magnetic field B2 is higher there. For a positively charged particle, the final result is reduced to a shift of its orbit in the z-direction parallel to the electric field. Thus, the electric field actually does work on the particle and increases its energy (the electron would move in the opposite direction). Since the motion of the leading center is very similar to a gradient drift in an inhomogeneous magnetic field, this process is called drift acceleration at the shock front. Despite the sharp increase in the magnetic field at the shock front, the magnetic moment of the particle is retained, at least for v >> u1. An immediate consequence

7.7

Shock Wave Acceleration

95

Fig. 7.5 Drift acceleration at the shock front. The solid line is the trajectory of a particle crossing the shock front (dotted line), u1 is the plasma velocity (~ 0.1с) when approaching the front (Kirk 1994). Field B is directed along the negative y-axis, field E is directed in the direction of the z-axis, and plasma flows are directed from left to right in the direction of the x-axis. Field E shifts the particle along the z axis and increases its energy

of this is the fact that even in the case of strong shock waves, the energy gain is modest. For example, a typical maximum compression of the magnetic field (B2/B1) by a factor of 4 leads to an increase in energy, also by a factor of 4, for a nonrelativistic particle and only 2 times for a relativistic particle. Effective drift acceleration on shock waves is more important for electrons than for ions. The reason is that most electrons (i.e., thermal electrons) have gyroradii much less than the front thickness, so that their motion is adiabatic, while thermal ions tend to have a gyroradius close to the front thickness and therefore do not experience reflection. In addition, thermal electrons can be reflected, while slower moving ions with a narrower distribution function generally have pitch angles within the loss cone and therefore are not reflected. Various attempts have been made to expand the basic theory of such acceleration in order to increase the energy gain in some way. However, in most cases the increase did not exceed a factor of the order of 10. Obviously, a different mechanism (such as diffusion acceleration on shock waves, see below) is required to explain the more significant acceleration, like the acceleration of cosmic rays. The movement of particles in an electromagnetic field is reversible. A potential problem with the shock drift acceleration mechanism is that rarefaction deceleration can counteract shock acceleration. However, if the pitch-angle acceleration occurs far upstream or downstream of the shock front, it will isotropize the particle distribution and introduce irreversibility into this process. Below, we consider the effect of scattering upon acceleration on a shock wave and describe a simple model for accelerating particles on both sides of the shock discontinuity, taking into account diffusion (Fig. 7.6). In the rest frame of the shock front, the plasma carries fluxes of turbulence waves with a velocity u1 from the region ahead of the front to the region behind the shock front, where its velocity becomes u2 < u1. Within each region, there is no change in the energy of particles during scattering, if we neglect the dispersion of phase velocities. However, when crossing the discontinuity, a

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Acceleration of Particles on the Sun

Fig. 7.6 Scattering and acceleration of particles during the passage of a shock front (Völk 1981). The difference in plasma velocities at the front Δu = (u1 - u2) is a source of MHD energy for particle acceleration

particle with momentum p undergoes two successive collisions with two scattering centers moving with a relative velocity ± (u1 - u2), which leads to an energy increment ΔЕk = p(u1 - u2). Consider a shock front surrounded by a scattering-free zone where there is no pitch-angle scattering. Further downstream and upstream, there are regions in which scattering creates an isotropic particle distribution. Generally speaking, the calculation of finite distribution functions is a very difficult problem. Even if the particles falling on the front from the right form part of the isotropic distribution, some particles can be reflected at the shock front, while others can pass through the shock front. The microscopic picture of diffusion acceleration on shock waves clearly reveals the physics of the process. Let us estimate the change in the momentum of a particle when it crosses the shock front and then comes back. When a particle passes from an upstream region to a downstream region for the case –u1/v1 μ1 < 1, the change in momentum p1 + Δp1 = p2(1 - μ2Δu/v2), where μ1 is the cosine of the particle pitch angle in the region in front of front (upstream). Suppose that the same particle is scattered downstream, so that only its pitch angle changes. Then, upon its return to the upstream region, it acquires a new momentum p1 + Δp1 = p2(1 - μ2Δu/v2), with -1 < μ2 < -u2/v2. The probability of a particle crossing the front is proportional to the relative velocity of the particle and the front, i.e. ||μv + u|, if the particle distribution is isotropic. Therefore, the average pulse increment per cycle, up to a first-order factor in Δu/v, will be

7.7

Shock Wave Acceleration

97

Δp 4Δu = p1 3v

ð7:14Þ

Thus, the increment in momentum per collision is a first-order factor in Δu/v. That is why this acceleration is called the first-order Fermi process, while collisions of a particle with randomly moving scattering centers would lead to a second-order increment. Indeed, it can be shown from the macroscopic solution of the transport equation that far upstream (where the distribution function falls exponentially), all particles are dragged back to the shock front. At the same time, in the region far downstream (where the distribution is spatially uniform), some particles are scattered back to the front, while others are carried away by advection in the opposite direction. The spectrum for the stationary state can be calculated from the balance of the total number of particles with momenta greater than p + Δp, crossing the front towards the downstream region and the number of particles crossing the front with momentum greater than p minus particles that escape without returning. The spectrum index is determined by the expression s=

3u1 3u1 = Δu u1 - u2

ð7:15Þ

If there are no particles entering the system far upstream, then some kind of injection process is needed that could accelerate a small number of particles to a certain initial momentum, from which the actual acceleration of particles begins. If particles far upstream have a power-law spectrum of the form A1 = A0p-q, with exponent q < s, then the role of the shock wave is reduced to the generation of the spectrum f 2 ð0Þ =

s A p-q s-q 0

ð7:16Þ

that is, the final spectrum repeats the shape of the initial one, but has an increased intensity. It is interesting to note that the spectrum of accelerated particles (for q > s) has a power-law exponent s, which depends only on the degree of plasma compression u1/ u2, but does not depend on the diffusion coefficient κ. This result, however, can be modified by the influence of boundaries. Further, as noted above, with a single crossing of the front, the particle energy increases by an amount of the order of Δu/ v1. This means that in order to increase the momentum, say, by a factor of p/p0 the particles must cross the front pv1/Δup0 times. In addition, the assumption about the isotropy of the distribution function loses its validity even for particles with energies above the thermal one (as is observed, for example, near the Earth’s bow shock wave), or in the case of a relativistic shock front. On the whole, however, diffusion acceleration at the shock front is a slow process. So that the increase in the energy of the particle is pv = 2Еk, N2 scatttring with a change in energy is necessary when crossing the front, where N = v/Δu, р and v are the momentum and velocity of the particle. In addition, for effective

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Acceleration of Particles on the Sun

acceleration, the condition v >> u (injection problem) must be satisfied, otherwise the particles will simply flow from the region upstream through the front to the downstream region. At the same time, at large time scales, this acceleration mechanism can be quite effective. For example, it is considered quite suitable for the formation of an anomalous component of cosmic rays at the boundary of the heliosphere (see Chap. 5).

7.8

Combined SCR Acceleration

Even a brief presentation of the problem clearly shows how diverse and complex the processes of particle acceleration in space (in particular, in the plasma of the solar atmosphere) are. Until now, no theoretical or empirical model of acceleration has been able to satisfactorily explain, for example, the totality of data on the spectrum, composition, charge state, and other properties of accelerated solar particles. Under these conditions, researchers often turn to the concept of multiple (multiple) acceleration of particles on the Sun (or near it). Its essence boils down to the idea that a certain combination of accelerating mechanisms, which, moreover, can be in a certain hierarchy to each other, is most likely working on the Sun. For example, consider the acceleration of particles in the fibrous corona model (Vlahos 1989, 1994). In this model, it is assumed that the active region on the Sun is an ensemble of small magnetic tubes (fibers), their characteristic radius is ≤10–100 km, and the tubes themselves move randomly with a characteristic velocity u = 0.5 km s-1 (Fig. 7.7). Under certain circumstances, many regions of energy release (“hot spots”) can form—regions of dissipation of the energy of the magnetic field, i.e., current sheets (or, in another terminology, “micro-flares”), which will initiate the flare itself. On the other hand, during the evolution of “hot spots”, apparently, a lot of shock waves are formed, which can be efficient and fast particle accelerators. Drift Fig. 7.7 Catastrophic interaction of thousands of current sheets in the fibrous corona model (Vlahos 1989, 1994). The particle gains energy in a stochastic manner when interacting with many regions of magnetic reconnection (dark circles)

7.9

Flares, CMEs, and Two Classes of Solar Proton Events

99

acceleration on a separate wave is a coherent (regular) process, but acceleration on N waves becomes stochastic. In this case, acceleration by a direct electric field in the reconnection region, obviously, can serve as an injector of particles for subsequent stochastic acceleration. This combined pattern of “diffuse reconnection” and “multipoint acceleration” has its own difficulties, in particular, for the formation of shock waves, it requires too high temperatures in the corona, incompatible with observations. Therefore, stochastic acceleration with preliminary injection of “seed particles” from the reconnection region (s) looks more promising in the context of coronal reconnection. Over the past two decades, the concept of multiple acceleration has been enriched with new content. In particular, new models of particle acceleration in extended magnetic structures of the solar corona were proposed and developed: acceleration in the presence of CME, double injection of relativistic SCRs, a model of two sources, acceleration in rapidly expanding and evolving coronal loops, etc. It was also shown that the spectra of the source considered in a wide range of SCR energies (from ≥10 MeV to ≥10 GeV), admit various approximations, including a power function with a flare, which may indicate multiple (at least double) acceleration. Therefore, the inclusion of data on the spectra of the SCR source in the general picture of the generation of energetic solar phenomena allows a deeper understanding of the unsolved problems of particle acceleration on the Sun.

7.9

Flares, CMEs, and Two Classes of Solar Proton Events

In the most general terms, the model of the dynamics of the combined disturbance in the solar atmosphere can be represented in the form of the diagram shown in Fig. 7.8. Magnetic reconnection occurs at the apex of flare magnetic loops in the corona and is accompanied by the generation of strong Alfvén waves or fast shock waves that move up and down from the reconnection region. This region serves as a source of accelerated solar particles, which form the fast (impulsive) SCR component. Particles going downward penetrate (“settle”) into the chromosphere and generate gamma radiation (see Chap. 8), while particles going upward leave the Sun and are observed in interplanetary space as impulsive proton events. On the other hand, a CME with a powerful shock wave can form over the reconnection region. The latter is capable of accelerating a large number of particles to significant energies and, thereby, forming the second, delayed or gradual SCR component. Such a scheme for the formation of two SCR components or, respectively, two classes of solar proton events (SPEs), as it turned out recently, is not always valid. However, it has a strong observational rationale. First of all, as already noted, the solar flares themselves are usually divided into impulsive and gradual, depending on the duration of the soft X-ray burst (Table 3.1). The flares of the two classes have different temporal and spatial characteristics, and also differ in their energy, the presence or absence of CME, etc. These differences prompted researchers to carry out a similar analysis of data on solar proton events (SPE) recorded near the Earth.

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Acceleration of Particles on the Sun

Fig. 7.8 High-energy particle generation scheme taking into account the magnetic reconnection process in the solar atmosphere (Yoshimori et al. 2000)

Table 7.1 Properties of impulsive and gradual solar proton events (Reames 1995– 1999)

Parameters Particles 3 He/4He Fe/O H/He Q(Fe) Duration Longitude cone Radio type Chronograph (CME) Solar wind Events/year

Impulsive Electron-rich ~1 ~1.23 ~10 ~20 Hours 10, >30, >60, and >100 MeV correspond to the magnetic rigidity of protons R > 0.14, >0.24, >0.34 and >0.44 GV, respectively (see formula (7.4)). Neutron monitors on the Earth’s surface sense the arrival of SCRs starting from an energy of about 433 MeV (R ≈ 1 GV). The groundbased network of cosmic ray stations as a whole (neutron monitors, muon telescopes, and ionization chambers) makes it possible to record SCRs in the range of rigidity ≥1–10 GV. Stratospheric measurements provide valuable information about solar protons in the energy range of about 100–500 MeV. Finally, large muon detectors and other non-standard installations provide unique information about solar particles of extremely high energies (≥100 GeV). The use of two characteristics of charged particles (E and R) turned out to be very convenient not only for describing the motion of particles in magnetic fields, but also for representing their spectra. Figure 8.1 shows some examples of spectra of known proton events in energy (E) and rigidity (R) representations. The left and middle panels show the differential and integral spectra, respectively, obtained from SCR measurements near the Earth. These data are important, first of all, for calculating the geophysical effects of SCR and assessing their radiation hazard in near-earth orbits. As for the nuclear-physical effects of SCR in the solar atmosphere, their study requires information on the shape of the spectrum and the absolute number of accelerated particles directly in the source. As an example, the right panel shows the reconstructed spectra of the source for two proton events, and one of them (February 23, 1956) still remains the largest in the entire history of SCR observations. All the above estimates and data on the spectra are not yet accurate enough and are, of course, tentative, but it is important to note that accelerated protons, alpha particles and other ions have sufficient energy to lead to an excited state of the nuclei

8.1

Nuclear Reactions in the Sun’s Atmosphere

105

Fig. 8.1 Typical spectra of large proton events from observations near the Earth (left and middle panels) and at the source (right panel) (for details and references see, e.g., Miroshnichenko 2001, 2014a, b)

of various elements in the solar atmosphere, especially nuclei C, N, O, Fe (Fig. 8.2). Removal of excitement occurs by the emission of gamma quanta of a certain energy. Radiation is usually observed in the form of narrow lines characteristic of certain nuclei, and individual nuclei can emit several lines. The number of lines emitted and their intensity depend on the charge of the nucleus, the type of the incident particle and its energy. For example, a carbon nucleus produces the most intense 4.444 MeV line when it collides with an accelerated alpha particle. One of the lines from a nitrogen nucleus with an energy of 5.105 MeV (not the most intense) is formed in a collision with an accelerated proton. In the case of an oxygen nucleus, an intense line with an energy of 6.129 MeV is excited by collisions with fast alpha particles and protons with almost the same probability, etc. The excited iron nucleus also emits several intense gamma lines, of which the most interesting are the lines with energies of 0.847, 1.238, and 1.811 MeV. Theoretical calculations show that the greatest contribution to the generation of nuclear lines is made by accelerated protons and alpha particles with energies of ~1–100 MeV/nucleon. In the nuclear interactions of SCRs, secondary neutrons, electrons, and positrons are also produced. The annihilation of electrons and positrons in the photosphere leads to the production of quanta with an energy of 0.511 MeV. When neutrons are captured by hydrogen nuclei, gamma quanta with an energy of 2.223 MeV are emitted in the photosphere (the so-called neutron capture line). Finally, if the energy of an incident proton exceeds 300 MeV, then pions are born, which, upon decay, also give gamma quanta, but already much

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Fig. 8.2 Scheme of nuclear reactions in the solar atmosphere under the action of SCR (>10 MeV/ nucleon) (Courtesy: Yu.D. Kotov, MEPhI, 2009). Nuclear reactions are accompanied by the generation of many secondary particles—electrons and positrons, protons and neutrons, as well as the generation of intense gamma radiation (including in the line of neutron capture by hydrogen nuclei with an energy of 2.223 MeV)

higher energy (>90 MeV). To generate flare neutrinos with energies ≥1 GeV, large fluxes of solar protons with energies up to ≤100 GeV are required. All of these types of nuclear radiation, including neutrons, are often referred to as neutral emission from flares.

8.2

Neutrons and Gamma Rays

As noted above, neutral emission from solar flares, including neutrons, was theoretically predicted long before its discovery. Flare neutrons were first recorded on the SMM satellite on June 21, 1980. The detection of high-energy solar neutrons (up to 400 MeV) is rarely possible on the Earth’s surface using the global network of standard neutron monitors (NM). In the late 1990s, a worldwide network of 5 solar neutron telescopes (SNT) was also created. The complete statistics of neutron events, however, does not exceed 30 cases over almost 30 years of research. One of the most outstanding events took place on September 7, 2005. At the time of the outbreak, neutron detectors in the western hemisphere of the Earth were in the most favorable position (noon at the sun point). Figure 8.3 clearly shows, first of all, neutron peaks on neutron monitors in Mexico City (Mexico) and Mount Chacaltaya (Bolivia), 5- and 2-min data, respectively. Also given are 2-min readings of two SNT energy channels in Bolivia for neutrons with energies >40 MeV and >80 MeV. The

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Fig. 8.3 Flare neutrons as observed on September 7, 2005 at neutron monitors (NM) and solar neutron telescopes (SNT) in Mexico and Bolivia (Sako et al. 2006). The bold and gray lines show the observational data and the results of theoretical calculations, respectively

moment 17:36:40 UT corresponds to the time of the maximum for the hard X-ray flux as measured by the GEOTAIL satellite. The gray curves show the expected (calculated) neutron count rates obtained from the neutron monitor data in Bolivia (Fig. 8.3). Figure 8.4 shows the spectra of flare gamma radiation—theoretical (left) and observed (right). The calculated spectrum was obtained for the same indices of the spectrum of accelerated protons and electrons. The dotted line is the bremsstrahlung

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Fig. 8.4 Generation of gamma rays from the Sun: Left—theoretical gamma-ray spectrum from solar flares (Ramaty and Lingenfelter 1995); right—observational data for a typical gamma-ray burst on April 27, 1981 (Murphy et al. 1991)

of electrons. The main lines of nuclear excitation, the neutron capture line by hydrogen, and the positron annihilation line are shown. Positrons appear during β-decay of radionuclides, which are born in reactions between accelerated and “background” ions. For comparison with theory, observational data are presented for a well-measured and well-studied “typical” gamma-ray burst on April 27, 1981. The solid line in the flare spectrum corresponds to calculations (Murphy et al. 1991) under the assumption that the ratio of the number of accelerated helium ions (alpha -particles) to the number of protons (hydrogen ions) is 4Не/1Н = 0.5. Most of the excitation lines in the spectrum belong to the C, N, O, Ne, Mg, Si, and Fe nuclei. The generation of lines is mainly due to protons with energies of 10–30 MeV/nucleon (maximum of the interaction cross section). In the overwhelming majority of cases, the removal of arousal occurs almost instantly. For example, in the case of generation of a line with an energy of 4.438 MeV, the average lifetime of a carbon nucleus in an excited state is only 6.1 × 10-14 s. For the 6.129 MeV line from the oxygen nucleus, the corresponding value is 2.7 × 10-11 s. Secondary neutrons are also produced in these “instantaneous” nuclear collisions. An important consequence follows from this fact: the time profile of the generation of flare neutrons turns out to be identical to the profile of line gamma radiation in the energy range 4–7 MeV. The spectrum also shows two delayed lines of great interest— 0.511 MeV (annihilation of positrons and electrons) and 2.223 MeV (capture of neutrons). Their delay relative to the emission of “instantaneous” excitation lines for a time of about 100–140 s is explained by the fact that both the formation of positron sources and the generation of neutrons occur at considerable depths in the solar photosphere, where the matter density exceeds 1014 cm-3 (see Fig. 8.2). Linear radiation is superimposed on the bremsstrahlung continuum from energetic electrons. This continuum dominates at photon energies below 1 MeV and, in most

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cases, above 10 MeV. In some flares, gamma quanta from the decay of pions with an energy of 10 MeV–3 GeV are observed.

