Water Snowline in Protoplanetary Disks [1st ed.] 9789811574382, 9789811574399

Table of contents :
Front Matter ....Pages i-xiii
Introduction (Shota Notsu)....Pages 1-10
Modeling Studies I. The Case of the T Tauri Star (Shota Notsu)....Pages 11-43
Modeling Studies II. The Case of the Herbig Ae Star (Shota Notsu)....Pages 45-82
Modeling Studies III. Sub-millimeter H\(_{2}\)\(^{16}\)O and H\(_{2}\)\(^{18}\)O Lines (Shota Notsu)....Pages 83-111
ALMA Observation of the Protoplanetary Disk Around HD 163296 (Shota Notsu)....Pages 113-128
Summary and Future Works (Shota Notsu)....Pages 129-132
Back Matter ....Pages 133-134

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Springer Theses Recognizing Outstanding Ph.D. Research

Shota Notsu

Water Snowline in Protoplanetary Disks

Springer Theses Recognizing Outstanding Ph.D. Research

Aims and Scope The series “Springer Theses” brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected for its scientific excellence and the high impact of its contents for the pertinent field of research. For greater accessibility to non-specialists, the published versions include an extended introduction, as well as a foreword by the student’s supervisor explaining the special relevance of the work for the field. As a whole, the series will provide a valuable resource both for newcomers to the research fields described, and for other scientists seeking detailed background information on special questions. Finally, it provides an accredited documentation of the valuable contributions made by today’s younger generation of scientists.

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Shota Notsu

Water Snowline in Protoplanetary Disks Doctoral Thesis accepted by Kyoto University, Kyoto, Japan

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Author Dr. Shota Notsu Star and Planet Formation Laboratory RIKEN Cluster for Pioneering Research Saitama, Japan

Supervisors Prof. Hideko Nomura Division of Science National Astronomical Observatory of Japan Tokyo, Japan Prof. Shin Mineshige Department of Astronomy, Graduate School of Science Kyoto University Kyoto, Japan

ISSN 2190-5053 ISSN 2190-5061 (electronic) Springer Theses ISBN 978-981-15-7438-2 ISBN 978-981-15-7439-9 (eBook) https://doi.org/10.1007/978-981-15-7439-9 © Springer Nature Singapore Pte Ltd. 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, 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 Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Supervisors’ Foreword

This thesis presents the pioneering work on a critical observational test of the planet formation theory based on the theoretical study of the H2 O snowline, beyond which H2 O takes a form of ice, in the protoplanetary disks, the place where planets are formed. Since the water snowline is thought to divide the regions of rocky and gas-giant planet formation, the location of the snowline is essential for the planet formation process. The author proposed a novel method to locate the snowlines using high dispersion observations of water vapor lines. The basis of this method lies in the sophisticated chemical modelling and line radiative transfer calculations. That is, the author obtained the water vapor distribution in the disks using the chemical reaction network which includes photoreactions and gas-grain interaction. In addition, the author simulated transition lines of water vapor in the disks to find that relatively weak transition lines with moderate excitation energies are best tracers of water snowline. Furthermore, the author observed submillimeter lines of water vapor towards a disk using ALMA (Atacama Large Millimeter/submillimeter Array) to obtain the upper limit of the line fluxes with the highest sensitivity so far. The author’s finding is unprecedented and is truly valuable to locate the snowlines in the disks. This method will contribute in a great deal towards a complete understanding of the planet formation processes as well as of the origin of water on rocky planets, including our Earth, by future observations with ALMA and SPICA (Space Infrared Telescope for Cosmology and Astrophysics). Tokyo, Japan Kyoto, Japan August 2020