8.3

Astrophysical Consequences and Applications

Data on flare neutrons and gamma radiation (i.e., neutral radiation from the Sun) have proved to be a very valuable source of new information about solar flares and the solar atmosphere. They allow a deeper study of the properties of plasma in the regions of acceleration and interaction of accelerated particles, the features of nuclear interactions in solar conditions, acceleration mechanisms and the spectrum of accelerated particles, the content of various elements on the Sun (especially the 3 He/4He ratio during flares). So, for example, from the ratio of the intensities of gamma lines with energies of 2.223 MeV and (4–7) MeV, one can estimate the spectrum index and the number of accelerated protons in the source at an energy Ep ≤ 50 MeV. The same parameters for protons with energy Еp ≥ 50 MeV can be obtained from the ratio of fluxes of gamma quanta with energy Еγ ≥ 30 MeV to the flux of neutrons with energy Еn ≥ 20 MeV, etc. This method is mainly suitable for reconstructing the SCR spectrum in a source in the energy range of 10–100 MeV. Using data on neutrons of higher energy, it is possible to expand this interval to energies Ep ≤ 1000 MeV. The uncertainties and limitations of this method are due to an inaccurate description of the processes of generation of gamma radiation and neutrons in flares and the properties of the interaction region of accelerated particles (thick and thin targets, angular distribution of SCR, elemental composition of accelerated particles and surrounding plasma, etc.). In particular, the enrichment of SCR with heavy particles can significantly affect the number of generated neutrons. Due to the uncertainties in the 4He/1H ratio, which can vary greatly from flare to flare (see Table 6.1), as well as the composition of accelerated and background particles, the flare geometry, etc. the proton spectrum index also changes in the range 2.5–4.5. Figure 8.5 provides a summary of the nuclear physics processes associated with the generation of gamma radiation. The main astrophysical applications of solar gamma astronomy are also indicated: the study of the composition of the solar atmosphere, photospheric content of 3He, the spectrum of accelerated particles, etc. Thus, gamma astronomy of flares serves as a link between the physics of the Sun as a star, nuclear physics and plasma physics (through particle acceleration). Of particular interest are data on the content of 3He in the photosphere. In cosmology, it is generally accepted that the primary stable isotope of helium 3 He was formed in the process of nuclear fusion at an early stage of the evolution of the Universe, and its content imposes certain restrictions on cosmological models. It is impossible to determine spectroscopically the 3He abundance at the Sun, therefore, indirect, but independent estimates of the 3He/1Н ratio, for example, from data on the gamma line with an energy of 2.223 MeV, are extremely important. The fact is that flare neutrons are captured not only by hydrogen nuclei 1Н with the generation

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Fig. 8.5 Gamma-ray spectrum from the flare of June 4, 1991 as observed by the CGRO/OSSE spacecraft (Share and Murphy 2000). Some nuclear-physical processes associated with the generation of gamma radiation are noted. The main astrophysical applications of solar gamma astronomy are indicated: the study of the composition of the solar atmosphere, the content of 3He in the photosphere, the SCR spectrum, etc.

of deuterium 2H (a stable isotope of hydrogen) and the emission of a gamma quantum with an energy of 2.223 MeV (this radiation is sometimes also called the deuterium line). 1

H þ n → 2 H þ γ ð2:223 МэВÞ

ð8:1Þ

but also with 3He nuclei with the formation of tritium (a radioactive isotope of hydrogen). 3

He þ n → 1 H þ 3 H

ð8:2Þ

In this latter reaction, neutrons are captured without generating gamma radiation (radiationless capture). The formed tritium undergoes β-decay with a half-life of 4500 ± 8 days (12.32 years), while 3He is again formed, etc. As a result, the number of neutrons participating in the generation of the 2.223 MeV line in the photosphere and the flux density of this radiation strongly depend on the concentration of 3He nuclei in the solar atmosphere. Indeed, the cross sections for reactions (8.1) and (8.2)

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Table 8.1 Observational data of 3He content in the photosphere (Miroshnichenko 2014a, b) He/1H (×10-5) 10 terrestrial days. Recently, Maehara et al. (2012) discovered 365 superflares on Sun-like stars. The data were obtained from observations on the Kepler spacecraft. These observations indicate that superflares are associated with much larger sunspots than appear on the Sun, and occur much more frequently on rapidly rotating stars. Among 365 flares, the authors identified 14 superflares on stars similar to the Sun (these are slowly rotating type G main sequence stars, which have a rotation period of more than 10 terrestrial days and an effective surface temperature within 5600 °K < Teff < 6000 ° K). Based on these data, the frequency of superflares of various energies was estimated. So, at an energy of ~1034 erg, one such flare can occur once in 800 years, and at an energy of ~1035 erg, once in 5000 years. Simple calculations (Shibayama et al. 2013), combined with the results of analysis by Maehara et al. (2012), show that at the current level of solar activity, superflares with energies of ~1034 erg can occur on the Sun once every 800 years. Recall that the energy of the solar flares observed so far is 100 times less. In addition to these estimates, it should be noted that the differential energy distribution of superflares has a power-law shape with an exponent αG = -1.5 ± 0.3

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Fig. 9.2 The frequency of superflares in type G stars (histogram at the bottom) (Shibayama et al. 2013), in comparison with the frequency of solar flares. The solid bold line in the histogram shows the differential frequency distribution of superflares on stars like the Sun, with an exponent of 1.5 ± 0.3. Dashed, dotted, and dash-dotted lines are power-law distributions of solar flares in the extreme ultraviolet, in soft and hard X-rays, respectively. The thick red line corresponds to the theoretically expected power function with exponent 1.8; the blue oval is the most powerful solar flare

(see for details Aschwanden 2012), which is close to the solar flare distribution exponent αS = -1.8 (Fig. 9.2). Moreover, as it may be shown, the exponent for peak fluxes of soft X-ray (SHR) radiation αX = 1.98 ± 0.11 remains unchanged (invariant) during three solar cycles. In fact, only this type of solar (flare) activity can be convincingly explained theoretically: the value of αX agrees with the predicted value of the exponent αF = 2.0, which follows from the model by Aschwanden (2012) of fractal diffusion self-organized criticality (FD-SOC) for solar plasma. It is interesting to note that superflares on stars like the Sun, solar flares, microflares, and nanoflares are located approximately (roughly) near the same line corresponding to a power law with exponent 1.8 (bold red line in Fig. 9.2) for a wide range of energies from 1024 up to 1035 erg.

Chapter 10

Energetic Particles in the Geosphere

“Gutta cavat lapidem”—“A drop wears away a stone”. P. Ovidius Naso

As known, the ionosphere and the neutral atmosphere of the Earth are constantly exposed to energetic charged particles of extraterrestrial origin, first of all—of galactic cosmic rays, and at sometimes—and of particles accelerated by the Sun. In addition, particles of radiation belts (ERBs) are always present in the Earth’s magnetosphere. This corpuscular environment of the Earth, along with the electromagnetic radiation of the Sun, plays a huge role in the physics of near-Earth space and in solar-terrestrial relations in general. Below we briefly consider some of the effects caused by the action of energetic particles on various layers of the ionosphere and atmosphere (Fig. 10.1). In recent decades, significant progress has been made in understanding the geophysical effects of cosmic rays, especially of solar origin, so to illustrate these effects, as in the previous chapter, we again turn to SCR. Their impact leads to such phenomena as the absorption of short radio waves in the ionosphere (the PCA effect in the polar caps of the Earth), the depletion of the ozone layer (O3), and increased conductivity in the global electrical circuit (GEC) of the atmosphere. In this case, changes in the parameters of Schumann resonances in the “Earth-ionosphere” waveguide and deterioration of the transparency of the atmosphere are also observed. In addition, at the heights of the stratosphere, and especially in the lower atmosphere (troposphere), there are processes of generation of some cosmogenic isotopes-radionuclides (radiocarbon 14C and radioactive isotopes 10Ве, 26Al, 36 Cl). Numerous nitrogen compounds are also formed here, including NOx nitrates (i.e., nitrogen oxide and dioxide—NO and NO2, respectively). It also cannot be ruled out that SCRs can directly or indirectly (through the global electric circuit, GEC) affect the dynamics of purely tropospheric (meteorological) phenomena (for example, atmospheric vorticity).

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 L. Miroshnichenko, Solar-Terrestrial Relations, https://doi.org/10.1007/978-3-031-22548-2_10

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Fig. 10.1 Diagram of the structure of the Earth’s atmosphere (http://csep10.phys.utk.edu/astr161/ lect/earth/atmosphere.html)

10.1 Earth’s Atmosphere and Cosmic Rays Cosmic rays (mainly GCR) occupy a huge energy range, covering 15 orders of magnitude (from ~106 to ~1021 eV). The Sun is also a source of cosmic rays, and the SCR fluxes after powerful solar flares can reach very high values. However, the characteristic value of their energy usually does not exceed 109–1011 eV. Therefore, the division of cosmic rays into galactic and solar rays reflects the essence of the matter, since both the characteristics and the sources of SCR and GCR are completely different. The impact of cosmic rays of particles on near-Earth space occurs through two main channels: ionization of the ionosphere-atmosphere and nuclear interactions with the substance of the lower atmosphere (troposphere), mainly with nitrogen and oxygen atoms, which are the main components of the Earth’s atmosphere. Both of these processes strongly depend, first of all, on the energy of primary cosmic particles, as well as on the density of gas in different layers of the atmosphere, i.e. on the height of interaction. For example, several decades ago, the effect of absorption of radio waves at frequencies of ~30 MHz in the Earth’s polar caps (PCA) was discovered and well studied. The PCA effect is entirely due to the additional ionization of the atmosphere at altitudes of 30–110 km during the invasion of solar protons with energies of 10–30 MeV. Similarly, the ionization process is the reason for the massive formation of nitrogen oxide ions NO, as well as oxides NO2, NO3, N2O5, HNO3 at altitudes of about 15 km and higher (Fig. 10.1). Moreover, in the

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Earth’s Atmosphere and Cosmic Rays

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case of the arrival of SCRs, the main invasion of solar protons with energies less than 100 MeV occurs at high latitudes (within the auroral zone). In contrast, the generation of cosmogenic isotopes, for example, is associated with nuclear interactions of primary cosmic rays in the atmosphere below 30 km. At the same time, cascades of a large number of different secondary particles are born in the atmosphere (Fig. 8.2). Secondary particles are then absorbed with increasing atmospheric density, some of them reach the Earth’s surface, and the most energetic ones (for example, muons) can penetrate to considerable depths (up to several kilometers). To understand the features of the effect of ionizing radiation on the atmosphere, it is important to note that the modern atmosphere consists mainly of nitrogen (78–79%) and oxygen (20–21%). These gases are known to be highly reactive, which explains their exceptional role in atmospheric physics (see, for example, Sect. 10.4). Other gases make up no more than 1%. The original atmosphere of the Earth, apparently, was similar in composition to a protoplanetary nebula and close to the modern gaseous atmospheres of giant planets. Then it was lost and replaced by gases released from the earth’s crust. It is possible that comets, planetesimals and cosmic dust had a significant influence on the formation of the modern atmosphere. It is also believed that almost all the oxygen in the atmosphere is of biogenic origin. Several layers are clearly distinguished in the structure of the atmosphere (Fig. 10.1). The main weather events form in the surface layer called the troposphere, where downdrafts and rises are constantly moving. The air pressure at the top of the troposphere is only 10% of the pressure at the Earth’s surface (at sea level). There is a thin transition layer between the troposphere and stratosphere, called the “tropopause”. Above the troposphere is the stratosphere, dominated by horizontal air currents. The thin ozone layer in the upper stratosphere has a high concentration of ozone, which is formed and varies according to the mechanism proposed by the outstanding English geophysicist S. Chapman 80 years ago (see Sect. 10.5 for more details). The ozone layer absorbs ultraviolet radiation from the Sun and protects the Earth’s surface, its biosphere from dangerous excessive radiation. Above the troposphere, there are vast layers of the mesosphere and ionosphere (or thermosphere), where many atoms are ionized (O+, N+, NO+, He+, H+ and others), i.e. lost some of their electrons. The structure and properties of the ionosphere are mainly determined by the vertical distribution of the concentration of free electrons. The degree of ionization of the ionosphere affects, in particular, the propagation of radio waves over long distances. The ionosphere is also the medium where the auroras are generated. The structure and dynamics of the ionosphere are very sensitive to the level of solar activity. As already noted, when invading the Earth’s atmosphere, primary cosmic rays destroy the nuclei of the most common elements in the atmosphere—nitrogen and oxygen—and generate a cascade process in which all currently known elementary particles participate (Fig. 10.2, right). In particular, such secondary particles as protons and neutrons, mesons, electrons, as well as γ-quanta and neutrinos are produced. The path traveled by a cosmic ray particle in the atmosphere before the

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Fig. 10.2 Primary cosmic rays in space, a cascade of secondary cosmic rays in the Earth’s atmosphere, and hard secondary muons at various underground depths (Shea and Smart 2000)

collision is usually characterized by the amount of matter in grams enclosed in a column with a cross section of 1 cm2, i.e. express the range of particles in g/cm2 of atmospheric matter. This means that after passing through the atmosphere x g/cm2 by a proton beam with an initial intensity I0, the number of protons that did not collide will be equal to I = I0 exp. (-x/λ), where λ is the average path of a particle. For protons, which make up the majority of primary cosmic rays, the range λ in air is approximately 70 g/cm2. The protons experience their first collision with the atmosphere on average at an altitude of 20 km (x ≈ 70 g/cm2). The thickness of the atmosphere at sea level (sea level) is equivalent to ≈1030 g/cm2, i.e. corresponds to about 15 nuclear ranges for protons. Hence it follows that the probability of reaching the Earth’s surface without experiencing collisions is negligible for a primary particle. Therefore, on the Earth’s surface, cosmic rays are detected only by the weak effects of ionization created by secondary particles. Since the particles of cosmic rays differ in their energies by ~1015 times, very different methods and devices have to be used to study them (Fig. 10.2, left). In this case, for example, equipment installed on satellites and space rockets is widely used. In the Earth’s atmosphere, measurements are carried out using small balloons and large high-altitude balloons; various ground installations (detectors) are used on its surface. Some of them reach the size of about 3000 km2 (for example, the “Project Auger” Observatory in Argentina), others are located either high in the mountains, or deep underground, or at great depths in the ocean, where only secondary particles of high energies penetrate. For almost 70 years, the worldwide network of stations for studying cosmic ray variations—standard neutron monitors and muon telescopes—has been

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continuously registering cosmic rays on the Earth’s surface. Observations at large (non-standard) installations for studying extensive air showers (EAS) provide unique information about GCR and SCR. Outside the atmosphere, cosmic rays, as one of the main factors of space weather, are studied on a regular basis using satellites and interplanetary probes (up to the heliosphere). The radiochemical analysis of the content of isotopes formed by cosmic rays in meteorites, lunar regolith and in other samples of extraterrestrial matter provides valuable information about high-energy particles of solar and galactic origin. Separating isotopes formed by solar and galactic particles is possible due to the difference in their energy spectra. The SCR flux is richer in particles of low energy. For this reason, SCRs can penetrate into matter only to a small depth. In this case, they lose their energy mainly on the ionization of target atoms, and not on the formation of isotopes. GCR particles spend most of their energy on nuclear interactions, moreover, in deep layers of the target. Thus, the number of isotopes will depend differently on the depth of the layer in the target when irradiated with solar and galactic particles. The indicated difference in the energy spectra of GCR and SCR leads to significantly different ionization profiles in the atmosphere.

10.2

Ionization and Conductivity of the Atmosphere

As can be seen from Table 10.1, cosmic ray fluxes are the only source of ionization in the atmosphere at altitudes h = 3–35 km. Thus, cosmic rays determine almost all electrical properties of the atmosphere: the formation of ions, the electrical conductivity of air, the formation of thunderstorms, the occurrence of lightning, etc. Atmospheric electricity plays an important role in weather and climate changes. Cosmic ray fluxes are modulated by solar activity. Thus, we have the following chain: variations in solar activity → modulation of the cosmic ray flux → changes in the atmospheric electricity circuit and, finally, → changes in weather and climate. In this chain, after powerful “solar storms”—the generation of flares and ejections of coronal matter, in addition to modulation of GCRs, another agent appears—solar cosmic rays, which cause a number of interesting effects in the atmosphere. Calculations of ionization altitude profiles for specific solar events were carried out by Table 10.1 Average annual rates of ion production in the Earth’s atmosphere for various natural sources of ionization (Ermakov and Stozhkov 2003) Ionization source Natural radioactivity (h < 3 km) Galactic cosmic rays (everywhere in the atmosphere) Solar cosmic rays and precipitation (polar latitudes, sporadic) UV and X-solar radiation (h > 50 km) Solar wind (ionosphere) Lightning (regions with thunderstorm activity, h < 10 km)

Rate of production, pair/s 20%) decrease in ozone content at high latitudes in the stratosphere, above the level with a residual air pressure of 4 mbar (Fig. 10.7). Of course, the total energy of fast solar protons penetrating into the Earth’s atmosphere during individual SPEs is not comparable with the energy coming from the Sun in the form of electromagnetic radiation (solar constant Q = 1360 W/m2). This means that the SCR energy is completely insufficient to maintain, for example, a typical stratospheric disturbance. This disproportion, however, becomes less sharp, if we bear in mind that the geomagnetic field concentrates the main SCR flux at high latitudes, where the effects of electromagnetic radiation are minimal, especially under local winter conditions. Therefore, it is natural to expect that possible meteorological effects from SCRs will manifest themselves more clearly just at high latitudes and will be more pronounced in winter. As mentioned above, this is precisely the situation that was observed after two SPEs in August 1972. The effects of depletion of the Earth’s ozone layer after solar flares were observed in many other cases, for example, in September–October 1989, in May 1990, in October 2003, in December 2006. Along with the well-studied phenomenon of PCA mentioned above, the depletion of the ozone layer is one of the most reliable atmospheric SCR effects. Next, we will consider a few more examples of less (and/or poorly) studied, and/or only supposed (expected), atmospheric effects of cosmic rays in the chain of solar-terrestrial connections. Among these effects, a special place is occupied by the undoubted effect of SCR on the global electrical circuit (GEC).

10.6

Global Electrical Circuit

The problem of global atmospheric electricity (or global electrical circuit, GEC) has been around for about 100 years. For the first time, the idea of the GEC was put forward by C.T.R. Wilson (1922). The current atmospheric electricity scheme assumes that there is a certain potential difference between the ionosphere and the Earth’s surface, which generates an electric current directed downward in areas with good weather. In this case, the ionosphere, by definition, is a highly conductive medium, and in the stratosphere and troposphere, the charges necessary for the

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Fig. 10.8 The simplest diagram of the GEC machine in the Earth’s atmosphere with several elements with different resistance (ionosphere, stratosphere, troposphere, surface of the Earth) and ionizing radiation fluxes (Markson 1978)

transfer of current are provided due to the ionization of the air by cosmic rays (see Table 10.1) and lightning discharges. The GEC passes through several regions (Fig. 10.8) with different values of electrical resistance (ionosphere, stratosphere, troposphere, Earth’s surface). The main generator of atmospheric electricity is generally considered to be thunderstorms in areas with inclement weather. In detail, the picture of the formation of thunderclouds, the separation of charges in the atmosphere and the generation of lightning turns out to be quite complex (see below). Equatorial and low latitudes are characterized by smaller changes in conductivity due to the invasion of energetic particles than high or polar latitudes. The main generator of electricity is tropical thunderstorms, which create an ionospheric potential of about 250 kV over most of the Earth. In the polar regions, the potentials “day-night” and “pole-pole” are created due to the interaction “solar wind-magnetosphere-ionosphere”. The “heart” of the atmospheric electrical machine is a thundercloud, more precisely, a set of simultaneously “working” one and a half thousand thunderstorms, distributed in the lower part of the atmosphere—the troposphere. A thundercloud does not live so long—from an hour to several hours. But some thunderstorms are being replaced by others that form in the troposphere in the neighborhood. Observations from satellites show that the frequency of lightning discharges over the ocean surface is, on average, an order of magnitude lower than over continents in the tropics. One of the reasons for this asymmetry is intense convection in continental regions, where the land is effectively heated by solar radiation. The rapid rise of heated air saturated with moisture contributes to the formation of powerful convective clouds, in the upper part of which the temperature is below— 40 °C. As a result, particles of ice, snow grains, hail are formed, the interaction of which against the background of a fast ascending flow leads to the separation of charges. Over the oceans, the height of the clouds is on average lower than over the continents, and the electrification processes are less efficient. Recently, another factor has been discussed—the difference in aerosol concentrations over the ocean

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Fig. 10.9 Various phases of a thundercloud life: (a) formation; (b) maturity phase; (c) degradation phase. The numbers indicate: 1—the area of the warm front; 2—area of the cold front; 3— ascending stream of moist ionized air; 4 and 5—extensive air showers (EAS) of secondary cosmic particles generated by primary GCRs with energies E ≥ 1014 and 1015 eV, respectively; 6— electrical discharges inside the cloud; 7 and 8—digits directed down and up, respectively; 9— negatively charged shielding layer; 10—positive charge at the base of the cloud; J—is the current from negative ions flowing from the ionosphere to the top of the cloud (Ermakov and Stozhkov 2003)

and continents. Since aerosols serve as condensation nuclei necessary for the formation of particles in supercooled air, their abundance over land increases the likelihood of strong electrification of the cloud (Fig. 10.9). A quantitative analysis of this factor requires detailed experiments that are just beginning. Among other characteristics of the cloud, Fig. 10.9 mentions the possible participation of cosmic rays of high and ultrahigh energy E ≥ 1014–1015 eV in a thunderstorm discharge. According to one of the modern hypotheses, lightning discharges are caused by the so-called “extensive air showers” (EAS) of charged secondary particles, which are generated by primary GCR particles with an energy E > 1014 eV during their interaction with the nuclei of the Earth’s atmosphere (e.g., Ermakov and Stozhkov 2003). An alternative hypothesis assumes that lightning discharges are caused by avalanches of energetic electrons that are formed (accelerated) in strong electric fields of a thunderstorm cloud (e.g., Gurevich et al. 1999). In both cases, charged particles (EAS or electrons) act as a trigger for the generation of lightning. Both hypotheses are currently being intensively developed theoretically and tested experimentally.

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Cosmic Rays: A Trigger for Tropospheric Processes?

About 30 years ago Pudovkin and Raspopov (1992) proposed a general, rather detailed, but complex scheme of the possible influence of cosmic rays of galactic and solar origin on the troposphere (Fig. 10.10). With all the conventionality of this scheme, it can be seen from it that the main (energetic) effect on the earth’s atmosphere is exerted by the sun with its electromagnetic radiation (95%), while no more than 5% remains on the other effects. In this case, GCR and SCR look like a “lateral branch” of this influence. At the same time, already at the level of the middle and lower atmosphere (see Fig. 10.1), the authors admit direct physical and chemical interactions of energetic solar particles (protons) and GCRs with atmospheric particles. It is in the lower atmosphere that, apparently, the main factor associated with cosmic rays comes into play, namely, the appearance of free charges in ionized air. Free charges (especially negative ions) can serve as nuclei for condensation of water vapor, which contributes to the formation of clouds and, ultimately, leads to a change in the transparency of the atmosphere. In other words, as noted in the diagram, the

Fig. 10.10 General scheme of the influence of solar activity and cosmic rays (GCR and SCR) on tropospheric processes (Pudovkin and Raspopov 1992)

10.7

Cosmic Rays: A Trigger for Tropospheric Processes?