Prof. Hideko Nomure Prof. Shin Mineshige

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Parts of this thesis have been published in the following journal articles. Chemical structures of protoplanetary disks and possibility to locate the position of the H2O snowline using spectroscopic observations. The above is the original title of this doctoral thesis accepted by Kyoto University on March 25th, 2019 (Degree Report No. k21574). Figures, tables, and some texts in these papers are reproduced with permission from American Astronomical Society (AAS). Paper I, “Candidate Water Vapor Lines to Locate the H2 O Snowline through High-Dispersion Spectroscopic Observations. I. The Case of a T Tauri Star” Shota Notsu, Hideko Nomura, Daiki Ishimoto, Catherine Walsh, Mitsuhiko Honda, Tomoya Hirota, T. J. Millar 2016, The Astrophysical Journal, 827, 113 DOI: 10.3847/0004-637X/827/2/113 Paper II, “Candidate Water Vapor Lines to Locate the H2 O Snowline Through High-dispersion Spectroscopic Observations. II. The Case of a Herbig Ae Star” Shota Notsu, Hideko Nomura, Daiki Ishimoto, Catherine Walsh, Mitsuhiko Honda, Tomoya Hirota, T. J. Millar 2017, The Astrophysical Journal, 836, 118 DOI: 10.3847/1538-4357/836/1/118 Paper III, “Candidate Water Vapor Lines to Locate the H2 O Snowline through High-dispersion Spectroscopic Observations. III. Submillimeter H216O and H218O Lines” Shota Notsu, Hideko Nomura, Catherine Walsh, Mitsuhiko Honda, Tomoya Hirota, Eiji Akiyama, T. J. Millar 2018, The Astrophysical Journal, 855, 62 DOI: 10.3847/1538-4357/aaaa72 Paper IV, “Dust Continuum Emission and the Upper Limit Fluxes of Submillimeter Water Lines of the Protoplanetary Disk around HD 163296 Observed by ALMA” Shota Notsu, Eiji Akiyama, Alice Booth, Hideko Nomura, Catherine Walsh, Tomoya Hirota, Mitsuhiko Honda, Takashi Tsukagoshi, T. J. Millar 2019, The Astrophysical Journal, 875, 96 DOI: 10.3847/1538-4357/ab0ae9

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Acknowledgements

First of all, I sincerely would like to thank Prof. Hideko Nomura for continuous encouragements, supports, and accurate advices. She was an associate professor of Tokyo Institute of Technology (and from April 2019 she is a professor of National Astronomical Observatory of Japan), and she has also been my substantial supervisor for my research since when I was a fourth-year undergraduate student. Since she is an expert on not only star and planet formation, but also astrochemistry and physics of interstellar medium, I studied a lot of knowledge and important viewpoints from her. Thanks to her, now I have great interests for star and planet formation processes and protoplanetary disks. I am very grateful to Dr. Takanori Sasaki for his daily supports and deep discussions. Since he is also an expert on planetary sciences, he gave me a lot of ideas and viewpoints for my research and studies. Prof. Shin Mineshige, Dr. Keiichi Maeda, Dr. Shiu-Hang (Herman) Lee, and Dr. Norita Kawanaka are also the staffs of groups which I belonged to (the group of theoretical sciences), and gave me a lot of useful and instructive advices. The whole contents of the research reported in this thesis are on the basis of collaborative researches with Prof. Hideko Nomura, Mr. Daiki, Ishimoto, Dr. Catherine Walsh, Dr. Mitsuhiko Honda, Dr. Tomoya Hirota, Dr. Eiji Akiyama, Dr. Takashi Tsukagoshi, Dr. Alice S. Booth, Prof. T. J. Millar, and other collaborators. I would like to thank them very much for discussing with me and giving me a lot of useful ideas and comments. I am grateful to Dr. Ryo Tazaki, Dr. Tomohiro Ono, and other members of past and present planetary science group in Department of Astronomy, Kyoto University, for giving me a lot of useful advices in seminars and daily discussion time. I am grateful to Prof. Inga Kamp, Dr. Stefano Antonellini, Dr. Itsuki Sakon, Dr. Chris Packham, Prof. Hiroshi Shibai, and Prof. Takao Nakagawa and others for their useful advices about the possibility of infrared high-dispersion spectroscopic observations (e.g., SPICA and TMT/MICHI). I also thank Prof. Ewine van Dishoeck, Dr. Satoshi Okuzumi, Dr. Akimasa Kataoka, Dr. Satoshi Ohashi, and others for giving me their useful comments about disk structures, calculations of

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Acknowledgements

emission lines, and ALMA observations. Our numerical studies were carried out on SR16000 at Yukawa Institute for Theoretical Physics (YITP) and computer systems at Kwasan and Hida Observatory (KIPS) in Kyoto University, and PC cluster at Center for Computational Astrophysics, National Astronomical Observatory of Japan. ALMA Data analysis was carried out on the Multi-wavelength Data Analysis System operated by the Astronomy Data Center (ADC), National Astronomical Observatory of Japan. This work is mainly supported by Grants-in-Aid for JSPS (Japan Society for the Promotion of Science) fellows (Grant Number; 16J06887), and by the Astrobiology Center Program of National Institutes of Natural Sciences (NINS) (Grant Number; AB281013). In this thesis, figures, tables, and some texts are reproduced with permission from American Astronomical Society (AAS) and Astronomy & Astrophysics (A&A), ESO. Our work makes use of the following ALMA data: ADS/JAO.ALMA #2015.1.01259.S, ADS/JAO.ALMA #2013.1.00601.S, and ADS/JAO.ALMA #2016.1.00884.S. ALMA is a partnership of European Southern Observatory (ESO) (representing its member states), National Science Foundation (USA), and National Institutes of Natural Sciences (Japan), together with National Research Council (Canada), National Science Council and Academia Sinica Institute of Astronomy and Astrophysics (Taiwan), and Korea Astronomy and Space Science Institute (Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, Associated Universities, Inc/National Radio Astronomy Observatory (NRAO), and National Astronomical Observatory of Japan. Although the contents of this thesis are in the field of the star and planet formation, I have also studied the stellar flares, especially superflares on solar type stars, since 2010 when I was a first-year undergraduate student. Through conducting superflare studies, I have obtained the knowledge for solar and stellar physics, and photometric and spectroscopic observations. Such knowledge is also useful to understand the studies of star and planet formation (for example, the activity of young stars and spectroscopic observations of disks). In addition, there are more than 15 superflare papers which I was a first author or a coauthor published so far. Furthermore, the experiences of superflare studies give me a reason and a lot of passions to step forward the way of an astrophysicist. I am very grateful to Prof. Kazunari Shibata, Dr. Daisaku Nogami, Dr. Satoshi Honda, Dr. Hiroyuki Maehara, Prof. Yosuke A. Yamashiki, Dr. Yuta Notsu, Mr. Kosuke Namekata, Mr. Kai Ikuta, Dr. Takuya Shibayama, and others, who are the members of superflare studies. I am grateful to all of the past and current members of Department of Astronomy and Astronomical Observatories, Graduate School of Science, Kyoto University, for their various supports to my research activities. Finally, I thank my parents, brothers, and grandparents with my deepest gratitude for their sincere understandings and powerful supports. I could not have finished this thesis without their continuous encouragement and supports. I would also like to thank many teachers and friends for helping me in my life so far. I am glad if this thesis will be their pleasures.

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 The Overview of the Protoplanetary Disks . . . . . . . . . . . . . . . 1.2 The Definition of the H2 O Snowline in the Protoplanetary Disks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 The Positions of the H2 O Snowline and the Roles of Water Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Previous Direct Imaging Observations of Protoplanetary Disks 1.5 Previous Spectroscopic Observations of Strong Water Lines . . 1.6 Purposes and Structure of This Thesis . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Modeling Studies I. The Case of the T Tauri Star . . . . . . . . . . . 2.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 The Disk Physical Model . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Overview of Disk Chemical Structure . . . . . . . . . . . . . 2.1.3 Gas-Phase Reactions . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.4 Gas-Grain Interactions . . . . . . . . . . . . . . . . . . . . . . . . 2.1.5 Water Emission Line Profiles . . . . . . . . . . . . . . . . . . . 2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 The Distributions of H2 O Gas and Ice . . . . . . . . . . . . 2.2.2 The Overview of Ortho-H2 16 O Lines from the T Tauri Disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 The Case of a Candidate Ortho-H2 16 O Emission Line . 2.2.4 The Case of a Ortho-H2 16 O Emission Line that Probes the Hot Surface Layer . . . . . . . . . . . . . . . . . . . . . . . . 2.2.5 The Case of a Ortho-H2 16 O Emission Line that Probes the Cold Water Resovoir . . . . . . . . . . . . . . . . . . . . . .