141

Solar activity Stored energy of cooled steam

Solar energy

ionization

min max

CR ionization

clouds Condensation

Albedo

Input output Gain > 107

weather and climate phenomena

−90°

−60°

−30°

0°

30°

60°

90°

latitude

Fig. 10.11 The mechanism of GCR influence on tropospheric processes (Krymsky 2002). Left—“two-stage amplifier” of the effect of ionization on the atmospheric albedo. On the right is the latitudinal distribution of solar energy input, which determines vaporization, with a maximum at the equator. The latitudinal course of ionization generated by CR has two maxima, the amplitude and position of which changes somewhat during the 11-year SA cycle. It is completely different from the latitudinal behavior of absorption of solar energy (light), which has a maximum at the equator. The difference between the two latitudinal distributions should contribute to the emergence and maintenance of meridional air circulation in the atmosphere, i.e. the movement of air masses mainly along the geographic meridian (from the equator to the poles)

atmosphere becomes a “gray filter” for the electromagnetic radiation of the Sun. All these processes develop against the background of variations in the level of solar activity (including changes in the solar wind power), which determines the frequency of events and SCR fluxes, and also modulates the GCR intensity (for example, during an 11-year cycle). Already in this example, one can see the complex, “multi-storey” (multi-link) nature of the impact of solar activity on the Earth’s troposphere. The complexity of the problems associated specifically with cosmic rays is that there is no direct relationship between the SA level and the magnitude, for example, ΔT°C. Obviously, cosmic rays play the role of a mediator and/or trigger in the transfer of energy from solar disturbances into the Earth’s atmosphere. Let us consider in general outline the scheme of a possible trigger mechanism, which is based on the enhancement of the weak effect of cosmic rays on powerful tropospheric processes. A schematic of such a “two-stage amplifier” is shown in Fig. 10.11 (Krymsky 2002). His idea is reduced to a change in the reflectivity (albedo) of the Earth in relation to solar electromagnetic radiation under the influence of cosmic rays. The albedo changes over time. The albedo of cloudiness and the Earth’s surface itself changes most noticeably. In this case, the main influence on the Earth’s climate is exerted by variations in the albedo of the cloud cover, with which the variations in the albedo of the earth’s surface are directly related. So, with an increase in cloud cover, the temperature of the surface air decreases, which leads to an increase in the snow (ice) cover and, accordingly, the albedo of the Earth’s surface layer, and vice versa. In the diagram of Fig. 10.11 (left), the “input signal” of the amplifier is ionization from cosmic rays, which, through additional condensation of water vapor, leads to increased cloudiness. This leads to an increase in the cloud albedo, and then the albedo of the earth’s surface. In other words, cloud formation regulates

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the albedo of the atmosphere (the reflection of sunlight back into space), i.e. the supply of solar energy to the surface of the Earth. Obviously, the “output signal” of the amplifier can be various weather and climate phenomena. The mechanism of occurrence of one of these phenomena becomes clear from the right side of Fig. 10.11. Indeed, the latitudinal distribution of ionization in the atmosphere (a doublehumped curve with maxima at latitudes of about ±60°) is completely different from the latitudinal behavior of absorption of solar energy (light), which has a maximum at the equator. The difference between the two latitudinal distributions should contribute to the emergence and maintenance of meridional air circulation in the atmosphere, i.e. the movement of air masses mainly along the geographic meridian (from the equator to the poles). What should be the gain in such a circuit? Comparing the fluxes of energy supplied to the Earth’s atmosphere by solar radiation (“solar constant” 1.36 × 103 W/m2) and galactic cosmic rays (≈10-5 W/m2 at particle energy E > 0.1 GeV), we obtain the gain k ≈ 1.36 × 108. Tinsley and Deen (1991) were the first to estimate k > 107. As follows from Fig. 10.11, the value of k can change during the transition from the maximum to the minimum of solar activity, which significantly modulates the GCR flux. As for the specific physical models linking the formation of clouds with cosmic rays, at present the most substantiated ones are based on two different hypotheses. One of them assumes that due to the ionization of the atmosphere by cosmic rays, the number of condensation nuclei increases, on which water droplets of the future cloud are formed. In the second hypothesis, it is believed that the ionization of air by cosmic rays modulates the entire “ionosphereEarth” electric current circuit. This, in turn, affects the properties of the cloud through the influence of charge effects on the freezing of drops. In this area, serious field and laboratory experiments at the microphysical level are already being carried out or are being planned. For example, let us mention one of them—a very large-scale experiment called CLOUD (Cosmics Leaving Outdoor Droplets); it has already been carried out since November 2009 at the International Center for Nuclear Research (CERN) in Switzerland (Kirkby 2009). The experiment uses an aerosol chamber with a diameter of 4 m and a cylindrical diffusion chamber (usually called a Wilson chamber) with a diameter of 0.5 m, which are irradiated by accelerated protons from the accelerator (Proton Synchrotron at CERN), and the proton beam simulates the GCR flux at any height and latitude. The chambers are filled with air and water vapor, and also contain small additives of rare gases and aerosols; they are capable of operating at any temperature and pressure that may occur in the real earth’s atmosphere. This is the first time that a high-energy particle accelerator has been used for atmospheric physics purposes. The main goal of the experiment is to test the mechanisms of water vapor condensation in the presence of cosmic rays. The expected results could dramatically change the understanding of weather phenomena and the causes of climate change.

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Other Cosmic Ray Effects in the Atmosphere

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Other Cosmic Ray Effects in the Atmosphere

As follows from the above, GCR and SCR cannot pretend to be the main factor in the system of solar-terrestrial connections. But their role and contribution to the problem of solar-terrestrial relations have been evaluated and understood so far clearly insufficiently, especially if we are talking not about cause-and-effect aspects, but about physical mechanisms. Below, using SCR as an example, we provide additional evidence in favor of the real physicochemical effect of ionization on the state of the earth’s atmosphere. In addition to the well-studied effects of the depletion of the ozone layer, the formation of nitrates and cosmogenic isotopes, discussed above, it should be noted, in particular, disturbances in the GEC, variations in the parameters of Schumann resonances in the Earth-ionosphere waveguide, and deterioration of atmospheric transparency after the intrusion of SCR fluxes. The effect of SCR on the vorticity of the atmosphere in the northern hemisphere of the Earth was also statistically revealed. The contribution of GCR and SCR and their relative role in the chain of solarterrestrial connections remain insufficiently studied. But it is important to emphasize that it is precisely the observations of atmospheric SCR effects that put the problem on a real basis, especially in terms of understanding the physical mechanisms of the observed and expected (assumed) effects. For example, we will give data on disturbances in the global atmospheric electricity chain after powerful solar flares. Figure 10.12 shows how the air-to-Earth current density over the South Pole changed as measured in the stratosphere during the prominent solar event on November 22, 1977 (Cobb 1967, 1978). This almost classical proton event was clearly recorded in a wide range of energies—from ~10 MeV (on satellites) to several GeV (according to observations on the Earth’s surface, on neutron monitors). The corresponding flare at 09:45 UT with heliocoordinates N24°, W40° was moderately strong (score 2B), the flux of protons with energies ~10 MeV was also moderate (≥330 pfu), however, geophysical effects of this flare appeared quite clearly. For example, typical absorption of short radio waves in the polar cap (X-ray diffraction effect) began as early as 11:00 UT, reached a maximum at about 14:00 UT, and then continued for 3.5 days. Fig. 10.12 Variations in the air-to-Earth electric current density measured over the South Pole after a large SCR flux from the November 22, 1977 flare into the polar stratosphere (Cobb 1967, 1978)

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Figure 10.12 shows that on the eve of the outburst, the current density had a normal altitude profile, and already on November 23 and especially on November 24, the current density increased sharply (approximately two times at altitudes of 25–30 km). Then it began to decrease rather quickly and by November 26 returned to almost the initial (pre-flare) level. The behavior of the GEC parameters during the event on February 16, 1984 was studied in even more detail, when it was possible to simultaneously measure the total conductivity of the atmosphere, the vertical electric field, and the vertical current density (for details see Miroshnichenko 2008). The admittance and the magnitude of the vertical current reacted especially sensitively to the SCR invasion. Particularly strong fluctuations in the parameters of the electric field in the stratosphere were observed during the large proton event on January 20, 2005. In particular, a strong increase in vertical conductivity was noted simultaneously with a sharp increase in the flux of energetic protons near the Earth. After the maximum of the proton flux, sudden jumps in the magnitude of the vertical electric field were also observed for several hours (for details see Miroshnichenko 2008). These examples show that the effect of SCR on the atmospheric electricity circuit can be detected by direct observation (measurement). There are, however, SCR effects that can only be detected by statistical analysis. These include, in particular, variations in the parameters of the so-called Schumann resonances in a waveguide formed by two conducting shells—the ionosphere and the Earth’s surface. Schumann resonances (SR) are resonant electromagnetic waves in the Earth-ionosphere cavity with a fundamental frequency of about 8 Hz and higher-order modes spaced by about 6 Hz. After their prediction and theoretical discussion by Schumann (1952), they were widely studied for several decades. At present, it is generally accepted that lightning discharges from a cloud to the Earth’s surface in the processes of global thunderstorm activity are the main sources of SR excitation. Since SCRs, as we have seen, change the conductivity conditions in the Earth-ionosphere waveguide, noticeable variations in the SR parameters should be expected during solar proton events (SPE). Such variations were indeed detected from observations during two large SPEs in October 1989 and March 1991. Figure 10.13 shows the results of the epoch superposition analysis for nine SPEs of the 22nd solar cycle (left) and for 24 solar electron events (SES) for the period 1994–1995 (on right). It can be seen that during SPE, the SR parameters (frequency, attenuation, amplitude) fluctuate approximately twice as strong as during SPE. The superimposed epoch method also revealed changes in the behavior of cyclonic eddies in the atmosphere over the North Atlantic. The area of the Arctic Front in the North Atlantic off the southeastern coast of Greenland is one of the most cyclonic places in the earth’s atmosphere. This region has long been of particular interest for the study of solar-atmospheric relations as an area of intense formation and development of extra-tropical cyclones, which strongly affect the weather of middle latitudes. It was previously shown that cyclonic activity is definitely influenced by various heliogeophysical phenomena. However, the physical mechanism responsible for these effects remains unclear. In particular, it was suggested (see above) that air circulation in the lower atmosphere can be closely related to SCR

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Fig. 10.13 Variations in the parameters of Schumann resonances (SR) in the Earth-ionosphere waveguide during solar proton (left) and electronic (right) events. The first row from the top—fluxes of energetic protons and electrons; the second, third and fourth rows are the frequency, attenuation and amplitude of the SR, respectively (for details see, e.g., Miroshnichenko 2008)

and GCR particles with energies from ~0.1 to several GeV. Veretenenko and Thejll (2005), analyzing upper-air sounding data, found a significant decrease in atmospheric pressure near the Arctic front of the North Atlantic, which appeared to be in correlation with fluxes of solar protons with energies >90 MeV (Fig. 10.14).

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Fig. 10.14 Average values of the sums of the relative “vorticity” at different heights over the North Atlantic in the winter periods of 1980–1996 during solar proton events. The data for 48 SPS were used; the day of the beginning of the event was chosen as the zero day (Veretenenko and Thejll 2005)

To analyze variations in pressure and vorticity index, presumably associated with the intrusion of SCR flows, 48 SPEs were selected for the period 1980–1996. The average daily values of the geopotential height were considered for the main pressure levels in the troposphere (300 and 500 mb). The dotted line in Fig. 10.14 shows the mean vorticity level for all days, and the dotted lines correspond to one, two, and three standard deviations of σ. A distinct (above 3σ) increase in the relative vorticity near the Greenland coast during the SPE is seen. This may serve as evidence that SCR invasions can participate in the generation of cyclones and enhance it. The most difficult situation is with the confirmation of a fundamentally important effect—the change in the transparency of the atmosphere under the action of cosmic rays. As has been demonstrated by many researchers, large magnetospheric disturbances associated with solar flares are accompanied by certain changes in the state of the lower atmosphere. As a rule, atmospheric disturbances go through two stages in their development. The initial (“early”) stage is accompanied by an increase in zonal

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circulation and a decrease in air temperature in the high-latitude stratosphere. The “late” stage is remarkable in that the temperature of the stratosphere increases, and the zonal circulation becomes weaker. After some energetic solar events (powerful flares, shock waves, CMEs), the proton event and geomagnetic disturbance may overlap in time. In this case, the effects from SCRs and from magnetospheric electrons released during a geomagnetic disturbance can be isolated and distinguished from each other due to the time delay of the geomagnetic disturbance relative to the arrival of solar protons. Their bulk comes to the Earth’s orbit after 1–10 h, depending on the energy of the protons, while the main phase of the geomagnetic disturbance occurs much later (usually within 24–36 h after the solar event). It is at this second stage that magnetospheric electrons play an important role. The above-described general physical concept of the influence of solar activity on the lower atmosphere and climate (Fig. 10.10) was based on extensive data accumulated, in particular, by the Russian network of actinometric stations. In combination with data on the global distribution of cloudiness, synchronous changes in cloud density after powerful solar flares were found. Hence, in antiphase with the cloudiness density, changes in solar insolation S0 on the Earth’s surface (“meteorological” solar constant) were found. Further, the authors of this concept took into account that cosmic rays are actually the only agent that is controlled by solar activity and can affect physicochemical processes in the lower atmosphere, including changes in cloud cover. Finally, it was suggested that the change in the solar energy flux entering the lower atmosphere (i.e., the variability of the atmospheric transparency) is due to variations in SCR and GCR fluxes, which are modulated by solar activity. With such prerequisites, the research group of Pudovkin in 1993–1997 managed to find some observational evidence in favor of the proposed connection. Thus, it was shown that the first stage of atmospheric disturbance after a powerful solar flare is due to solar protons with energies E > 90 MeV, while the second is associated with a Forbush decrease in the GCR flux. It turned out that with a decrease in the GCR flux, solar insolation S0 on the Earth’s surface increases, i.e. the atmosphere becomes more transparent. Hence, it is reasonable to assume that the intrusion of an additional SCR flux should have the opposite effect, i.e. reduced transparency. Some evidence of such effects has been obtained using the epoch superposition method (Fig. 10.15). The difficulty in studying the expected atmospheric SCR effect is that protons with energies E > 90 MeV arrive mainly in the polar zones of the Earth, where conditions for actinometric observations are not very favorable. Therefore, the first attempts to find the effect (Roldughin and Vashenyuk 1994) using data from the Murmansk and Arkhangelsk observatories for six separate SPEs led to uncertain results. Pudovkin et al. (1997) analyzed the actinometric data of the Olenek subauroral observatory (latitude N68.5°). At the same time, five intervals of 9 days each were identified, when the meteorological conditions made it possible to measure the S0 value daily. In 1980–1984 five SEP events were selected that met the necessary conditions. As seen in Fig. 10.15, S0 decreases by 5–10% during a proton event. Unfortunately, due to the small statistics of events and the large scatter of S0

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Fig. 10.15 Variations of solar insolation S0 (“meteorological” solar constant) on the Earth’s surface during solar proton events for the period 1980–1984 (Pudovkin et al. 1997). Point t = 0.0 corresponds to the day of the beginning of the event; the vertical lines show the standard deviations of the measured S0 values

values, it turned out to be impossible to obtain a statistically significant value of dS0. Nevertheless, the tendency of S0 to decrease in the course of the event can be traced quite clearly. It should be noted, however, that the last two points in Fig. 10.15 fall outside this trend, probably due to insufficient temporal resolution. Obviously, for the same reason, the two-step transparency variation mentioned earlier is also not visible in this figure. Although these results are not convincing enough, solar proton events are likely to cause the effect of lowering atmospheric transparency, probably in combination with the contribution of other cosmophysical factors during geophysical disturbances. In this regard, we mention strong evidence that changes in the current density in the GEC lead to changes in the properties of clouds (Tinsley and Yu 2004). Since the SCR invasion definitely causes an increase in the vertical electric current through the atmosphere, it seems quite reasonable to assume that the SCR effect on clouds is realized in an intermediate form through the GEC. Thus, the contribution of SCR and GCR to the system of solar-terrestrial connections should be recognized as very important, at least as part of the physical mechanism, which definitely affects the amount of solar energy entering the lower atmosphere. At the same time, it would be a deliberate exaggeration to ascribe too great a role to cosmic rays in the hierarchy of possible physical agents in the “Sun-Earth” system (Chap. 11).

Chapter 11

Hierarchy of Solar-Earth Relations

An imperturbable system in everything Complete harmony in nature,—Only in our ghostly freedom We recognize the discord with her”. F.I. Tyutchev

The energy of solar disturbances on the difficult path from the Sun to the Earth passes through the interplanetary medium and several invisible earthly shells—the magnetosphere, ionosphere and atmosphere. This explains one of the main features of the solar-terrestrial relation system (STR)—their “multi-storey” (mediation). In other words, in the chain of physical processes connecting the Sun with the Earth, there is a certain structure, sequence in time and space, i.e. there is a kind of hierarchy of STR. This inevitably leads to another important feature—the nonlinear nature of solar-magnetospheric, solar-atmospheric, and solar-biosphere relations. The simplest STR scheme is shown in Fig. 11.1. Among the main effects in the chain of solar-terrestrial connections, in our opinion, it is necessary to highlight, first of all, the effect on the magnetosphere and ionosphere, solar-tropospheric connections and heliobiology (the Sun and the biosphere). Of particular interest is the influence of solar activity on the rotation of the Earth (the Sun and the lithosphere). The question of the possible impact of the resonant structure of the Solar System on solar activity and solar-planetary relations in general is of fundamental importance. Finally, the energy and information aspects of solar-terrestrial relations (theories and models of physical mechanisms) are of fundamental importance. From the content of the previous chapters, it is clear how multifaceted and rich in physical ideas the problem of solar-terrestrial relations (STR) and solar-terrestrial physics (STP) in general. Within the framework of a small textbook, it is impossible to present in any detail even the main results of research, observations and experiments. Therefore, below we will give only a few, the most striking examples of the revealed connections, focusing on their possible physical mechanisms.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 L. Miroshnichenko, Solar-Terrestrial Relations, https://doi.org/10.1007/978-3-031-22548-2_11

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Fig. 11.1 The simplest diagram of solar-terrestrial relations

11.1

Extreme Solar Events and Magnetic Storms

Let’s start our consideration with the most famous solar and geophysical disturbances—powerful solar flares and large magnetic storms. Quite recently it became clear (thanks to the analysis of old magnetic data) that on September 2, 1859, a magnetic storm was registered, which turned out to be the largest in the entire history of instrumental observations. Its cause was the historically first observed solar flare on September 1, 1859. This flare, as it is now retrospectively believed, was accompanied by the ejection of a powerful magnetic cloud (CME), which became the direct cause of the storm with a record decrease in the geomagnetic index Dst ≈ 1760 nT (about the geomagnetic indignation see Sect. 9.3). This value is consistent with a decrease in the horizontal component of the geomagnetic field ΔH = 1600 ± 10 nT at the Colaba Observatory (India) at local noon (Fig. 11.2). During the storm, sparks were noted in telegraph devices in Europe, America and Australia. Among other geophysical effects, extensive auroras were also observed in this event, and at rather low latitudes (for example, on the Hawaiian Islands and in Santiago, Chile). According to modern estimates (e.g., Tsurutani et al. 2003), the energy of the September 1, 1859 flare and the velocity of the corresponding CME were extremely high, but not unique. In our time, other energetic events (they are called “extreme solar events”, or ESEs) with higher parameters are sometimes recorded, so that a storm of this order may occur again. According to their characteristics, extreme events (flares, storms, etc.) are on the high-energy “tails” of their energy distributions. Empirical data for such energetic “tails”, however, are extremely scarce (sketchy), so that the shape of the tail distributions cannot be reliably established. Consequently, the probabilities of occurrence of such energetic events cannot be

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Extreme Solar Events and Magnetic Storms

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Fig. 11.2 Magnetogram obtained during the historical helio-geophysical disturbance on September 1–2, 1859 (Tsurutani et al. 2003) at the Colaba Observatory (near Bombay, India)

estimated with any reasonable accuracy. In addition, the “saturation mechanisms” for extreme solar events are still unclear; there is insufficient understanding of the physical processes underlying the most powerful flares, storms, etc. The Sun and the magnetosphere have finite dimensions, the magnetic fields on the Sun and in the magnetosphere are also limited, so that some kind of “cutoff effect” during the energy release must take place. Even if it is possible to theoretically show that ESEs obey a lognormal distribution, it does not yet follow from this whether or not, say, flares with energies >1034 erg or magnetic storms with Dst < -1760 nT are possible. It should be recognized that empirical statistics for extreme solar flares (ESF) with the energies >1032 erg and extreme magnetic storms with Dst < -400 nT remains rather scarce. The tails of their distributions remain essentially unknown, so that distributions can be confidently constructed only for flares and storms in the region of moderate and low energies, where the number of observed events is statistically significant. In any case, according to studies by Kane et al. (1995), the previously established canonical “upper limit” for flares of ~1032 erg can be violated “with a large margin”. This was demonstrated by the example of a giant flare on June 1, 1991 with a score X12. Its total energy could be from ≤2 × 1033 to ~1034 erg, depending on the assumed mechanism of energy release (non-thermal or thermal). The resources of one active region (AR) seem to be insufficient for the generation of such a huge energy. Therefore, the authors do not exclude that such a flare may be associated not only with local, but also with global trigger instability of the corona. On the other hand, an interesting empirical technique has recently been proposed for

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estimating the probability of large solar flares (Ishkov 1998, 2012, 2017). The technique is based on a certain physical parameter—the rate of change (emergence) of a new magnetic flux. If the flux is large enough (~1013 Weber), and the rate of its change exceeds 109 Weber/s, then large flares can be expected in this AR with a high probability. The parameters included in the proposed method (AR area, change in spot configuration, behavior of their polarity, etc.) are quite accessible to observations. Thus, there are already serious observational prerequisites for testing a number of hypotheses about the mechanisms of generation of extreme solar events (ESEs). At the same time, it seems that it is still far from a clear understanding of the physical mechanisms of ESE. For more than two decades, there has been a discussion about the relative role of flares and CMEs in geophysical disturbances, about the methods of their prediction, and hence about the mechanisms of their generation on the Sun. Studies show that there is apparently no unambiguous relationship between the power of the flares, the velocity and magnitude of the CME magnetic field, and the intensity of the subsequent magnetic storm (MS). However, MS researchers definitely agree that the strongest magnetic storms are actually associated with powerful solar flares. This means that strong MSs and large flares have a common cause—magnetic reconnection on the Sun. As for the frequency of such events, the time of our instrumental observations of solar activity is still very limited (150–250 years). Therefore, there is no complete certainty that we have already managed to fix some kind of ESE (flare or storm) at the limit of its “saturation”. Can the Sun generate flares with energies of ~1038– 1039 erg? Most likely—no! However, an energy of ~1035 erg seems to be attainable for our Sun. One thing is clear: the effects of a subsequent Extreme Magnetic Storm (EMS) can be catastrophic. We now turn to a description of the statistical properties and physical characteristics of another outstanding phenomenon in the system of solar-terrestrial relations—a magnetic storm (MS).

11.2

Main Characteristics of Magnetic Storms

Magnetic storms are strong disturbances of the Earth’s magnetic field, sharply disrupting the smooth daily course of the elements of terrestrial magnetism. Storms are observed simultaneously all over the Earth. At low and middle latitudes, the changes in the magnetic field of the storm are on average: for the induction δВ = (12) × 10-7 T, for the intensity δН = (0.08-0.16)A/m. Their maximum values are, respectively, 5 × 10-7 T and 0.4 A/m. With an increase in geomagnetic latitude, the amplitudes of magnetic disturbances increase and reach the highest values in the auroral zone (62–67° geomagnetic latitude). The duration of the MS is different: from several hours to several days. The number of storms depends on solar activity; it grows with an increase in SA. Within 1 month from 0 to 8 MS can be observed. According to the degree of intensity, MSs are subdivided into very large, large, moderate and small. The higher the MS intensity, the less often it is observed.

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Main Characteristics of Magnetic Storms

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Fig. 11.3 Typical variation in the geomagnetic field during a magnetic storm observed on June 5–6, 1967 (universal time) at the mid-latitude Honolulu Observatory (Hawaii, geomagnetic latitude 21°N): 1—initial phase; 2—main phase; 3—recovery phase

Although no storm repeats another, magnetic storms show common characteristics. Figure 11.3 shows an example of a “classic” magnetic storm with all the features and elements of its temporal structure: 1. Sudden onset of a magnetic storm SC (Sudden Commencement), or SSC—Sudden Storm Commencement. Some storms begin with a sudden increase in the horizontal component of H by 15–20 nT throughout the entire Earth in 1–2 min. 2. Initial phase. Within 1 h after SC, the H-component increases and remains at a level of 30–50 nT higher than before the storm. In many storms, the initial phase is absent. 3. Main phase. A continuous decrease in H, usually by 100–200 nT over several hours. 4. Recovery phase. After reaching the minimum value, the H-component slowly, approximately exponentially, returns to normal. 5. Irregular fluctuations. They are observed for all three components of the MS and have a wide range of periods: from fractions of a minute to several hours (~3 h). Characteristics 3–5 can be repeated several times in different forms (stronger or weaker, with alternation). At high geomagnetic latitudes, such repetitions are manifested in the form of polar magnetic substorms. At low geomagnetic latitudes, they are seen in sharp decreases in the aperiodic variation (Dst-index). Specific geomagnetic pulsations are observed at all phases of the storm. The Earth’s magnetosphere is a “blunt obstacle” for the solar wind plasma (Fig. 11.4). With a supersonic flow around this obstacle, a standing bow shock is formed in its frontal part (in the sunflower region) at a distance of about 10–12 Earth radii RE. In the anti-solar direction, the lines of force of the magnetosphere are elongated in the form of a “tail” (magnetotail), which can be traced to a distance of about 1000 RE. The outer boundary of the magnetosphere is called the magnetopause and can be 100–200 km thick. The position of the magnetopause depends on the flux density (momentum) of the solar wind particles. In some strongly disturbed periods, it can approach distances of 6.6–8.0 Earth radii. The region surrounding the magnetopause contains the plasma of the solar wind after the shock wave and is called the magnetosheath, or transition region. The

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Magnetosheath Magnetopause Cusp Magnetotail

Solar

Plasmasheet

Neutral point Wind Plasmasphere Bow Shock

Fig. 11.4 An idealized two-dimensional (flat) model of the Earth’s magnetosphere and the simplest scheme of solar wind flow around it

geomagnetic field at high latitudes has a rather complex structure. The most notable feature of the polar magnetosphere is the polar depressions—cusps. The cusp is a funnel-shaped region of weak magnetic field around the neutral point, where direct penetration of the solar wind up to the upper atmosphere becomes possible along the geomagnetic field lines. The size of the polar cusp on the daytime side is from 2° to 5°, or ≈1200 km in its upper part and 12 km—at the Earth’s surface. On the night side, there is another region, which is called the polar cusp in the tail of the magnetosphere. This cusp outlines the boundary of the auroral oval in the night sector. Between these two cusps is an area called the polar cap. On the night side of the magnetosphere there is an extensive plasmasheet, which has a special neutral point, where the reconnection of the lines of force of the northern and southern hemispheres of the Earth takes place. Closest to the Earth’s surface, above the ionosphere, at an altitude of ≥1000 km, is the plasmasphere—a region of cold plasma of ionospheric origin with high density. It extends up to 3RE (and sometimes up to 7RE). In this region, the lines of force of the dipole magnetic field and the plasma located on them rotate with the Earth. In addition to the plasmasphere, the trap created by the geomagnetic field effectively traps a small group of very energetic particles that form the Earth’s radiation belts (ERBs). ERBs were discovered in 1958: the inner proton belt—in experiments on the American satellites Explorer-1, -3, the outer electron belt—in experiments on the third Soviet satellite. ERBs consist mainly of electrons and protons with energies from ~100 keV to several hundred MeV. These energetic particles have a very diverse origin—solar wind, GCR and SCR, anomalous

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Main Characteristics of Magnetic Storms

155

component of GCR, and even the Earth’s ionosphere (for more details, see Sect. 5.3). The ERB particles fill almost the entire region of the dipole/quasi-dipole magnetic field in the Earth’s magnetosphere. From the point of view of the physics of magnetic storms, it is important that these particles serve as the basis of the MS mechanism. Disturbances of the magnetosphere are known to be caused by variations in solar plasma fluxes from active regions of the Sun. An interplanetary shock wave is ahead of the enhanced solar wind flux. If it reaches the Earth’s magnetosphere, then it manifests itself in the form of a sudden onset of MS (SSC). The compression of the magnetosphere manifests itself on Earth in the form of an initial MS phase. The response of the magnetosphere is an increase in the so-called ring current and, as a consequence, a decrease in the horizontal component of the geomagnetic field at middle and low latitudes. The ring current exists even during quiet periods (without a storm) due to the drift of captured protons with energies of tens to hundreds of keV. This quiet ring current flows over a distance of 2.5–4 RE. It is the effective current created by protons drifting westward and electrons drifting eastward in the Earth’s dipole field. The drift movement is mainly due to the gradient force ΔB and manifests itself as a current directed to the west. A typical decrease from tens of nT to ~200 nT lasts from several hours to a day or more. The value of the Dst-index rather accurately represents the intensity of the main phase of the storm. The decrease in the field in the main phase is explained by the enhancement of the quiet ring current. It has been firmly established by recent satellite experiments that the ring current exists at distances from 3 to 5 RE during the main phase. This is due to the penetration of new particles into the magnetosphere or the acceleration of the plasma available in it to energies of the order of thousands of eV. These processes, in turn, are caused by reconnection of the lines of force of the interplanetary and geomagnetic fields and fluctuations in the size of the magnetosphere when interacting with an enhanced flux of solar plasma. As a result, an annular storm current is formed inside the magnetosphere. The increased current flowing in the westerly direction generates a magnetic field directed opposite to the geomagnetic field, and thus weakens it (the main phase of the MS). In this case, the magnetic field of the ring current almost completely compensates for the compression effect at the boundary of the magnetosphere. According to Kovtyukh (2007), the effect of compression of the real geomagnetosphere at the Earth’s surface is weakened by almost ten times. Thus, the ring current serves as a kind of buffer: it reduces the effect of the “cosmic storm”, protecting the Earth and its biosphere from sudden jumps in the magnetic field. If it were not for the ring current, biological systems would have to adapt to the much less comfortable, rapidly changing conditions of sudden changes in the magnetic field, atmospheric pressure and weather. In this sense, we can even talk about the ecological significance of the ring current during magnetic storms. The recovery phase of geomagnetic storms is associated with the decay of the ring current, i.e. with the onset of diffusion of trapped particles in the magnetosphere. The main mechanisms of particle loss are Coulomb scattering and charge exchange of protons with neutral hydrogen: i.e. reactions of the type H+ + H $ H + H+. Various

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Fig. 11.5 On the left is a photograph of a typical aurora. On the right is the auroral oval over Antarctica as observed over the south polar cap on September 11, 2005 from the satellite IMAGE (NASA). Australia is visible in the upper left corner

plasma instabilities have recently been invoked to explain both the decay of the current and the micropulsations observed during the existence of the ring current. Sharp changes in magnetospheric-ionospheric current systems manifest themselves on the Earth’s surface in the form of irregular magnetic disturbances. Magnetospheric storms are associated with coronal mass ejections (CMEs) and solar flares, and are caused by the arrival of high-speed solar plasma (see Sect. 3.4) and an associated shock wave (SW) into the vicinity of the Earth. Some geomagnetic storms have a 27-day recurrence due to the return of active solar regions after the Sun’s revolution. Magnetic storms have a pronounced 11-year dependence and are practically absent in the years of minimum solar activity. For a more complete understanding of the physics of the magnetosphere, it should be noted that the MS is an integral part of a complex geophysical process—a magnetospheric storm. This concept includes a magnetic storm proper, magnetospheric substorms, as well as aurora polaris, ionospheric disturbances, X-ray and low-frequency radiation. Of these global geophysical disturbances, the aurora is known to be the most spectacular (Fig. 11.5). By their nature, auroras are the optical glow of the upper layers of the atmosphere (mainly excited nitrogen and oxygen atoms) bombarded by auroral radiation— particle fluxes from the auroral magnetosphere with energies ranging from hundreds of eV to hundreds of keV. These particles are accelerated during magnetospheric substorms. Some of these particles, pouring out into the atmosphere, cause auroras. It was found that the shape of auroras and their dynamics are closely related to specific electrodynamic phenomena occurring in the magnetosphere—magnetospheric substorms. During substorms, the magnetosphere becomes unstable. The return to the state with lower energy is explosive and is accompanied by the release of ~1022 erg of energy in 1 h, which causes the atmosphere to glow (auroral substorm).

11.3

Energetics of the Magnetosphere

157

The auroral magnetosphere is the region of the Earth’s magnetosphere projecting onto the auroral zone, or the auroral zone. The term “substorm” was introduced in 1961 by Akasofu to denote disturbances, lasting ~1 h just in the aurora zone. In the auroral magnetosphere, the dynamic competition between the magnetic fields of the Earth’s dipole and external sources creates conditions for the development of explosive instabilities—magnetospheric substorms. Thus, auroras are the result of the complex interaction of the solar wind with the geomagnetic field. When fast electrons interact with atoms and molecules of the atmosphere, X-ray bremsstrahlung of electrons is generated. Bremsstrahlung photons with energies above 20 keV penetrate the atmosphere to an altitude of 25–30 km. Auroras also emit infrasonic waves with periods from 10 to 100 s, which are accompanied by fluctuations in atmospheric pressure with the amplitudes of 1 to 10 dyn/cm2. During MS, significant interference occurs in short-wave communication, the upper atmosphere heats up with heat transfer downward into the troposphere, which contributes to the development of circulation movements in it and the appearance of cyclones. Some frequencies of geomagnetic pulsations are close to heart rates, therefore, during MS, they can adversely affect the condition of patients (see Chap. 12).

11.3

Energetics of the Magnetosphere

In this section, we will discuss issues related to the energy of a magnetic storm. The main interest in this problem is the mechanism and rate of solar wind energy input into the magnetosphere, as well as the role of individual components of the interplanetary magnetic field in the processes of energy transfer from solar disturbances to the magnetosphere. According to available estimates, the average speed (power) of solar wind energy input into the magnetosphere is about 3 × 1018 erg/s = 3 × 1011 W. In this case, the total energy of a large magnetic storm can reach 2 × 1024 erg. Recall, for comparison, that with a large solar flare, a total energy of ~2 × 1032 erg is released. The complexity of the problem in the interaction “solar wind-magnetosphere” is that the magnetosphere can take only part of the energy coming from the solar wind. In other words, it is necessary to solve a double problem—to find an effective physical mechanism, and also to estimate its efficiency—energy transfer coefficient. Below we consider the most important physical hypotheses and empirical facts that give general ideas about the geoeffectiveness of the solar wind. The kinetic energy flux of the solar wind falling on one hemisphere of the Earth in the absence of a magnetic field can naturally be described by the formula (e.g., Olsson et al. 2004): W sw =

1 1 3 ρV 2 2 sw

πR2E

ð11:1Þ

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Hierarchy of Solar-Earth Relations

where VSW is the solar wind speed; RE is the average radius of the Earth (6371 km); ρ is the mass density of particles in the solar wind. In this formula, the first factor ½ is due to the fact that only one hemisphere is considered; the energy flux is determined only by the parameters of the solar wind, and the magnitude of the interplanetary magnetic field (IMF) is clearly not included. Until recently, the WSW parameter was not often used when discussing the energetics of the magnetosphere. However, as recently revealed by numerical MHD modeling (Palmroth et al. 2004), it correlates quite well with the total energy entering the ionosphere for those cases when the variations in energy transfer obey the parameters of the solar wind plasma rather than changes in the IMF direction . . . It may seem strange that the scale of length in the definition of WSW is the Earth’s radius. Although the size of the planet Earth, it would seem, should not be of great importance in determining the amount of solar wind energy entering the magnetosphere, they are important in determining the amount of energy entering the ionosphere, since the “contact area” of the Earth with its plasma environment is proportional to RE2. Using the WSW parameter, an interesting question can be discussed: does the average net effect of the magnetosphere serve only to protect the Earth from the flow of solar wind energy, or is it intended to act more like an “antenna” and amplify the received input energy? On the other hand, back in 1981, to describe the effective energy connection between the solar wind and the magnetosphere, S.-I. Akasofu suggested using an empirical epsilon parameter: ε = 4πl0 2 μ0 - 1 V sw B2 sin 4 ðθ=2Þ

ð11:2Þ

where l0 = 7RE is the effective radius of the magnetosphere; B—interplanetary magnetic field (IMF) module; μ0—dimensionless magnetic permeability of the medium; q is the angle of rotation of the IMF relative to the plane of the ecliptic. It is defined as the polar angle between the IMF direction in projection onto the y-z plane and the z-axis in the Geocentric Solar Magnetospheric System (GSM). In Cartesian coordinates, the IMF vector can be decomposed into three components (4.4). Then the corresponding expressions for the IMF components and angle θ will take the form: Btr 2 = By 2 þ Bz 2

θ = tan - 1 By =Bz

ð11:3Þ

and now in formula (11.2), instead of the modulus B of the interplanetary field, one can use the value of its transverse component Vtr. It can be seen from (11.2) to (11.3) that the Akasofu parameter is dependent on the ratio of all three IMF components. Recently, it was found that the Bz component of the IMF plays a special role in energy transfer (see below). The parameter ε is used quite often, and in many cases it gives a reasonable estimate of the total energy entering the interior of the magnetosphere. At the same time, a number of researchers believe that the viscous interaction (friction) between the solar wind and the magnetosphere should be taken into account. A certain fraction of the energy consumed in this case must then be taken

11.3

Energetics of the Magnetosphere

159

into account when assessing the total energy balance of the magnetosphere. Efforts have also been made to find other parameters that, when describing energy transfer, give a better correlation with auroral measurements. However, this path did not lead to a more accurate estimate of the amount of transmitted energy. Solar wind geoeffectiveness, i.e. the efficiency of its energy transfer to the Earth’s magnetosphere is maximum at a negative (southern) orientation and at large values of Bz. The physical essence of the effect is that the southern Bz-component causes magnetic reconnection with the geomagnetic field in the dayside region of the magnetopause. This, in turn, leads to the rapid injection of magnetic energy and particles into the magnetosphere. If the situation with Bs 20–30 MeV and electrons with E ~ 0.1–1 GeV of the internal ERB. Much later, when many details of the interaction of the “solar wind-magnetosphere” became known, the possibility of penetration of solar wind particles into the magnetosphere (through polar cusps) was revealed. It was then shown that the majority of ERB particles are of solar origin; earlier they were part of the solar wind. The acceleration of particles to significant energies occurs already in the magnetosphere itself. In addition, at the boundaries of the E and L ranges, in which the ERBs exist, a significant contribution is made by other sources (for more details, see Panasyuk et al. 2006). In particular, anomalous cosmic rays, consisting of singly charged ions with E/Mi ~10–20 MeV, make a certain contribution to the fluxes of high-energy ions with Z > 1 in the ERBs at L = 2–3 (Adams et al. 1991). At low altitudes, they fall into dense layers of the exosphere, lose electrons, and become trapped. SCR protons with E > 1 MeV, born during solar flares, are captured in a geomagnetic trap at L ~7–8 and are also part of the ERBs. In the range of up to several hundred keV, adjacent to the ring current, the ionospheric source (accelerated ionospheric ions) must be taken into account. Thus, in fact, the ERB is an open dynamic system that interacts with both external factors and the “underlying surface” in the form of the ionosphere . . . The mechanism of particle capture in a geomagnetic trap can be illustrated in Fig. 11.6 for the case when particles (cosmic rays) enter the magnetosphere from the outside. It is seen that high-energy particles (1) move in relatively simple orbits. Due to the presence of the Earth’s solid body, some trajectories end (interrupt) on the earth’s surface. With a decrease in the energy (rigidity) of particles, their orbits become more complex and form intermediate loops. If the loops cross the surface of

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Fig. 11.7 The motion of trapped particles in the Earth’s magnetosphere: Larmor rotation around the line of force (spiraling) with a period of T1; swinging (bouncing) from pole to pole and reflections between magnetic (mirror) mirrors (mirror points) with a period of T2; drifting rotation (drifting) around the Earth (transition from one field line to another) with a period of T3: http://www. kosmofizika.ru/spravka/ad_invars.htm

the Earth, then their trajectories are also interrupted. At low energies, particles have closed trajectories (15), i.e. are trapped in the magnetosphere. The motion of trapped particles with energy E ≤ 1 GeV in the Earth’s magnetosphere can be described by the superposition of three quasiperiodic motions— Larmor rotation around a field line (spiraling) with a period of T1, bouncing from pole to pole, and reflections between magnetic mirrors (mirror points) with a period of T2 and drifting around the Earth (transition from one field line to another) with a period of T3. Each of these periodic motions can be adiabatic if, in a given region of the magnetosphere, the characteristic time of variation of the magnetic field is much longer than the rotation period of a particle of a given energy. In this case, the spatial inhomogeneities of the field should be sufficiently small for the characteristic dimensions of rotation. Each of the three periodic motions of a particle in the magnetosphere has its own adiabatic invariant: μ is the magnetic moment, i.e. magnetic flux (“density of lines of force”) through the Larmor circle, J is the integral of longitudinal action and Φ is the magnetic flux encompassed by the drift trajectory of the particle (Fig. 11.7). Due to the preservation of the invariants μ and J, the trajectory of the particle drift around the Earth is uniquely determined. The adiabatic invariant is a parameter that characterizes the motion of a particle and remains practically constant with a slow change in the physical conditions that determine its existence in a given region of space. When a captured particle moves in a geomagnetic trap, its magnetic moment μ (the first adiabatic invariant, erg/G) and the integral of the longitudinal action J (the second adiabatic invariant) are preserved:

11.4

Dynamics of Trapped Radiation in the Earth’s Magnetosphere

μ=

E sin 2 α B

J =p

1 - B=B3 ds

163

ð11:4Þ

Here E, p and α are the energy, momentum and local pitch angle of the particle; B is the magnetic field at the top of the line of force; В3—magnetic field at the point of reflection of the particle. The integral of the longitudinal action J (analogue of the angular momentum, the product of energy and time) is calculated by integration along the magnetic field line between the points of reflection of the particle. A characteristic feature of the motion of charged particles in a geomagnetic trap is a triple periodicity: each captured particle can be considered as a rapidly spinning Larmor top, which, smoothly swaying along the lines of force, periodically turns around the Earth. The drift around the Earth in longitude for particles with different charge signs occurs in opposite directions (electrons move to the east, protons to the west). Drift in a magnetic field has several varieties; in the magnetosphere, gradient drift and drift due to the curvature of field lines are decisive. Special mention should be made of the third invariant of particle motion Ф = BS, which is the flow of the geomagnetic field (in units of G × cm2) through the equatorial plane outside the given L-shell (S = 1 cm2). In other words, the third adiabatic invariant is the magnetic flux through the drift trajectory. With deformations of the drift shell, the drift trajectory follows the changes in the shell. If the value of B/(dB/dt) is close to the period of the T3 particle drift around the Earth, then the third invariant will not be preserved. In this case, however, the quantity В/(dB/ dt) > {Т1, Т2}, so that the first two invariants μ and J are preserved. The magnetic field on a given L-shell will change, while E/B = const due to conservation of μ, and the particle can pass to another L-shell with a corresponding change in energy E. If the value B/(dB/dt) ~ {Т1, Т2}, then the Larmor motion of the particle and its oscillations between the points of reflection cannot be considered independent motions. In this case, μ and J are violated, the equatorial pitch angle of the particle changes, and it can fall into the loss cone and spill out into the atmosphere. Particles with different energies E and pitch angles α0, injected at some point of the trap, gradually populate a closed toroidal surface—a drift shell. The meridional section of this shell coincides with the lines of force of the magnetic field, and the equatorial—with the lines of constant induction of the field (in a dipole field, they are circles). The set of drift trajectories of particles with different p and α eventually fills a layer with a thickness of the order of the Larmor radius. This layer is usually called the L-shell, and the three-dimensional motion of the particle is reduced to two-dimensional (in the coordinates {L, B}). Therefore, the experimental distributions of ERB particles are most simply and naturally described and systematized in the McIlvine coordinates {L, B}, where L is the dimensionless parameter of the drift shell, B is the local magnetic field induction. For the dipole magnetic field, which describes the majority (core) of the geomagnetic trap, L is the distance from the tops of the field lines to the center of the Earth in terrestrial radii (a dimensionless quantity).