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2.3 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Influence of Model Assumptions . . . . . . . . . 2.3.2 Critical Density and the Assumption of LTE . 2.3.3 Requirement for the Observations . . . . . . . . . 2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 Modeling Studies II. The Case of the Herbig Ae Star . . . . . . . . 3.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 The H2 O Gas and Ice Distributions . . . . . . . . . . . . . 3.2.2 The Overview of Ortho-H2 16 O Lines from a Herbig Ae Disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 The Case of Candidate Ortho-H2 16 O Emission Lines . 3.2.4 The Case of the Less Suited Ortho-H2 16 O Emission Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.5 The Candidate Ortho-H2 16 O Line Fluxes . . . . . . . . . 3.2.6 The Radial Distributions of Normalized Cumulative Line Fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Influence of Model Assumptions on the Line Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Critical Density and the Assumption of LTE . . . . . . . 3.3.3 Previous Water Line Observations in Herbig Ae Disks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.4 Requirement for the Observations of Candidate Ortho-H2 16 O Lines . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4 Modeling Studies III. Sub-millimeter H2 16 O and H2 18 O Lines . 4.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 The Disk Physical Structures and Molecular Abundances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Water Emission Line Profiles from Protoplanetary Disks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 The Profiles of Sub-millimeter Water Emission Lines 4.2.2 The Local Intensity and Optical Depth Distributions . 4.2.3 The Normalized Radial Cumulative Line Fluxes . . . . 4.2.4 The Properties of All Other Sub-millimeter Water Emission Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4.3 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Influence of Dust Emission on Water Line Properties 4.3.2 Influence of Different H2 O Snowline Positions and Line Velocity Resolutions . . . . . . . . . . . . . . . . . 4.3.3 Requirement for the Future Observations . . . . . . . . . 4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5 ALMA Observation of the Protoplanetary Disk Around HD 163296 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Observation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Setup of Our Observation and Data Reduction . . . 5.1.2 Targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Water Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Upper Limit of the Water Line Fluxes . . . . . . . . . 5.2.2 Matched Filtering Analysis . . . . . . . . . . . . . . . . . . 5.3 Dust Continuum Image and Radial Profiles . . . . . . . . . . . 5.4 The First Detection of 13 C17 O in a Protoplanetary Disk . . 5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 Summary and Future Works 6.1 Modeling Studies I, II . . . 6.2 Modeling Studies III . . . . 6.3 ALMA Observations . . . . 6.4 Future Works . . . . . . . . . References . . . . . . . . . . . . . . .

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Curriculum Vitae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

Chapter 1

Introduction

Abstract This chapter is the introduction section of our thesis, “Water snowline in protoplanetary disks”. Observationally locating the position of the H2 O snowline in protoplanetary disks is important to understand the planetesimal and planet formation processes, and the water trail to rocky planets. The line profiles from disks are usually affected by doppler shift due to Keplerian rotation. Thus, the line profiles are sensitive to the radial distribution of the emitting regions of lines. However, water lines which have been obtained by previous infrared spectroscopic observations mainly traced the disk surface and the cold water reservoir outside the H2 O snowline. Thus, they are not good direct tracer of the H2 O snowline. In this thesis, we proposed a method to locate the H2 O snowline position more directly by analyzing the H2 O line profiles which can be obtained by high dispersion spectroscopic observations across a wide wavelength rage (from mid-infrared to sub-millimeter, e.g., SPICA, ALMA) and selected based on specific criteria. Keywords Protoplanetary disks · Astrochemistry · Snowline · Planet formation

1.1 The Overview of the Protoplanetary Disks Around young newly formed stars (e.g., Herbig Ae/Be stars, T Tauri stars), rotating accretion disks called “protoplanetary disks”, are formed. The disks are composed of gas and dust grains, and contain the building blocks which will form planetary systems (e.g., Armitage [7]). They are active environments for the creation of simple and complex molecules (e.g., Caselli and Ceccarelli [14], Henning and Semenov [30], Pontoppidan et al. [81]). The disk physical and chemical environments determine the planet properties, such as chemical composition and mass (e.g., Öberg et al. [68]), and water is one of the key molecules in star and planet forming regions.

© Springer Nature Singapore Pte Ltd. 2020 S. Notsu, Water Snowline in Protoplanetary Disks, Springer Theses, https://doi.org/10.1007/978-981-15-7439-9_1

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1 Introduction

Fig. 1.1 The outline picture of the disk physical and chemical structures and grain evolutions around the H2 O snowline

1.2 The Definition of the H2 O Snowline in the Protoplanetary Disks In the hot inner regions of disks, H2 O ice evaporates from the surface of the grains. In contrast, it is frozen out on the dust-grain surfaces in the disk outer cold parts. The border of these two regions is he H2 O snowline [28]. Outside the H2 O snowline, the solid material is enhanced with the supply of H2 O ice, dust grains can stick at higher collisional velocities and efficient coagulation are promoted (e.g., Wada et al. [108]), since dust grains are covered with water ice mantles. Thus, the gaseous planet core formation is promoted in such regions, and we can regard the H2 O snowline in disk midplane divides the regions of gas-giant planet and rocky planet formation (e.g., Hayashi [28, 29], Öberg et al. [68]). The disk physical and chemical structures and grain evolutions around the H2 O snowline are summarized in Fig. 1.1.