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A characteristic feature of the motion of charged particles in a geomagnetic trap is a triple periodicity: each captured particle can be considered as a rapidly spinning Larmor top, which, smoothly swaying along the lines of force, periodically turns around the Earth. The drift around the Earth in longitude for particles with different charge signs occurs in opposite directions (electrons move to the east, protons to the west). Drift in a magnetic field has several varieties; in the magnetosphere, gradient drift and drift due to the curvature of field lines are decisive. The leading center of the particle swings along the line of force of the magnetic field, reflecting (changing the direction of its motion) at the so-called mirror points (m). The position of these points is symmetric relative to the plane of the geomagnetic equator and depends only on the equatorial pitch angle α (0) of the particle— the angle between the vectors of the magnetic field and the particle velocity at the top of the field line: Bm = B0/sin2α0, where Bm is the field induction at the point of reflection of the particles, and B0—at the top of the same line of force (in the equatorial plane). The quantity Bm/B0 does not depend on the energy, mass and charge of the particle and is called the mirror ratio. As the particle approaches the mirror point, the angle α between the vectors of the magnetic field and the particle velocity (local pitch angle) increases and at the moment of reflection reaches 90 degrees. The trajectory of a particle with α0 = 90 degrees lies in the plane of the geomagnetic equator. With a decrease in α0, the reflection points approach the Earth. At sufficiently small α0, the particle falls into the so-called loss cone (see below) and perishes in the upper atmosphere. If the point of reflection of the particle is below 100 km, the probability of atmospheric losses is high. The pitch angle at the top of the field line for a particle that is considered to have died in the atmosphere is called critical and is determined by the formula. sin 2 αx =

B0 Bm

ð11:5Þ

where B0 and Bm are the magnetic field strengths at the top of the field line and at an altitude of 100 km, respectively. The area of pitch angles less than the critical one is called the loss cone. The loss cone only roughly estimates the real losses of particles during pitch-angle diffusion, since the boundary of the atmosphere is a conditional concept, its height fluctuates (in particular, depending on the level of solar activity), the absorption of particles is not absolute, etc. For a dipole field, the value of the loss cone is determined from the expression sin 2 α =

1 L ð4 - 3=LÞ 3

1=2

ð11:6Þ

In the real magnetosphere, the field strength at the equator at large distances is less than the dipole field and, accordingly, the loss cone is smaller. At low altitudes ( 1 m, duration of the order of several days). However, this radiation is already outside the transparency window of the ionosphere and is recorded only on board the spacecraft. In the region of ultra-low frequencies ( f < 5 Hz), the ionosphere becomes transparent again, and these waves can be recorded on the Earth’s surface. So, only a narrow band of the solar spectrum in the near ultraviolet, visible and infrared radiation reaches the Earth’s surface, as well as a small section of the radio spectrum, which depends on solar activity, but has a low power—less than 1014 W. Running a little ahead, we note that for this reason it is unlikely that solar radio waves play a significant role in the biosphere, although the biological effectiveness of radio emission has been proven in laboratory experiments. Compared to optical radiation (4 × 1026 W), corpuscular radiation (SCR— 21 10 W, solar wind—1020 ÷ 1022 W) does not play a significant role in the energy balance of the Sun. However, its role in the problem of solar-terrestrial relations, as we have already known, is very large, since the fluxes of solar particles are very variable. An electromagnetic wave can be conventionally represented in the form of two vectors—electric and magnetic. Their changes in space and time reflect the vibrations of a real physical entity—the energy of the EMF of the wave field. Sometimes, to characterize an electromagnetic wave, only the electric component of the field is used (in units of μV/(m × Hz)). It is in such units that Fig. 12.3 shows the spectrum of the electromagnetic field observed on the Earth’s surface.

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Influence of the Sun on the Biosphere

Fig. 12.3 The spectrum of the electromagnetic field on the surface of the Earth (Vladimirsky 1977). The vertical axis is the strength of the electric vector E, the horizontal is the oscillation frequency f in Hz. The arrows mark the frequencies (top) at which short-period oscillations (SPO) of the geomagnetic field are observed, caused by changes in solar activity, and the corresponding periods (bottom); I, II and III—“transparency windows”

Horizontal segments I-III in the lower part of the Fig. 12.3 are corresponding to three “transparency windows”. Two of them are in the radio range—this is cosmic radio emission at waves of 1 mm–30 m (III) and the intrinsic radio noise of the atmosphere with f ~ 103 ÷ 104 Hz (II), caused by electric discharges such as thunderstorms, etc. The third window falls on the region of very low frequencies ( f < 5 Hz). Shaded lines show the scales of changes in the field strength in some frequency intervals due to the development of a powerful solar flare and the subsequent magnetic storm with a sudden onset. It can be seen that in the region of extremely low frequencies ( f < 1 Hz), the wave amplitude in the process of geophysical disturbance can vary up to two orders of magnitude. At ultra-low frequencies, the generation of electromagnetic waves is closely related to the geomagnetic field and trapped radiation belts (see Sect. 11.2). These are no longer ordinary radio waves, but oscillations of the Earth’s magnetic field itself, excited by the solar wind flowing around the magnetosphere. They are called so: short-period oscillations (SPO) of the geomagnetic field (or geomagnetic micropulsations). Pulsation parameters correlate well with solar activity (via the solar wind and interplanetary magnetic field). In many types of micropulsations, an 11-year SA cycle and its harmonics are clearly traced. Significant changes are observed in individual frequency bands of pulsations when the Earth passes through the IMF sector boundary or through the front of an interplanetary shock wave. Everything said above about low-frequency oscillations of the magnetosphere suggests that they may be part of the STR mechanism. But is the contribution of natural EMFs to the cosmobiological situation on Earth really so serious? Running a little ahead, let us answer this question in the affirmative. To date, a huge number of statistical results have been accumulated, confirming the important role of geomagnetic and other disturbances in near-Earth space in heliobiological effects. Theoretical studies of possible mechanisms of SPS are also widely carried out, in particular, mechanisms of a trigger nature. Naturally, the most convincing arguments in favor

12.2

The Role of Geomagnetic Pulsations

181

Fig. 12.4 Simulation of the Earth’s EMF disturbance in laboratory conditions. The diagram of the experiment with rabbits is shown on the left, the ECG of rabbits is on the right. The lower curve is the ECG of the control animal, the upper curve is the ECG of a rabbit in an electric field with a strength of 1 V/m and a frequency of 8 Hz. Arrows indicate anomalies in the form of an ECG (Volynsky and Vladimirsky 1969)

of one or another heliobiological hypothesis can only be provided by model or biomedical experiments. Unlike any measurements (observations) in natural (space or geophysical) conditions, when neither the underlying background nor the input parameters of the measured signal are known exactly, an experiment in the laboratory makes it possible to reproduce the background quite accurately (or get rid of it) and set the initial characteristics of one or another acting factor. To date, the most impressive results have been obtained by artificially exposing biological objects to electromagnetic fields of natural intensity. It is not technically difficult to reproduce the disturbance of the natural EMF of the Earth in the laboratory. It is enough to send a signal of the required frequency and amplitude from the generator to a capacitor or solenoid (Fig. 12.4) and place an experimental animal in it. In recent years, such experiments have been carried out in a number of laboratories in different countries. In particular, very clear results were obtained at the Crimean Medical Institute (Simferopol) in 1969–1982. Already after the first experiments in Crimea, it was found that a weak ultra-low-frequency field significantly affects the cardiovascular system (CVS) of warm-blooded animals (rabbits, dogs). For 3 h, the experimental animals were in an electric field with a strength of 1 V/cm and a frequency of several Hz. A decrease in heart rate was found in animals. If you increase the duration of exposure (or repeat it for several days for the same 3 h), then quite serious disturbances in the work of the heart can occur (Fig. 10.4). This was also confirmed by pathological studies. Subsequent experiments, carried out at EMF frequencies of about 1, 2 and 8 Hz, showed that the field acts more effectively on the cardiovascular system if its work was already somehow disturbed before the experiment. The latter circumstance is of fundamental importance for assessing the impact of magnetic storms on patients with hypertension and other CVS diseases (see Sect. 12.2). Model experiments to study the biological effects of sporadic helio-geomagnetic disturbances have not yet gained the proper scope. But it is already becoming

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obvious that the information accumulated in this area is very useful. However, due to many methodological difficulties, the successes of experimental heliobiology should not be exaggerated. Nevertheless, their long-term results convincingly indicate the electromagnetic nature of the main acting heliobiological agent. In other words, an important ecological factor has been discovered in the habitat—amplitude-spectral variations of the electromagnetic background of low and ultra-low frequencies. The study of quasiperiodic (cyclic) variations of various biological parameters provides important information on the nature of heliobiological effects. Such studies open up a vast new area of solar-terrestrial physics—the connection between the rhythm of solar activity and the rhythms of the biosphere.

12.3

Cosmic Rhythms in the Biosphere

So far, we have dealt with heliobiological effects of a mostly sporadic nature. Meanwhile, the study of any dynamic system must necessarily include the study of both its spatial structure and temporal organization (e.g., Yagodinsky 1975). The temporal dynamics of biological processes is studied by chronobiology. A very important part of this dynamics is made up of fluctuations in biological indicators— the subject of research in biorhythmology. It is now recognized that all biological systems at all levels of an organization operate in a self-oscillating mode. The latter are externally manifested as biorhythms—cyclical changes in the indicators of the body’s vital activity (physiological biological, etc.). In this case, the appearance of certain rhythms in the system can be associated with the so-called frequency capture (and forced synchronization). It is important to emphasize that any series of measurements of any parameter (in a laboratory or in natural conditions) can be represented as a set of elementary vibrations. Therefore, all properties of the series are described in terms of the theory of oscillations (amplitude, phase, period, frequency, phase, amplitude/phase spectra, periodogram, power spectrum of oscillations, etc.). The vast literature on biorhythms has accumulated many observations of periodic changes in a wide variety of parameters in a wide frequency range. The semidiurnal and diurnal rhythms have been studied in most detail for many organisms. The discovery of a rhythm with a period of about 7 days gave rise to the question of the natural (and not historical) origin of the calendar week. Some researchers attach special importance to this period, considering it evolutionarily conditioned. In ancient times, many peoples believed in the magical power of the number 7, and today psychologists find traces of this “magic” number in the peculiarities of human perception of information. In any case, this approach does not contradict the leading concept of heliobiophysics that the rhythmic fluctuations of the helio-geomagnetic indicators set the “biological clock” and in the process of evolution integrated into the endogenous rhythm of biological systems. For humans, in addition to the mentioned rhythms, cyclical changes in vital activity indicators are known with periods of about a month (26–29 days), 6 months,

12.3

Cosmic Rhythms in the Biosphere

183

Fig. 12.5 Fundamental harmonics of periodic changes in solar activity (SA), magnetic activity (MA) and the most important biological rhythms (Vladimirsky 1977)

a year, about 3 years, about 7 years (the so-called macro-rhythms). At the level of systems of organisms, fluctuations in the number of certain populations are well known. These “waves of life” are most clearly observed with periods of about 3–4 and 10 years. Moreover, the peaks of these waves do not have to coincide with the corresponding peaks of solar activity. This “mismatch” between solar and biological rhythms is explained mainly by a complex interaction (hierarchy) between living organisms on the Earth’s surface (see below for more details). In the study of circadian (so-called circadian) rhythms, it was found that they can be forcibly synchronized by the corresponding environmental factors, first of all, by a change in illumination modes. As noted above, synchronization occurs as a frequency lock. Here there is an analogy with mechanical and electrical oscillatory systems when they are exposed to an external periodic signal. Apparently, other general laws of the nonlinear theory of oscillations are also applicable here. In particular, for solar-terrestrial physics in general (including heliobiology), it is very important to be able to synchronize with a very weak signal with a small value of the “detuning”. The driving force for biological self-oscillations can be, in principle, any periodically changing environmental factors. These should, apparently, include weather and climatic changes (precipitation, average temperatures of certain months, etc.) and, of course, such factors as electromagnetic fields, infrasound and others. All these environmental parameters are modulated by changes in solar activity and long-term tidal influences of the Moon. Figure 12.5 schematically shows the fundamental harmonics of periodic changes in solar and geomagnetic activities, as well as the most important biological rhythms. The dashed vertical lines mark the characteristic periods (frequencies) of the solar cyclicity, the solid vertical lines correspond to the rhythms of geomagnetic activity, and the short horizontal lines show the characteristic frequencies of the biorhythms. It can be seen that the synchronization of biorhythms (including macrorhythms) by environmental factors seems to be a widespread phenomenon. The almost complete

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coincidence of the periods of rhythms with the frequency structure of changes in the external environment definitely indicates the presence of synchronization.

12.4

Features of Heliobiological Rhythms

If synchronization takes place, then there is a correlation of the corresponding biological indicator with the index of the driving force, i.e. solar (geomagnetic) activity. Communication, however, has the characteristic that it can change from one geographic area to another. The reason is that the proper period in the ecosystem (for example, the population density of a given species) is determined by a set of local conditions, and the frequency capture is carried out according to the SA harmonic, whose period is closest to the proper period of the system. In case of incomplete coincidence (but closeness) of these periods, beats may occur. In this case, characteristic details should be observed on curves describing, say, the dynamics of populations (the “waves of life” mentioned above): the simultaneous presence of two periods with a changing ratio of amplitudes, a constant phase shift of the curve under consideration relative to the phase of the driving force. In many cases, the curves of population density fluctuations (insects, rodents) are strikingly similar to the described picture. The same considerations are obviously applicable in the case of spontaneously (at first glance!) Epidemics and epizootics, if we assume, as some researchers have done, that the epidemic process is self-oscillating. The system, in some approximation, can be considered at least as three related oscillators: fluctuations in the level of immunity of individuals susceptible to this disease, cyclical changes in the survival and virulence of the pathogen, fluctuations in the number of carriers of the pathogen. In such a system, synchronization can occur when an external “disturbing” frequency is applied to any of the above-mentioned oscillators (if certain relationships between their natural frequencies are observed). From the point of view of concepts of synchronization, it is easy to understand the geographic variability of the cyclicity of epidemic phenomena: the natural periods of oscillations in the system (as in the case of life waves) are determined by the totality of the external conditions of a certain region. Correlation with the indices of solar activity can arise when the frequency is “locked” at any harmonic, as long as the condition of frequency proximity is fulfilled. The amplitude of fluctuations of the “forcing” factor can be very weakly expressed in this case, synchronization will still occur. For different geographical areas (different pathogens, different diseases) and the nature of the synchronizing factor may be different. Thus, the hypothesis of forced synchronization of biorhythms can be very fruitful for understanding certain aspects of the relationship “solar activity—biosphere”. In particular, the presence of high harmonics of solar cyclicity in many periodically occurring biological processes becomes clear. The geographic variability of the relationship with solar activity of such phenomena as fluctuations in the number of populations and epidemics is explained. This hypothesis also serves as a good tool

12.4

Features of Heliobiological Rhythms

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Fig. 12.6 Cyclic variations in solar activity and mass reproduction of fur-bearing animals in Canada in the first half of the twentieth century: 1—muskrat; 2— mink; 3—hare; 4—lynx; 5—fox; 6—ilka; 7—coyote; 8—wolf (Yagodinsky 1975)

for analyzing the reasons for the incompatibility and and ambiguity (“non-reproducibility”) of some statistical results on heliobiological relationships, a fact that gave rise to doubts about the reality of such relationships. To describe causal relationships and temporal shifts of heliobiological rhythms, one often resorts to the well-known pair of equations for the predator-prey chain—the well-known Lotka-Volterra equations. It is interesting to note that they proposed their equations independently (Lotka 1925; Volterra 1926): ∂x = xðα - βyÞ ∂t

ð12:1Þ

∂y = - yðγ - δxÞ ∂t

ð12:2Þ

where y is the number of some predator (for example, wolves); x—the number of its prey (for example, hares). The derivatives dy/dt and dx/dt represent the rates of reproduction of two animal populations at time t, and the coefficients α, β, γ, and δ are parameters describing the features of the interaction of two populations. In other words, these two first-order nonlinear differential equations describe the dynamics of biological systems in their natural habitat. Within the framework of this approach, it becomes clear, in particular, the dynamics of populations of certain species of wild animals, birds, insects, fish, etc. The reasons for changes in the number of animals are explained by the complex influence of natural (geographical, climatic, forage, etc.) factors, as well as by the hierarchy of relationships between animals of different species. These connections can be twofold. In some cases, the breeding cycles of animals depend directly on the forage plant base and weather conditions (food), while in others they are mediated through a chain of biological relations of the “prey-predator” type (plus the presence of parasites, competitors, etc.). An illustrative example of this is the cyclical nature of fur-bearing animals in Canada (Fig. 12.6): the rather regular breeding periods of the muskrat and hare feeding on plant food are followed by increases in the number of their predators. Naturally, some time passes between the time of the greatest development of the population of harmless rodents and the period of growth in the number of foxes and wolves hunting them. Therefore, increases in the number of different species occur at

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Influence of the Sun on the Biosphere

different phases of the 11-year SA cycle, i.e. with some kind of time shift, depending on terrestrial conditions and the characteristics of the life of a given species. But, despite such deviations, there is a clear linkage of the breeding cycles to certain phases of the 11-year solar cycle. For example, it was found that the mass breeding of hares in a completely different geographical area (Yakutia) coincides with the minimum of sunspots, if the curve of the increase in the number of white hares is shifted by 5 years to the right relative to the curve for the number of sunspots. The enormous practical importance of taking these regularities into account is quite obvious, first of all, for planning the procurement of furs and the production of livestock products. It is equally important to learn how to scientifically predict epidemics, epizootics, epiphyties and other similar events in the biosphere at the level of microorganisms. The value of specific results in this area was noted as early as 1915 by A.L. Chizhevsky. On the example of data on the disease of diphtheria in Denmark in 1860–1910, he showed that there is an inverse relationship between the incidence of diseases and the level of SA, with a shift of the two curves by about 5 years. At the same time, when in 1894 doctors began to use the anti-diphtheria vaccine, the spontaneous course of the disease changed significantly, although the use of the vaccine, of course, did not “cancel” the found pattern. Let us consider one more feature of biological rhythms, namely the presence of high SA harmonics in biospheric processes. This feature is well manifested, in particular, in the annual variations in the thickness of the tree rings. Figure 12.7 shows the power spectrum of solar activity fluctuations (dashed line) and the corresponding data (power spectrum) for variations in the thickness of annual tree rings on the upper border of the forest in middle latitudes, in the Tien Shan mountains (solid curve). The length of the row for the thickness of the rings is about 300 years. It can be noted that not all periods of solar activity are represented in this series. Since the series is rather long, such a difference could be associated with the features of the landscape, and this assumption is apparently correct: as far as can be judged, the analyzed tree growth spectra significantly depend on the region and type of landscape. There are regions where there is no pronounced periodicity in the growth variability. In most cases, the rhythm is transferred to the ecosystem through weather and climatic factors, and it is now known that the set of periods in the variations of these parameters changes from one region to another. It was found that in a humid climate, growth variations correlate better with SA indices than weather and climatic indicators. This is evidence of the impact on the growth processes of those environmental variables that are controlled by solar activity, regardless of weather changes. Numerous observations have shown that not only electromagnetic fields are important for plant communities, but also the electrical state of the atmosphere. In particular, the so-called geo- and heliotropism of plants is definitely due to the action of the electric field of the atmosphere. Another important factor is undoubtedly variations in the intensity of UV radiation near the main absorption band of ozone (the so-called Gartley band from 200 to 300 nm). This range falls on the ultraviolet radiation of the Sun.

12.5

Cosmophysical Factors and Creative Activity

187

Fig. 12.7 Power spectra of variations in tree ring thickness (solid line) and solar activity (dotted line). The vertical axis is a value proportional to the square of the oscillation amplitude (in arbitrary units), the horizontal axis is the oscillation frequency (cycle/year), the numbers on the curves are the period values (Lovelius 1979)

The ozone layer in the stratosphere most strongly absorbs solar radiation with a wavelength of 253.65 nm. Fortunately, if we consider all atmospheric ozone at 0 °C and normal pressure, then an ozone layer only 3–4 mm thick can reduce the radiation intensity at this wavelength on the Earth’s surface to almost zero.

12.5

Cosmophysical Factors and Creative Activity

As can be seen from the previous section, the rhythm of the processes in the biosphere is synchronized with the cosmophysical periods. Therefore, it is quite natural to expect that the characteristic periods of SA fluctuations should be reflected in the phenomena of human civilization—in culture, economy and history. Indeed, in the scientific literature there is a lot of support for this assumption. Consider, for example, the creative activity of mankind over a long period of time.

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Fig. 12.8 Cycles of creativity in different areas of civilization (2—China and 3—Europe) depending on the level of solar activity (1) for the period 1400–1850 (Ertel 1998)

Figure 12.8 shows the curves of the creative achievements of prominent personalities in the fields of science, philosophy, literature and painting in areas as different as Europe and China, starting in 1400 AD. In the Middle Ages, Europe and China were essentially two independent civilizations, very different and practically isolated from each other. Nevertheless, as it turned out, the processes of cultural life turned out to be very similar in both areas. To show this, it took a lot of efforts of many scientists and years of historical, biographical and cosmophysical (geophysical) research. The first and main difficulty was the selection of data on outstanding scientists, philosophers, poets and artists to form homogeneous statistical series. Further, the natural question arose of where to get the necessary data on solar activity in the era when regular instrumental observations of the Sun were absent (until 1749). The radiocarbon method came to the rescue (see Sect. 8.3), which allows obtaining reliable, albeit indirect, data on the SA level at a particular epoch through variations in galactic cosmic rays. Of course, a scrupulous statistical analysis of the collected material was also needed. Radiocarbon data on solar activity (proxy) are presented in Fig. 10.8 in relative units and in “inverted form” (right scale), i.e. the maximum variations in the 14C radiocarbon content correspond to the minimum solar activity, and vice versa. In addition, for convenience of consideration, curve 1 for 14C is shifted upward relative to creativity curves 2 and 3. It can be seen that between 1400 and 1800 solar activity had two “anomalies”— two large minima of Spőrer and Maunder. The time series of creative activity was built by counting the number of works and the number of creators with averaging over each 5-year interval. This also took into account the most probable period of maximum productivity (efficiency) of a given creator. Further, the productivity of all

12.6

Economic “Kondratyev Waves”

189

creators was summed up for every 5 years. It is quite remarkable that “explosions” of activity in independent cultures occur simultaneously and in a similar way. We also note that among the studied non-European civilizations (China, Japan, the Ottoman Empire), Chinese culture provides the most convincing material for such a conclusion. At the same time, in the behavior of curves 2 and 3, attention is drawn to two features that require a separate explanation. First, at the Spőrer minimum, productivity grows until the end of the period, while at the Maunder minimum (1645–1715), it drops sharply 30 years before the end of the period. This difference may be related to the fact that the decrease (almost complete cessation) of solar activity (in terms of the number of sunspots) in the Maunder minimum was more extreme than in the Spőrer minimum. It seems that some average SA level is optimal for cultural prosperity, indicated by the horizontal line at the top of Fig. 12.8. In other words, almost zero SA in the second half of the Maunder minimum could be a very unfavorable factor for the flourishing of culture. These considerations are reinforced by the presence of shorter (11-year) fluctuations in creative productivity. Another feature is the following: creative activity falls for several decades after the Spőrer minimum, and then increases in the first decades of the Maunder minimum. The reason for this difference is probably due to the fact that at the end of the Spőrer minimum there was an optimal SA level, after which the creative productivity should inevitably decrease. On the other hand, a very deep SA depression at the end of the Maunder minimum was replaced by a trend towards the optimal level, i.e. unfavorable conditions soon disappeared, and an upsurge of creative activity began. Let us note, by the way, that our great compatriot M.V. Lomonosov was born just before the very beginning of the upsurge . . . It is quite obvious that the discussed intriguing problem requires further in-depth studies. At the same time, the fact that obvious “anomalies” of creative productivity are manifested independently in two such distant cultures means that the problem can be interpreted in terms of macroecology. At this early stage of real (scientific) heliobiological research, any hypothesis related to the state of the solar system is speculative. However, with the accumulation of new facts and convincing evidence in the field of STP, the situation may change, and now hypothetical statements will become indisputable concepts.

12.6

Economic “Kondratyev Waves”

If there are cosmophysical periods in the climate, changes in crop yields, in epidemic disasters and creative productivity, then it is difficult to imagine that these rhythms would not be reflected in the economy. The economic cycles that appear in the modern literature on the dynamics of economic indicators are well-known space (natural) periods. It was during the study of variations in economic indicators that it was first understood that the dynamics of a very complex system is described not by some kind of cycle (rhythm), but by their set, i.e. spectrum. The spectrum of

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Fig. 12.9 Data on economic conditions (“Kondratyev waves”) vs. SA. The turning points of economic fluctuations are very close to some maximums of the Wolf number (Ertel 1996). The dates of SA maxima and minima prior to 1749 were reconstructed from indirect historical and geophysical data (see Sect. 3.5)

economic cycles has a number of peaks, among which the most important periods (years) are distinguished: 3.5; 5.5; 8.0; 11.0; 18.0; 20–22; 54. Short periods (e.g. 3.5 years) can have certain regional characteristics. On the other hand, long economic cycles must belong to the entire world economy. These are the long “Kondratiev waves” (54 years old), named after the outstanding Russian economist N.D. Kondratyev (1892–1938). “Kondratyev’s waves” have been confidently traced in the world economic system since the beginning of the eighteenth century in many indicators at once— industrial production, wholesale prices, the number of “innovations” in industry, agriculture, etc. The parameters of the fluctuations change somewhat, reflecting the evolutionary changes in the world economy, but the cyclical nature as a whole persists to the present. There are many different points of view about the origin and nature of these vibrations, and thus it becomes clear that this question remains unresolved. In this book, we are primarily interested in the possible connection of the “Kondratyev waves” with solar activity and ecology. In other words, the question arises: is there a synchronism between the peaks of the “Kondratiev waves” and the cosmophysical parameters? The answer is in Fig. 12.9.

12.6

Economic “Kondratyev Waves”

191

Figure 12.9 shows the positions of the extreme points of the long “Kondratyev waves”—their maxima and minima (peaks and dips). These points are determined on the basis of considering a large array of data characterizing the state of the world economy since the end of the seventeenth century. Here, we took into account the results obtained by representatives of various economic schools, which operated with their own independent economic indicators (indices). The turning points in the trends of the world conjuncture are marked with arrows, circles also show the positions of the SA maxima. Those of them that are located near the extreme points of the “Kondratyev waves” are indicated by dark circles, the rest—by light circles. As can be seen from the graph, only in 2 cases out of 11 the difference between the dates of black circles (CA) and the dates of economic peaks-failures is 3 years, and on average does not exceed half a year . . . Figure 12.9 shows the positions of the extreme points of the long “Kondratyev waves”—their maxima and minima (peaks and dips). These points are determined on the basis of considering a large array of data characterizing the state of the world economy since the end of the seventeenth century. Here, we took into account the results obtained by representatives of various economic schools, which operated with their own independent economic indicators (indices). The turning points in the trends of the world conjuncture are marked with arrows, circles also show the positions of the SA maxima. Those of them that are located near the extreme points of the “Kondratyev waves” are indicated by dark circles, the rest—by light circles. As can be seen from the graph, only in 2 cases out of 11 the difference between the dates of black circles (SA) and the dates of economic peaks-failures is 3 years, and on average does not exceed half a year . . . Thus, changes in the world economy are definitely associated with variations in solar activity: if trends in the development of the world economy change, then this will certainly happen at the maximum of the solar cycle. The pendulum of the economy swings in time with the solar fluctuations. It is not important whether economic oscillations with a half-century period are self-oscillations or exogenous rhythms. It is clear that the world rhythm is brought into the economy by Nature.

Chapter 13

Future of Solar-Terrestrial Physics

We are children of the Cosmos. And our dear home So welded together and inextricably strong, That we feel merged in one, That at every point the world— the whole world is concentrated. A.L. Chizhevsky (“Terrestrial echo of solar storms”)

As already noted, solar-terrestrial physics as a whole has already gone far beyond the initial understanding of this term, and the fields of its research are closely intertwined with the fields of research of other sciences about the Earth and Space. For example, the physics of solar flares is a kind of cut through many areas of modern physics: from the kinetic theory of plasma to the physics of high-energy particles. Another example is heliobiology, where the interests of specialists from such distant fields as stellar physics, geophysics, biology, medicine, and psychology converged (and sometimes decisively collided!). Such areas of socio-cultural studies as history and archeology, economics and sociology were in the same row. At the same time, however, many fundamental problems remain unresolved and some of the most important processes that determine the essence of these scientific directions have not been investigated. Below, using specific and most convincing examples, we will try to discuss a number of them without pretending to be complete. Along with fundamental problems and concepts, the applied aspects of solarterrestrial physics are of great interest, in particular, radiation hazard in space, forecasting helio-geophysical disturbances, socio-economic losses due to fluctuations in space weather, and many others. Let us recall in this connection the words of A. Einstein: “Intellectual instruments, without which the development of modern technology would have been impossible, came mainly from observing the stars.” There is no doubt also the enormous ideological significance (Weltanschauung, or epistemology) of the results of solar-terrestrial physics.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 L. Miroshnichenko, Solar-Terrestrial Relations, https://doi.org/10.1007/978-3-031-22548-2_13

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13 Future of Solar-Terrestrial Physics

Solar Activity and Accurate Physical Measurements

For the reliability of conclusions in physics and astronomy (as well as in other natural sciences), the accuracy of physical experiments and the quality of astronomical observations are of fundamental importance. Meanwhile, in connection with the establishment of certain connections between solar activity and many terrestrial processes, a number of issues have been discussed in the vast cosmophysical and heliobiological literature for several decades (see, e.g., Zenchenko and Breus 2021), which cause great controversy, misunderstanding, rejection, etc., up to accusations of falsification of the results of observations and measurements. These include, for example, the problem of so-called macroscopic fluctuations in processes of different nature, the possible influence of solar activity on the accuracy of physical measurements, the so-called “artifacts” in astrophysical observations and recent discoveries, and the global problem of physical metrology in general. The study of macroscopic fluctuations in processes of various natures has been going on for more than four decades. The phenomenon of macrofluctuations was first discovered in biochemical experiments with various enzymes (Shnol 1985; Shnol et al. 1998), and its essence is as follows. Suppose that the activity of a certain enzyme is quickly measured in a certain volume of an aqueous solution, i.e. the rate of a chemical reaction. It turns out that with successive long-term measurements, velocity values are obtained that differ significantly from each other, and by an amount much greater than the error of the device. These values are not continuously distributed: they form a certain series of discrete quantities—“states”. Some of these “states” are rarely realized, others—much more often. The distribution of the states realized over some time has the form of a series of “peaks” separated by “dips”— values that are almost never encountered. The transition from one such state to another occurs in a relatively short time—less than 0.01 s. The most striking thing is that this transition occurs cooperatively-synchronously in a macrovolume or synchronously in two adjacent vessels (hence the name “macrofluctuations”—fast discrete changes in a parameter in a macrovolume). At first it seemed that this phenomenon is associated exclusively with aqueous solutions of proteins. However, as the long-term research program was carried out at the Institute of Biophysics of the USSR Academy of Sciences (Pushchino-on-Oka), it gradually became clear that the spectra of discrete states (histograms) are observed in processes of a very different nature, including such as electrophoretic mobility of inorganic particles, differences in time intervals between discharges in a relaxation generator on a neon lamp and a number of others. The nature of macrofluctuations remains a mystery, and a detailed discussion of this fundamental problem is beyond the scope of this book. We will consider here only one aspect of it—a possible correlation (or causation?) with solar activity. In this regard, important empirical laws were obtained concerning the effects of solar activity in physicochemical systems. Among them is the result shown in Fig. 13.1. It follows from the graphs in Fig. 13.1 that the amplitude of macrofluctuations increases sharply in the years of minimum solar activity. This is tantamount to the

13.1

Solar Activity and Accurate Physical Measurements

195

Fig. 13.1 The amplitude of macrofluctuations σ (%) reaches its highest values during the SA minimum. W—average monthly smoothed Wolf numbers, circles—average annual values of σ, dashed line— their approximation by the method of least squares. The data were obtained for chemical and biochemical reactions in solutions (Udaltsova et al. 1987)

statement that the epoch of minimum activity accounts for the greatest spread in the rates of chemical and biochemical reactions in an aqueous solution. The behavior of the amplitudes of macrofluctuations clearly shows an 11-year period, the average monthly data also shows a well-known period of about 2 years, and apparently there is also an annual period. A positive relationship was found between the amplitude of macrofluctuations and fluctuations in the critical frequencies of the ionosphere, i.e. with the variability of the electron concentration (when the latter is stable, the amplitude σ increases). It was also shown that the value of σ is very sensitive to the direction of the interplanetary magnetic field, and the effect of IMF sector boundaries is present both in the amplitudes of macrofluctuations and in the physicochemical indicators proper. Despite the revealed correlations, many details remain unclear in the problem of macrofluctuations Unfortunately, so far there is no convincing model of macrofluctuations. Nevertheless, the data on cosmophysical correlations obtained in the study of macrofluctuations are obviously in reasonable agreement with them. But the most important conclusion is that SA effects, apparently, are present in all physicochemical processes, i.e. it is not a purely biological, but a general physical phenomenon. Indeed, macro-fluctuations are inherent in at least all condensed media, all liquids and solids. Such an extremely responsible conclusion (Vladimirsky and Temuryants 2000) obviously requires serious experimental confirmation. If we operate with changes in the spectrum of states, then SA effects, in the opinion of these authors, will definitely be detected in any measurements with their proper accuracy. If such detailed information is not available, then you can limit yourself to the simplest estimate of the spectrum (the usual standard deviation, or variance). Here is one very illustrative example.

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Fig. 13.2 The root-meansquare deviation S in the measurements of the activity of the tritium standard as a function of Кp-index of geomagnetic activity (Avdonina and Lukyanov 1995). Registration was performed using a liquid scintillation counter

Figure 13.2 shows the results of a fairly routine measurement to control one of the radioactive standards—the tritium standard. Such measurements are carried out regularly, for a long time and for various radioactive standards used, in particular, in radiobiological research, in radiation medicine and other fields. In the case under consideration, the counting rate of N electrons from the β-decay of radioactive tritium was measured using a liquid scintillation counter (Avdonina and Lukyanov 1995). Earlier (1992) the authors of this experiment, studying rather long series (in the absence of drift in the average count rate), found preferable relatively narrow intervals of N, reminiscent of histograms of macrofluctuations. From the analysis of their material obtained for several different radioactive samples, they came to the preliminary conclusion that the observed variations in the count rate are due not to changes in the probability of radioactive decay, but to the instability of the detection efficiency of decay products in the photomultiplier-scintillator system. To check this conclusion, a series of special measurements “tritium standard— liquid scintillator” were carried out. The main result of processing these measurements is shown in Fig. 13.2: it turns out that the maximum spread of the counting rate falls on time intervals with a low value of the Kp-index, and in such intervals the counting rate itself slightly increases. Thus, based on the example of this and some other similar experiments, it can be argued that at this point, all the participants of the “triad”—solar activity, macrofluctuations and . . . “the idea of the influence of an uncontrolled factor on measurements” geomagnetic activity and ionospheric disturbance (Vladimirsky and Temuryants 2000). An uncontrollable factor, according to this hypothesis, can change the physicochemical properties of the detector—transparency, refractive index and viscosity of water or solution (see Sect. 12.1), the elastic coefficient of the filament (torsion pendulum), the structure of the n-p junction in a semiconductor element, and many others. This will inevitably lead to a change in the registration efficiency, which will lead to distortion of the measurement results.

13.1

Solar Activity and Accurate Physical Measurements

197

The change in the registration efficiency of various detectors under the influence of external conditions, as well as the calibration of detectors designed to study a specific physical phenomenon, are two well-known, eternal problems that are present in any experiment, both in the terrestrial laboratory and in space. In this case, as is customary in physics, we are always talking about controlled factors (registration efficiency) or controlled initial conditions (in the case of calibration). Therefore, in our opinion, the whole question is at what level of the threshold intensity (flow, counting rate, etc.) the search is carried out and the contribution of the “uncontrollable factor” is estimated. The authors of the hypothesis themselves admit that the effects described above are generally small and do not undermine the foundations of nuclear physics and mathematical statistics. For example, “if we check the classical axioms of statistics of nuclear readings by conventional methods using the entire array of measurements, then we will not be able to notice anything. To search for the temporal organization of the recorded impulses, more sensitive methods are needed . . .” . Within the framework of the proposed concept, the authors discuss the results of precise measurements of a number of the most important physical constants—the gyromagnetic ratio of the proton, the speed of light, the gravitational constant, and others. Further, the results of many fundamental experiments of the twentieth century (for example, attempts to register gravitational waves, variations in the neutrino flux from the interior of the Sun) are questioned (partly rightly). At the same time, some outstanding discoveries (for example, the registration of a neutrino burst from the Supernova SN1987A burst on February 23, 1987, variations of the “redshift” of distant galaxies, and others) are generally interpreted as “the most famous artifacts of the 20th century” . . . All existing measurement difficulties and their interpretation are the authors it is suggested to explain by the fact that the signal-to-noise ratio is unpredictably modulated by the influence of an uncontrolled factor. The latter changes the physical properties of a radiochemical solution, scintillator, semiconductor element, any condensed substance of the detector. Thus, there is an instability in the efficiency of registration. From personal experience, the author knows how carefully the details of an important experiment are thought over, what precautions are taken in order to exclude the influence of uncontrolled factors on the results of measurements (observations), and how the subsequent analysis of the data is methodologically scrupulous. Often it is necessary to deliberately “coarse” the sensitivity of the detectors, i.e. deliberately degrade the quality of the experiment, although the logic of research requires the opposite—to measure more and more subtle effects in as much detail as possible, etc. For example, the statistical reliability of rare muon bursts at the Baksan Underground Scintillation Telescope (BUST) for the period 1981–2006 there is no doubt that their correlation with solar flares has been shown, but the physical nature of the bursts is still a mystery (Miroshnichenko and Karpov 2004). There is no way to go into special details here. However, it should be admitted that the discovery of macrofluctuations and the hypothesis of an “uncontrollable factor” (whatever its nature) raise the global problem of metrology as a whole. Perhaps, this will require a correction of the most important foundations of the

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methodology of scientific research in the natural sciences. Remain unclear, in particular, questions about the reliability of non-reproducible “rare events”, as well as about the “threshold”, or “limits of sensitivity”, which may have already been reached by modern physical experiments. Be that as it may, a reasoned and impartial discussion about the nature of macrofluctuations and “uncontrollable factors” in physicochemical processes on Earth seems to be a very good stimulus for further in-depth analysis and new experiments.

13.2

Heliobiology and Medicine

In the previous chapter, we spoke in sufficient detail about the possible influence of natural electromagnetic fields (EMF) on the biosphere, analyzed the mechanism of this influence, and provided examples of magnetobiological experiments. Below we will talk about some new approaches to the problem of the influence of geomagnetic storms on the human body. It will focus on a special program for measuring electrical conductivity at biologically active points (BAP) of a person, on global telecommunications monitoring (the Heliomed project), as well as on the latest results of the analysis of medical statistics for periods of magnetic storms. In 1998, in Troitsk near Moscow (IZMIRAN), regular measurements of electrical conductivity at biologically active points (BAP) of a person were started. An almost constant contingent of 25–30 people of different ages and sex (IZMIRAN employees) is taking part in the measurements, which are still ongoing. Similar measurements have been or are being carried out in Odessa, Yakutsk, Simferopol, Kiev and other cities. Since then, a large amount of data has been accumulated in this long-term experiment using the method of electropunctural diagnostics, which are gradually being analyzed. As it turned out, “ordinary” healthy people, performing their standard duties at the workplace, react to heliogeophysical disturbances with certain physiological shifts, moreover, synchronously in different cities. At the same time, typological features of the response are observed, and there is a latitudinal effect (Ragulskaya and Khabarova 2001; Ragulskaya 2005, 2019). Here we will give only one example, interesting, first of all, from the point of view of the reaction of the human body to a single magnetic storm. Typical types of responses are shown in Fig. 13.3. The most essential features of the reaction are as follows. There is a reproducible and self-similar nature of the form of the reaction of the human body to various external influences, both in temporal and spatial scales, at all levels of the organization of the system, from the cell to the collectives of people. Figure 13.3 shows a characteristic three-phase form of an adaptive stress reaction (the level of individual organs, the human body as a whole, and the collective), as well as the dynamics of its course during the normal and pathological course of the process on calm and magnetically disturbed days. It was revealed that flare processes on the Sun and subsequent changes in the spectrum of natural ultra-low-frequency electromagnetic fields, cosmic rays and fluctuations of atmospheric pressure cause a stable and

13.2

Heliobiology and Medicine

199

Conductivity BAP (relative unit)

90 80 2 70

Region unperturbed norms

1

60 50 40 30 3 20 0

0 1 2 3 4 Days of reaction

days

Fig. 13.3 The reaction of the human body to a single magnetic storm based on measurements of conductivity at biologically active points (BAP). The characteristic type of amplitude changes in conductivity for different groups of subjects is given: 1—practically healthy people; 2—the reaction of the body with acute inflammation; 3—the reaction of a chronically ill person. The dashed horizontal line marks the level of the individual norm (Ragulskaya and Khabarova 2001)

reproducible human response, both at the level of functioning of individual systems (autonomic nervous system, internal organs, changes in the parameters of the cardiac cycle), and the body as a whole. The reaction of the body consists of the following three phases: (1) synchronization of the body with pronounced hyperfunctioning of all organs and systems (the first day, the subjects are not subjectively felt); (2) desynchronization with a tendency to hypofunctioning (the second—the third day from the start of the reaction); and (3) relaxation (up to 4–7 days). As much as possible, these three phases are recorded in healthy people (for details see http://helios.izmiran.rssi.ru/helioecology/ index.html). The long-term electropuncture experiment covered such cities as Yakutsk, Simferopol, Odessa, Kiev, St. Petersburg, Baku, Sofia and some others. It has recently been developed on a new methodological basis on a large regional scale. Since 2003, the work has been going on within the framework of the International project “Heliomed” (Russia, Ukraine, Bulgaria). The purpose of this telecommunications monitoring was to study the biotropic effects of space weather on humans. The new method is based on the creation of a distributed telecommunication network of scientific centers for long-term monitoring of the physiological parameters of the human body and the environment. The network began to operate on a single equipment and under a single research protocol with online registration of current data on a single portal (http://geliomed.immsp. kiev.ua). By 2010 the online database was more than 50,000 measurements of electrocardiograms (ECG) in years (data obtained in Moscow, Kiev, Simferopol, Yakutsk, Irkutsk, Saratov). According to the data taken from the first ECG lead, a characteristic phase trajectory of the signal is constructed in two-dimensional space,

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and then the behavior of the trajectory is investigated depending on external loads and the cosmobiological (geomagnetic) situation. The methodology, direction and level of research can be judged by some of the results formulated below. 1. There is a pronounced individual program of the body’s response to a sequence of stationary loads. 2. During magnetically disturbed days, an inversion of this program is observed. 3. If the shape of the current signal trajectory has a small number of trajectories similar to it, then this trajectory is an artifact: Σnj = 1,j ≠ i R V i , V j > B

≤ ðK
N Þ ) V i = artifact

ð13:1Þ

where N is the total number of days for which data is available for the selected patient; Vi—i-th trajectory, Vj—j-th trajectory, R(Vi, Vj)—correlation function; B— similarity threshold. If the value of the correlation function between two trajectories exceeds this threshold, then they are considered to have a similar shape. K*—group threshold (if the tested vector has the number of vectors that it looks like is less than the specified threshold, then the specified trajectory is considered to be an artifact). For the Heliomed data, the optimal values of the last two parameters are: B = 0.8 and K* = 0.1. The following picture emerges from the first results of the project. 1. There are at least 2–3 quasi-stable levels of heart functioning. 2. With additional physical activity (20 squats in 30 s), the studied biosystem passed into the main mono-state. When exposed to a single magnetic storm, the opposite effect was observed—the number of more chaotic states in the phase space increased. 3. Numerical modeling has confirmed that without external load in a ratio of 8:2, there is not a single portrait of cardiocycles, but a superposition of several topologically different phase states—dominant (more ordered) and several excited (more chaotic) ones. 4. Short-term chaotic fluctuations in the functioning of the heart for a healthy organism are an adaptive norm and are present in all considered ECG reconstructions. Summarizing the results obtained, two important conclusions can be formulated: 1. There are pronounced individual adaptation programs for the normal response of biosystems to cosmogeophysical factors. These programs vary slightly at the population level depending on health status, ethnicity, latitude, phase of the SA cycle, and season. 2. Health is a population norm, and illness should be considered an individual breakdown of the adaptation program. At the same time, the adaptive role of cosmogeophysical factors in the life of a given population turns out to be very multifaceted. They act, first of all, as a weak training factor for adaptationresistant members of the population. On the other hand, they also serve as a channel for rejecting non-viable members of the population and provide

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Magneto-Biological Effect (MBE)

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synchronization of individual times of biological objects during their interaction with each other. Further, these factors are the synchronizer of the general rhythms of the population and, finally, create conditions for the generation of new information in the process of evolutionary adaptation of biosystems as a whole. If we return to the ecological role of the magnetic storm, then it should not be considered either good or evil, but only a normal factor of the external environment, an objective synchronizer of the internal rhythms of an individual and society as a whole.

13.3

Magneto-Biological Effect (MBE)

Until recently, in helio-biophysical research, a mathematical apparatus based on the simplest statistical models was used to process and analyze observations. Such models usually do not take into account the multifactorial nature of the problem, i.e. high probability of simultaneous influence of helio-geomagnetic, meteorological, social and other factors. The nonstationarity of some processes is also not taken into account, for example, the wandering effect of the phase of helio-geophysical and biological rhythms. When studying the effect of a magnetic storm on a person (or the magneto-biological effect, MBE), its nonlinearity presents a particular difficulty, for example, the existence of biotropic amplitude-frequency windows of EMF exposure. It should be noted that in solar-terrestrial physics in general, for the study of heliogeophysical data series, such powerful modern methods as wavelet analysis, neural networks, and pattern recognition have long been used. However, in one of the most important areas of SPF—in heliobiology—such approaches have been ignored until now. Recently at the Space Research Institute of the Russian Academy of Sciences (or IRI RAN, Moscow) the applicability of these methods to the problems of heliobiology was critically examined (Ozheredov and Breus 2008; Ozheredov 2010) and their limitations were shown. It was concluded that when studying MBE, it is necessary to use modern methods of situational analysis. One of the particular tasks was to identify biotropic regions for the corresponding characteristics of space and terrestrial weather using pattern recognition methods. The authors relied on the well-known concept of the linear shell (Pyt’ev 2004), which is a logical continuation and development of the method of singular spectral analysis. This approach made it possible to obtain correct results under conditions of strong overlapping of the convex membranes constructed from the data on the incidence of myocardial infarction and the temperature/pressure of the atmosphere. Medical statistics for Moscow for 1992–2005 were used for the analysis. As it turned out, rapid jumps in the Kp-index associated with magnetic storms have significant biotropy (18.05%) in relation to acute myocardial infarction and acute cerebrovascular accidents. As for patients with essential hypertension (HD), it was possible to show that both factors—magnetic disturbance (Kp) and fluctuations in atmospheric pressure (AP)—act simultaneously. Moreover, their relative contribution to MBE is

202 1

w0

0.9 0.8

Normalized AP

Fig. 13.4 Linear division of the two-dimensional space of signs (Kp—index and AP—atmospheric pressure) to identify the effect of weather conditions on the blood pressure of patients with hypertension (HT). Both factors act simultaneously with a relative contribution to this impact: 6.0 (Kp): 4.8 (AP) = 5: 4 (Ozheredov and Breus 2008)

13 Future of Solar-Terrestrial Physics

w0

AP

0.7 0.6

w02 Kp

0.5

2

w0

0.4

= 6 4.8

Ap

0.3 0.2 0.1 0 0

w0 Kp 0.2

0.4

0.6

0.8

1

Normalized KP-index

expressed by the ratio: 6.0 (Kp): 4.8 (AP) = 5: 4, i.e. AP contribution to the MBE is 80% of the Kp contribution. For clarity, these results are shown in Fig. 13.4. Thus, one of the tasks of solar-terrestrial physics is the search for a certain configuration of the space of signs of ordinary and space weather and the determination of the critical region in this space. Only under this condition, the statement that when the vector of features enters the critical area, the selected biological response occurs, will have sufficient reliability and confidence. There is no doubt that the approaches developed at IZMIRAN and IKI RAN can be used, in particular, for automatic control of the influence of space and earth weather on humans in forecast systems based on satellite information. The fact that the “habitat” of the terrestrial biosphere is not completely isolated from space is no longer surprising. But the diversity and breadth of the range of reactions to cosmic influences cannot but amaze. To emphasize the significance of the magneto-biological effect, let us note that even the body of healthy male cosmonauts working at the orbital station “feels” magnetic storms (Breus 2003; Breus et al. 2016). As known, astronauts (cosmonauts) belong to a special “risk group”, since their adaptation system is overstrained by the action of another stressor factor—weightlessness. According to the data of medical measurements on board the Mir orbital station and on the Soyuz spacecraft, the astronauts during the geomagnetic disturbance were reliably observed changes in the heart rate and regulation of the vascular tone. These reactions had the properties of nonspecific and specific stress, and their features depended on the initial state of the organism and—the duration of the flight and the conditions of landing on Earth.

13.4

13.4

Astronautics Prospects

203

Astronautics Prospects

In this section, we will consider several of the most serious practical problems associated with the planning, preparation and implementation of flights of spacecraft (SC) for various purposes. First of all, it will focus on anomalies (failures) in the spacecraft operation under the influence of space weather factors. An interesting summary of data on such failures was obtained from the results of flights of service Soviet (Russian) satellites of the Cosmos series in 1970–1997. All satellites had circular orbits with an altitude of 800 km and an inclination of about 74°. In total, data from 49 satellites were selected, which were then analyzed in terms of the correlation between operational anomalies and solar-terrestrial disturbances. Figure 13.5 shows the glitch rate versus solar activity. As the SA parameter, the radio emission flux at a wavelength of 10.7 cm was used. The curve of the time course of the anomalies was then approximated by a polynomial of the fifth degree. The figure clearly shows the negative impact of the SA on the frequency of failures in the operation of onboard equipment. In particular, the general level of disruptions during periods of SA maximums was several times higher than during periods of minimum. As the correlation analysis shows, the correlation coefficient between the annual values of the outage frequency and the level of radio flux at a wavelength of 10.7 cm for the period 1970–1989 is about 0.6. The correlation between the frequency of operational anomalies and geomagnetic disturbances was also studied in detail, but the fraction of frequency variations due to the effect of charged particles on the electronics of satellites was not identified.

Fig. 13.5 The frequency of various anomalies in the operation of the service low-orbit satellites of the Cosmos series (broken line), its approximation by a fifth degree polynomial (thin solid curve) and the time variation of solar activity (histogram) in 1970–1997 (Chizhenkov 2002)

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If we talk about communication satellites, then we should first of all mention the well-proven American satellite system GPS (Global Positioning System). In the USSR (Russia), a similar system is called GLONASS (GLObal NAvigation Satellite System). The GLONASS system of the Russian Space Agency requires a very accurate measurement of time, accurate measurement of the unevenness of the Earth’s rotation. A small uneven rotation of the Earth (see Fig. 10.10) is enough to cause a malfunction in satellite systems, in navigation systems. Thus, the reliable operation of purely applied (technological and/or service) satellites definitely depends on at least three current parameters of space weather—radiation, geomagnetic disturbances and uneven rotation of the Earth. In the long term, one must also take into account the deceleration of satellites due to variations in the density of the Earth’s atmosphere (see Sect. 10.5). In recent years, systems of communication satellites have been developed for a new direction in health care—telemedicine. This is partly due to the great remoteness of certain regions of Russia from large cities. It is interesting to note that not only the Russian government is interested in digital broadcasting, but also many private enterprises. For example, the Gascom company continues to implement the program for creating the Yamal system. The fact is that today RAO Gazprom owns a network of gas pipelines with a length of more than 140,000 km, and a significant part of these kilometers is located in places where there is no wire ground communication. Therefore, it was necessary to create a satellite communications system “Yamal”, which is designed to provide modern types of communications for enterprises of the Russian gas industry. Another task of the system is associated with this task—monitoring the state of potentially dangerous objects (such a danger seems to be quite real, see Fig. 1.2). It includes the Yamal-100 communications satellite (90° E), a flight control center, a communications and data transmission network, a satellite digital television network, and a central joint satellite communications and television hub. With the help of this system, a number of telecommunication services are provided: telephony and data transmission, Internet access, digital television, the frequency resource of the Yamal-100 satellite. The satellite was put into operation in December 1999; its coverage area is practically all of Russia, the CIS countries, a number of countries in Europe and Asia. The terrestrial resource consists of 137 receiving stations. Currently, via the Yamal-100 satellite a number of central (Russian) television channels are working (Kultura, NTV, ART, AST, Daryal-TV, TNT, TB-3, MTV), three state television channels of Turkmenistan, as well as a number of regional TV companies in Russia. Now Gazkom is working on the development of a satellite communication system and plans to launch two more Yamal-200 satellites into orbit. We add to this that even on such a high-tech commercial satellite as Yamal-100, during the famous powerful outburst on July 14, 2000 (Bastille Day Event, BDE), there were malfunctions in the stellar orientation sensor system. This spacecraft was launched on September 16, 1999, and for the first time in Russia, the operation of a star sensor began on board, which determines the orientation from the survey of an arbitrary section of the starry sky. The failures were caused by the arrival of a powerful stream of accelerated particles from the Sun to the Earth’s orbit. There is

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Astronautics Prospects

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one more problem, interesting from the point of view of cosmophysics and very important for practical cosmonautics, namely, ensuring the radiation safety of manned spacecraft on interplanetary routes. There is one more problem, interesting from the point of view of cosmophysics and very important for practical cosmonautics, namely, ensuring the radiation safety of manned spacecraft on interplanetary routes. Today we are actually talking about a flight to Mars and back, which is supposed to be implemented in the next 15–20 years. Since in order to launch a spacecraft into a Martian orbit, it is necessary to perform several gravity assist maneuvers in interplanetary space, then part of its trajectory will inevitably pass in the regions where the IMF lines of force will be projected onto the beyond the limb sections of the Sun. Therefore, for planning such a flight, the heliolongitudinal distribution of solar proton events, including the invisible side of the Sun, is of interest. There are reasons to believe (see Sect. 7.8) that the distribution of solar proton flares (and SPEs) is symmetric in heliolongitude. Hence, we can conclude that about half of the SPE flares will be invisible to a Martian observer. This situation prompts us to think that it is necessary to have our own solar radiation detectors on board a manned spacecraft on the way to Mars. Optical, radio and X-ray sensors will provide the crew with useful predictive information. In other words, in the most optimal case, the crew of an interplanetary spacecraft should actually have an autonomous (onboard) system for monitoring and predicting the radiation situation almost along the entire route to Mars and during its stay on its surface . . . It is clear that this immeasurably complicates planning, preparation and conducting a Martian expedition. If we consider the time profile of the SPE, then the critical factor will be the time from the beginning of the event until the radiation-hazardous level of SCR intensity is reached. Depending on the propagation conditions, even for events “well connected” with the Sun, this time is probably on the order of 1.0 h. For practical estimates of the dynamics of fluxes and radiation doses depending on the distance to the Sun, one can use the empirical relationships given in Sect. 10.8. Such estimates for the Mars orbit are not yet available. However, to illustrate the problem as a whole, one of the “worst” cases of the radiation situation in the Earth’s orbit can be considered (Fig. 13.6). Figure 13.6 shows the time profiles of the SCR intensity from the observations of the neutron monitor at Apatity station (upper panel) and the dynamics of the dose rate (lower panel) from measurements on board the Mir orbiting space station (OSS) during a series of large proton events in September–October 1989. Above each step of the histogram (bottom panel) is written the maximum value of the parameter L on a given loop, which characterizes the effect of geomagnetic cutoff. It is interesting to note that the dose rate in the September 29–30 event had a two-peak structure, with a shift of about 4.5 orbits (4.5 h) relative to the beginning of the event (≤12:00 UT). At the same time, no unambiguous relationship was found between the dose dynamics measured on board near-Earth satellites and the data of individual ground-based detectors.

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13 Future of Solar-Terrestrial Physics

Fig. 13.6 Time profiles of SCR intensity from observations on the neutron monitor at Apatity station for the events of September 29 (1), October 19 (2), and October 24 (3) 1989 (top panel) and the time variation of the dose rate per one orbit (Arestova et al. 1991) from measurements with a scintillation detector on board the Mir space station (bottom panel)

The radiation effect due to a change in the geomagnetic cutoff rigidity, Rc, when coinciding with a large SPE may turn out to be more dangerous than in the case of a separate isolated SPE. This follows from a comparison of the results of dose measurements onboard the Mir orbital complex on September 29, 1989 and during a series of SPE and geomagnetic disturbances between October 19 and 24, 1989. At first, the radiation increased to 0.375 rad at 16:00 UT on September 29, 1989. Later, the dose increased to 1.5 rad; this happened at about 03:00 UT on October 19, 1989 during a large geomagnetic disturbance. The latter happened during the period when the proton event on October 19 was still in the process of development. This difference can be partly attributed to the fact that at the time of the maximum of the September 29 event, the Mir station was in conditions of maximum geomagnetic screening. However, it seems obvious that the effect of coincidence of a proton event and a large geomagnetic disturbance should not be underestimated.

13.5

Space Weather Forecasting

Probably, it will not be a great exaggeration to say that at the stage of inception and at the first stages of development, solar-terrestrial physics was primarily an applied (military) science. Suffice it to recall how important for the purposes of sea and air navigation and communications, for example, information about the state of the geomagnetic field and the ionosphere of the Earth has always been. Moreover, some of this information was extremely important during the war. At the same time, scientific and historical curiosities sometimes happened: for example, the radio emission of solar flares was first noticed (actually discovered) in February 1942 by British radio engineers who were preoccupied with fighting German submarines. Incidentally, the first ground-based increase in solar cosmic rays (SCR) was also recorded on February 28, 1942. In general, however, until the mid-1950s (before the beginning of the IGY—the International Geophysical Year), apparently, there was

13.5

Space Weather Forecasting

207

still no clear understanding the unity of astronomical (solar) and geophysical observations: geophysics and heliophysics developed in parallel, almost independent paths. On the other hand, it has long become clear that for practical (economic, defense and other) needs, forecasting disturbances in the geomagnetic field and ionosphere has become no less important than conventional weather forecasting. With the accumulation of knowledge about the nearest near-Earth shells (atmosphere, ionosphere, magnetosphere), confidence appeared that the Sun is the source and “conductor” of disturbances. It is no accident that in our time the term “space weather” is widely used, which implicitly indicates not only the sources and causes of geophysical “storms”, but also outlines the direction and ultimate goal of scientific research. Thus, a multifaceted task of solar-terrestrial physics arises—to create a scientific and methodological basis for predicting disturbances in near-Earth and interplanetary space. And although the fundamental aspects of the problem seem clear enough, the discussion has to start with a list of limitations and difficulties in this matter. First of all, it is necessary to understand the limits of forecasting solar, heliospheric and magnetospheric disturbances. It was found that all the strongest heliospheric and magnetospheric disturbances have solar causes. They are often associated with certain observational signs and manifestations of solar activity (flares, CMEs, spots, etc.). The experience of using these features for the purposes of statistical (empirical) forecasting by the method of expert assessments, however, allows only very uncertain horizons to be indicated; beyond them, dynamic forecasting is currently impossible due to the incompleteness of information and the complexity of the behavior of the systems under consideration. The fundamental difficulty in the mathematical prediction of solar flares and coronal mass ejections lies in the strong nonlinearity and complex unstable nature of the physical processes associated with them. A consequence of this is the strong sensitivity of mathematical models to small changes in the initial and boundary conditions. Non-statistical (physical) forecasting of solar flares and CMEs based on physical models is also greatly hampered by the lack of sufficiently accurate information about their root cause—the preparatory sub-photospheric processes. Diagnostics of the latter is just beginning to develop. A shorter-term forecast of geomagnetic storms based on observations of preparatory processes in the atmosphere of the Sun and the heliosphere requires the ability to accurately calculate the parameters of the interplanetary magnetic field and solar wind in the Earth’s orbit using them. Some hopes for at least partial overcoming of these difficulties are associated with more adequate theoretical modeling based on future stereoscopic reconstructions of the dynamic state of the corona and heliosphere using new spacecraft data. Unfortunately, the Sun sometimes behaves quite differently than we expect, i.e. “it doesn’t always work with us,” or “The Sun doesn’t cooperate with us”, as Margaret (Peggy) A. Shea, one of American leading forecasting experts, said several times at different conferences. Studies of extremely strong geophysical disturbances (for example, in October– November 2003), carried out so far, provide strong arguments in favor of statistical

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13 Future of Solar-Terrestrial Physics

forecasting principles based on the concept of the so-called “big flare syndrome” (Kahler 1982). According to this concept, the largest geoeffective events are associated with the largest outbreaks. In specific cases of ensuring radiation safety of manned space flights in near-earth orbits, the forecast is usually carried out on a semi-empirical basis. At the first stage, based on current observations of flare activity, quantitative diagnostics (assessment of possible parameters) of the solar proton event is carried out. Then, as data from satellites (for example, GOES) are received on real SCR fluxes, the forecast is refined, which ultimately makes it possible to obtain the expected dose loads on cosmonauts and calculate the dose rate dynamics during the SPE (see Fig. 13.6). Note that predicting geophysical disturbances and studying their physical basis suffer from the same limitations. Very often, modeling a process or environment (say, the ionosphere as a whole) turns out to be the only means of cognition. At the same time, for example, the ionosphere is an open system (both above and below), and the predictive capabilities of its models are limited by the uncertainty of the input data and initial conditions. The same is true for models of the magnetosphere, Earth’s atmosphere, etc. Therefore, the international ionosphere model (so-called IRI—International Reference Ionosphere) was created as a guideline for further scientific research and partly for practical needs. A similar reference model is also used for the magnetosphere (IGRF—International Geomagnetic Reference Field). For other important parameters of the interplanetary medium, solar and geomagnetic activity, special state standards (GOSTs) were developed in the Soviet Union, which summarized the most reliable scientific information and performed the same reference role. At present, active work on the creation of standard models for various cosmophysical factors is being carried out at the international level—within the framework of ISO (International Standard Organization). In addition, there are numerous Reference Books and Catalogues for sunspots, flares, SPEs, CMEs, magnetic storms and other heliogeophysical phenomena For example, note numerous Catalogues of SPEs, published by international working group (Dodson et al. 1975), then in Russia, e.g., Logachev et al. (2016). With regard to specific models for helio-geophysical forecasting, this broad topic is far beyond the scope of our presentation. It is pertinent to note here only one conceptual difficulty associated with insufficient understanding of the physics of flares and CMEs. The question is which manifestation of solar activity—a flare or CME—should be considered decisive in the chain of “cause-effect” in predicting magnetic storms. If before the discovery of CMEs, solar flares were central to this paradigm, then in the early 1990s a radically different alternative was opposed to this paradigm, and the controversy reached the point of completely denying the role of flares in favor of CMEs (Gosling 1993). The general picture of the development of events in the “Sun-Earth” system in both cases is shown in Fig. 13.7. New observations of flares and CMEs over the past 25 years, their comprehensive analysis and numerical modeling have significantly improved the understanding of the physical processes leading to the generation of both phenomena. Most likely, they represent two sides of a single MHD disturbance in the solar atmosphere (the “flare-CME” system, see a cover of this book). Even if the flare is not accompanied

13.5

Space Weather Forecasting

209

Fig. 13.7 Two paradigms “cause-effect” in solar-terrestrial relationships. On the left is a diagram in which a solar flare is believed to be the cause of a geomagnetic storm; on the right, CME is accepted as the main disturbing agent (Gosling 1993)

by CME, nevertheless, it provides useful diagnostic information, in particular, in order to determine the longitude on the solar disk, where the pair of perturbations “CME/interplanetary shock wave” originates. At the empirical level, the state of space weather is currently often assessed according to the NOAA (National Oceanic and Atmospheric Administration) fivepoint scale according to the following parameters (www.sec.noaa.gov/NOAAscales/ ): 1. X-ray score of a solar flare (R1–R5)—the maximum intensity of the solar electromagnetic radiation measured in near-earth orbit in the range of soft X-ray radiation 1–12.5 keV, at a wavelength of 0.1–0.8 nm. Exposure to maximum intensities leads to sudden ionospheric disturbances, disruptions in radio communications (“ionospheric storms”). The power of the X-ray burst (W/m2) varies from 10-8 ÷ 10-7 (class A) to 10-4 ÷ 10-3 (class X). 2. solar proton events (S1–S5)—measurement of the proton flux in near-Earth orbit, in units of the proton flux pfu (proton flux unit—the number of protons with energy >10 MeV in 1 cm2 per 1 s in a steradian = 1 pfu). The impact of events of points S2–S5 leads to disruptions of radio communications on the polar routes, and also creates a radiation risk for astronauts (“radiation storm”). The S1 score corresponds to a proton flux of 10 pfu; in the case of S5, the flux is 105 pfu. 3. geomagnetic storms (G1–G5)—disturbance of the geomagnetic field (“magnetic storm”) as a result of the impact on the magnetosphere of a solar plasma flow with increased density, temperature, particle velocity and with a southern orientation of the Bz component of the interplanetary magnetic field. Points are determined by 3-h values of the geomagnetic index Кp, which in this case has a range of values from 5 to 9.

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13 Future of Solar-Terrestrial Physics

Spaceship “Earth”. . .

Precision astronomical observations in space can serve as a clear example of how the prognostic and purely research tasks of solar-terrestrial physics are intertwined. Figure 13.8 shows sequential images of the near-solar space obtained by the LASCO coronagraph aboard the SOHO solar observatory at various points in time during the powerful solar flare on July 14, 2000. A sharp cloudiness of the image due to the action of energetic solar particles (“radiation storm”) is clearly visible. On this day, the LASCO/C2 coronagraph recorded a powerful coronal ejection directed strictly towards the Earth. Before that, another instrument, the Extreme-ultraviolet Imaging Telescope (EIT), recorded a powerful X-class flare near the center of the solar disk (observations of the Sun were carried out in the Fe XII 195 Å line). About half an hour later, a large flux of solar energetic particles (SEPs) came to Earth’s orbit, which caused “snow” in the images, since the electronic detectors of the cameras were bombarded by the SCR. Among a number of other instruments, on board the SOHO spacecraft there was also the so-called Coronal and Diagnostic Spectrometer (CDS), which recorded radiation from the solar corona in the extreme UV range. If the EIT telescope is aimed at registering flares, then the CDS spectrometer has a completely different observation area: it is designed to obtain unique information about the temperature, density, elemental composition and fluxes of very hot plasma captured in solar magnetic fields. However, CDS observations during the outbreak in question proved to be flawed and practically useless. Moreover, as a precautionary measure, the observations were interrupted to avoid any damage to the instrument. Thus, this outbreak gave the researchers a dramatic and very instructive lesson!. . . Let us now briefly summarize some of the results. Main effects. Usually, the following channels of the Sun’s influence on the Earth are considered in the STP chain: (1) Influence on the magnetosphere and ionosphere. (2) Solar-tropospheric connections. (3) Heliobiology (Sun and biosphere). (4) Solar activity and processes in the lithosphere (uneven rotation of the Earth, seismic

Fig. 13.8 Sequential images of the solar space obtained with the LASCO coronagraph aboard the SOHO solar observatory at various points in time during the powerful solar flare on July 14, 2000 (BDE). A sharp cloudiness of the image due to the action of energetic solar particles is clearly visible

13.6

Spaceship “Earth”. . .

211

phenomena). (5) Resonant structure and rhythms of the Solar System. (6) Energy and informational aspects of the Solar-Terrestrial Physics (STP). The last two channels have not yet been investigated enough and are almost not reflected in this book. Physical mechanisms of STP. According to modern concepts, the physical mechanisms and channels of action of the SA are distinguished by a great variety and complexity. Some SES mechanisms interact with each other, compete or reinforce each other. Their far from complete list looks like this: (1) Electromagnetic radiation of the Sun. (2) Shock waves in the solar wind. (3) Ionizing radiation (GCR and SCR). (4) Low-frequency pulsations of the magnetosphere. (5) Generation of infrasound in the polar atmosphere. (6) Formation of cosmogenic isotopes and nitrates. (7) Trigger mechanism in various SES phenomena. (8) Resonant connections in the solar system and earth’s shells. Solar-tropospheric connections. The variability of terrestrial weather and longterm climate fluctuations have attracted increased attention of astronomers and geophysicists in recent decades. At the same time, studies of solar-tropospheric relations are developing in several directions: statistical data, numerical modeling, physical (laboratory) modeling on Earth, and field experiments in near-Earth space. Their results can be summarized as follows: (1) The heliosphere affects the Earth’s climate (solar wind, IMF, cosmic dust, etc.). (2) The climate could have been influenced by irregular reversals of the geomagnetic field in the distant past. (3) There is an analogy with the processes observed in the Wilson chamber (the formation of fog droplets along the track of a passing charged particle). (4) Nucleation (condensation of water vapor) is important, primarily on negative charges in the atmosphere. (5) Artificial influence on precipitation by means of ionizing radiation is possible (experimental meteorology). (6) The influence of ionization on cloud formation can be tested in laboratory conditions, as is done at the Institute of Atmospheric Optics in Tomsk (Krymsky and Pavlov 2008; Krymsky et al. 2015) or at the CERN Charged Particle Accelerator (experiment CLOUD, see Sect. 10.6). (7) All electrical phenomena in the atmosphere are directly or indirectly related to cosmic rays (generation of charged particles in the atmosphere through ionization, the existence of free charges). The variability and ambiguity of solar-terrestrial relations (STR) as a whole for many years was one of the “stumbling blocks” on the way of understanding their physical mechanisms. The inability to indicate the exact initial and boundary conditions in the study of a particular STR phenomenon was the cause of skepticism among some researchers. In particular, the spatial-temporal variability of solaratmospheric relations is a serious problem. The response of the atmosphere (variations in pressure, temperature, cloudiness, etc.) to certain manifestations of SA can differ significantly depending on the region under study. The correlations between atmospheric characteristics and solar-geophysical factors turn out to be unstable over time: they can increase, weaken, change sign, or completely disappear depending on the considered time interval. As we already noted above in Chap. 10, the complexity of the problems associated specifically with cosmic rays

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is that there is no direct relationship between the SA level and the magnitude, for example, ΔT°C. Therefore, there is nothing surprising in the fact that the temporary instability of solar-climatic relations often gives rise to doubts about their reality. In this regard, an example of correlations found between low clouds and variations in galactic cosmic rays is indicative (Marsh and Svensmark 2000). High positive correlation between these values in 1983–2000 was considered evidence in favor of the mechanism of solar-climatic relations, including the effect of CRs on the state of cloudiness. Nevertheless, the violation of this correlation in the early 2000s called into question not only the effect of CRs on the intensity of microphysical processes in clouds, but also the contribution of CRs to the physical mechanism of solar-climatic relations. In this regard, one of the most important results of the work is to clarify the role of the stratospheric circumpolar vortex in changes in the large-scale circulation of the atmosphere (Veretenenko and Ogurtsov 2015). A ~60-year periodicity was revealed in the variations in the intensity of the circumpolar vortex. It is shown that the intensification of cyclonic processes at polar fronts of middle latitudes takes place only with a strong vortex. The evolution of the circumpolar creates a “background” (“underlying surface”) and serves as a probable cause of the temporal variability of solar-atmospheric relations. Influence on the thermosphere. In 2010, indirect evidence was published that solar activity has a long-term effect on the state of the Earth’s thermosphere (altitude interval ~200–800 km). Most artificial Earth satellites (AES) rotate at such altitudes. NASA specialists analyzed the degradation of the orbits of 5000 satellites orbiting in the range of altitudes of 200–600 km above the Earth in 1967–2010 (almost four cycles of solar activity). As is known, orbital degradation is caused by the aerodynamic drag of the thermosphere, i.e. its density. The results of the analysis show that at the reference altitude of ~400 km, the density of the thermosphere experienced significant fluctuations, and during the last four SA cycles, a tendency to its systematic decrease was observed. Moreover, in 2008–2009, i.e. at the minimum of the 23rd cycle, the density of the thermosphere was 28% lower than expected (based on the magnitude of its systematic trend in previous cycles). According to NASA estimates, in the current, previously unprecedented “dip” (minimum) in solar activity, the “collapse” of the thermosphere was 2–3 times deeper than at any other time in the history of space flights. Moreover, the collapse of the thermosphere turned out to be deeper than could be explained by its current models. It cannot be ruled out that greenhouse gases could have contributed to the change in the density of the thermosphere. However, in any case, this effect can be explained using all conceivable hypotheses and models of the thermosphere by no more than 40%. Trying to find an alternative explanation, NASA experts drew attention to the anomalous decrease in the flux of solar radiation in the extreme ultraviolet region (100–280 nm) in 2007–2009. Such a decrease, recorded in measurements on board the SOHO and TIMED spacecraft, as well as in suborbital flights of rockets, may just be the true (solar) reason for the decrease in density. Heliobiology. (1) Evidence that cosmophysical effects in the biosphere are real and are of great importance. (2) As for the unresolved heliobiological problems, the

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question of how much the last protracted minimum of the SA affected the life of the biosphere, when the magnetosphere “swelled” due to the weakening of the solar wind, remains unexplored . . . How much could the rhythm-setting role of the Sun have changed during this period? (3) If we remain on the basis of scientific knowledge about the Cosmos, then there is no fatalistic helio-conditioning of our entire life, its dependence on the whims of our “sovereign luminary”, but there is the concept of the unity of the organism and the environment (Umwelt). Moreover, there are some grounds to consider solar-terrestrial relations as a manifestation of general syndrome of the adaptation of living organisms to changing conditions of the solarterrestrial environment, or general evolutionary adaptation syndrome—GEAS (see, e.g., Obridko et al. 2013). Obvious changes in the Earth’s climate, numerous weather anomalies, more frequent natural, man-made, geopolitical and humanitarian disasters, growing social upheavals on a local and global scale—all this suggests that people should not exaggerate their “power over Nature.” In any case, we are still very far from being able to “control” phenomena of a cosmic and even planetary scale. However, many of them Science is already able to foresee, which allows them to be used for the benefit of people or to reduce their harmful effects. At the same time, however, we should not forget the words of A.L. Chizhevsky about the “insignificance . . . of the physical organization” of man in front of the “physical forces of nature.” Let us also recall the far-sighted warning of Friedrich Engels: “Let us not, however, be too deluded by our victories over nature. For each such victory, she takes revenge on us. Each of these victories has, however, first of all the consequences that we are counting on, but second and third, completely different, unforeseen consequences, which very often destroy the significance of the former”. At the same time, relying on the existing achievements of the STP and the concept of sustainable development of mankind, cosmophysicists need to maintain true scientific optimism and maintain a high spirit of creation.

13.7

Search for Alien Life. . .

The last phrase of previous paragraph is completely applicable to the search for alien life and to exobiology. It was conceivable demonstrated in the series of recent experiments (see, e.g., a detailed review by Alekseev et al. 2022). The experiments were carried out in 2006–2016 onboard the International Space Station (ISS). We emphasized that this topic has close relation to the problems of STR. In the ISS experiments fundamentally new data were obtained on the stability of the resting stages of aquatic organisms to the space flight factors (SFF). The results strongly modified the idea of the possibility of bringing Earth life forms to other planets with spacecraft and astronauts. It also can be used for creating of the extraterrestrial artificial ecosystem and for searching of extraterrestrial life. As noted by the authors (Alekseev et al. 2022), investigations to forward the use of animal and plant anabiosis, e.g. cryptobiosis, and some other forms of dormancy,

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in space exploration highlight several notable programs on exobiology. Biomedical support of humans in the absence of factors important to sustenance and development of every living being is one of the indisputable aspects of space exploration (Alekseev et al. 2007). Also, as known, development of life support systems, including systems incorporating the biological cycle, has been pursued since the initial space flights of cosmonauts (astronauts). Implementation of the central ecological life support systems (CELSS) for space crews requires prior all-around tests and studies in order to: (1) determine the biological impacts of the SFF on the life of individual organisms, as well as communities (populations and biocenoses); (2) develop technologies for cultivating highly productive populations of autotrophs and heterotrophs in the zero-gravity environment; (3) design hardware to sustain the vital functions of autotrophs and heterotrophs as members of space crew CELSS; (4) search for methods to preserve the gene pool aboard the space vehicle and on the planetary outposts; (5) optimize CELSS with consideration for microgravity and constant radiation exposure. The phenomenon of protracted biological resting can be viewed as the alternative to transportation of the active ecosystem (Alekseev et al. 2006). Persisting forms of life may be the cause for incidental colonization of planets by terrestrial organisms and vice versa. This illustrates the problem of biological survival in hostile environments on and beyond the Earth. The quarantine measures to be developed should establish a barrier to any illicit penetration of dormant life into the environment of the Earth or another planet. It should be said that the high protective properties of dormant stages of organisms to the effects of negative elements of the SFF are fundamentally different from the mechanisms and possibilities of overcoming negative effects in active stages of organisms, both aquatic and terrestrial. The increased viability of the diapausing stages of invertebrates and fish is based on the reduced level of the general metabolism of the organism and the related functions such as respiration, feeding, movement, etc., which are reduced to zero in the stages most deeply immersed in biological dormancy. This determined the possibility of long-term (up to 2 years in the conducted experiments) maintaining of the viability of these stages in the atmosphere-deprived Biorisk and Expose-R modules on the outer side of the ISS. The second important adaptation of these stages, which determined their increased resistance to significant temperature fluctuations outside the ISS, as well as to the damaging effects of neutron radiation and the high-energy part of the solar radiation spectrum (for details see (Alekseev et al. 2022)), is their almost complete dehydration and replacement of water in cells with protective antifreeze substances (trehalose, etc.). Finally, most of the organisms used in these experiments were embryos that stopped development at the early stages of development (usually gastrula). Non-specialized cells of embryos have increased resistance to negative influences, in comparison with tissue cells, and the embryos themselves are enclosed in multilayer membranes that increase their protection from external mechanical, chemical and energy (ultraviolet) influences. In the light of these results it should be noted that previous studies of the effects of the space flight factors were carried out on organisms of a wide evolutionary range

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from bacteria to humans, but always in an active state (e.g., Kislovsky 1971, 1982; Ozheredov and Breus 2008; Zenchenko and Breus 2021). The level of adaptive capabilities of active organisms is not comparable with the resting stages, and the mechanisms of adaptation to the SFF are radically different for them. This determined the necessity of their separate study and consideration in the form of independent scientific directions (Alekseev et al. 2006, 2007, 2019, 2022).

*** If we talk about the worldview side of solar-terrestrial physics and the physics of the Cosmos as a whole, then one cannot but recall our wonderful compatriot M.V. Lomonosov. The world space, “the vastness of immeasurable places”, in his apt expression, the starry sky, the heavenly bodies are the favorite image and object of contemplation of M.V. Lomonosov:

An abyss has opened, full of stars; There is no number of stars, the bottom of the abyss. A grain of sand like in the waves of the sea How small is a spark in eternal ice, Like fine dust in a strong whirlwind, In fire as fierce as a feather, So I’m deep in this abyss, I’m lost, tired of thoughts. Evening Meditation on God’s Majesty in the case of the great northern lights (1743).

Probably, the same feelings at the sight of the starry sky were experienced almost two centuries later by our other poet—V.V. Mayakovsky (“Already the second. . .”, 1930):

Look how quiet the world is. The night overlaid the sky with a stellar tribute. At these hours you get up and say Centuries, history and the universe.

And I would like to end our story with verses by the outstanding English poet of the nineteenth century, Alfred Tennyson (1809–1892). In his poem Ulysses, he prophetically wrote: “To strive, to seek, to find and not to yield”. These words contain a whole life program for young researchers.

Instead of an Afterword

As noted in the Foreword, this book is partly personal. From personal experience, I recall the history of our dispute with B.M. Vladimirsky on the nature of muon bursts observed in close conjugation with ground-based SCR enhancements (see, for example, Karpov et al. 1998; Miroshnichenko and Karpov 2004). B.M. Vladimirsky did not agree with our interpretation of the nature of the bursts. He considered the “Baksan effect” (e.g., Karpov et al. 1998) to be an artifact caused by the influence of heliopathic weather on the registration efficiency (sensitivity) of muon counters. Under the influence of this dispute, we presented a special report (Karpov and Miroshnichenko 2008) at the 30th International Conference on Cosmic Rays (July 2007, Merida, Yucatan, Mexico), in which a new interpretation was given. The main idea boiled down to the assertion that rare but large events represent a special, little-studied area in physics, biology and other sciences, by analogy with the above-mentioned macrofluctuations. In December 2009, on the initiative of B.M. Vladimirsky even discussed the possibility of publishing a joint article in the journal “Geomagnetism and Aeronomy” with an analysis of all the arguments “for” and “against” when interpreting the “Baksan effect”. Unfortunately, due to a significant difference in approaches, this feature was never implemented. Our point of view, stated in the Mexican report, allowed at least to obtain more reasonable estimates of the burst intensity (see below). The authors (Karpov and Miroshnichenko 2008) have suggested a new statistical method for search of weak signals of various natures. This method is applied when average value of a signal does not give statistically significant excess over an average background of the device. The method uses a property of statistical distributions to increase number of the large fluctuations far from the mean value. Suggested method provides extraction of such deviations caused by a weak signal. The method of additional fluctuations is most useful in the search experiments working near to a limit of accuracy of the detector. Authors applied this method to interpret some peculiarities of muon bursts observed at the Baksan Underground Scintillation

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Telescope (BUST) in close correlation with a number of GLE events of solar cosmic rays. Thus, the additional counting rate of a signal will make up only 0.6σ or 11% from full amplitude of the found burst. Therefore, the SCR flux obtained by suggested method of additional fluctuations is about 10 times less, than estimated earlier by Karpov et al. (1998) with use of full amplitude of the burst. This greatly facilitated the physical interpretation of the Baksan effect. In particular, as a result of our approach, we obtained more realistic estimate of the amplitude of the muon burst observed during the GLE event of 29 September 1989. And this is only one from possible examples of delayed discussions. Anticipating coming publication of the book by Böthmer and Daglis (2022) with a sounding title “Space Weather. Physics and Effects”, we are confident that both books will complement each other successfully, although they will present separate issues from different points of view. In any case, as we have already noted many times, many problems in this research area are still awaiting solution. Leonty Miroshnichenko, IZMIRAN, December 2021.

Appendices

Geocentric Solar Ecliptic System The Geocentric Solar Ecliptic System (GSE) has its X-axis pointing from the Earth towards the Sun and its Y-axis is chosen to be in the ecliptic plane pointing towards dusk (thus opposing planetary motion). Its Z-axis is parallel to the ecliptic pole. Relative to an inertial system this system has a yearly rotation.

Geocentric Solar Equatorial System The Geocentric Solar Equatorial System (GSEQ) as with the GSE system has its X-axis pointing towards the Sun from the Earth. However, instead of having its Y-axis in the ecliptic plane, the GSEQ Y-axis is parallel to the Sun’s equatorial plane which is inclined to the ecliptic. We note that since the X-axis is in the ecliptic plane and therefore is not necessarily in the Sun’s equatorial plane, the Z-axis of this system will not necessarily be parallel to the Sun’s axis of rotation. However, the Sun’s axis of rotation must lie in the X-Z plane. The Z-axis is chosen to be in the same sense as the ecliptic pole, i.e. northwards.

Geocentric Solar Magnetospheric System The Geocentric Solar Magnetospheric System (GSM), as with both the GSE and GSEQ systems, has its X-axis from the Earth to the Sun. The Y-axis is defined to be perpendicular to the Earth’s magnetic dipole so that the X-Z plane contains the dipole axis. The positive Z-axis is chosen to be in the same sense as the northern magnetic pole. The difference between the GSM system and the GSE and GSEQ is simply a rotation about the X-axis. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 L. Miroshnichenko, Solar-Terrestrial Relations, https://doi.org/10.1007/978-3-031-22548-2

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