1.3 The Positions of the H2 O Snowline and the Roles of Water Molecules Icy pebbles, planetesimals, and/or comets coming from beyond the H2 O snowline may bring water to rocky planets (e.g., Morbidelli et al. [54–57], Walsh et al. [110], Ida and Guillot [37], Matsumura et al. [48], Sato et al. [96], Raymond and Izidoro [89]). In the case of disks around solar-mass T Tauri stars, the H2 O snowline will exist at a few au from the central star (e.g., Hayashi [29]). If we change the physical conditions such as the central star luminosity, the dust-grain size distribution, and the mass accretion rate in the disk, the H2 O snowline position will change. Recent theoretical studies, such as Davis [16], Garaud and Lin [25], Min et al. [52], Oka et al. [69], Martin and Livio [45, 46], Du and Bergin [19], Harsono et al. [27], Mulders

1.3 The Positions of the H2 O Snowline and the Roles of Water Molecules

3

Fig. 1.2 The snowline distance (Rsnow ) as a function of the mass accretion rate with various dust grain sizes for a typical T Tauri disk [69]. The orange, green, blue, red, and black curves represent the snowline positions with dust grain sizes of 1 mm, and 100, 10, 1, 0.1 µm, respectively. The dashed and solid curves represent the results without and with icy grain opacity, respectively. This figure is originally reported in Oka, A., Nakamoto, T., & Ida, S. (2011, ApJ, 738, 141, “Evolution of Snow Line in Optically Thick Protoplanetary Disks: Effects of Water Ice Opacity and Dust Grain Size”, DOI: https://doi.org/10.1088/0004-637X/738/2/141), and reproduced with permission from American Astronomical Society (©AAS)

et al. [58], Piso et al. [75], Sato et al. [96], investigated H2 O snowline evolutions, and showed that it will migrate as the dust grain size grows and the mass accretion rate decreases (see also Fig. 1.2). The H2 O snowline position is inside 1 au in some cases, and it means that as the disk evolves, the water-devoid planetesimal formation within the H2 O snowline is more difficult. Martin and Livio [45, 46] calculated the H2 O snowline evolutions in a disk with self-gravitational heating and a dead-zone, and suggest that enough mass and time is existed in the disk to form the terrestrial planets from water-devoid planetesimals at 1 au. According to Ros and Johansen [91], dust-grain growth due to the condensation from millimeter to around 10−1 meter sized pebbles is possible on only ∼103 years around the H2 O snowline. Such pebbles are efficiently concentrated by streaming instabilities, pressure bumps, and vortices, and then grow up into planetesimals, even in young age (< 106 yr). Banzatti et al. [8] recently argued a sharp discontinuity in the radial profile of the dust emission spectral index around the H2 O snowline, due to replenishment of small grains through fragmentation because of the change in fragmentation velocities. Dust aggregates disrupt with collisions, and pile up at the region slightly outside the snowlines due to the sintering effects [70]. They have been discussed to explain the multiple gap and rings of the young disk HL Tau (e.g., ALMA Partnership et al. [3]). According to Zhang et al. [112], The innermost gap position (13 au) is coincident with the expected H2 O snowline position. Banzatti et al. [8] and Okuzumi et al. [70] reported the H2 O snowline position of HL Tau is 3000 K) and large values of Einstein A coefficients, and exist in the near- to mid-infrared wavelength regions where dust emission becomes optically thick in the disk surface.

1.6 Purposes and Structure of This Thesis In this thesis, we proposed a method to locate the H2 O snowline position more directly by analyzing the Keplerian profiles of H2 O lines which can be detected by high dispersion spectroscopic observations across a wide wavelength rage (from

8

1 Introduction

mid-infrared to sub-millimeter, e.g., ALMA, SPICA) and selected based on specific criteria. First of all, we calculated the chemical structures of protoplanetary disks using self-consistently derived physical models of a typical T Tauri disk [66] and a typical Herbig Ae disk [65] to get the H2 O gas and ice abundances, as opposed to assuming the H2 O snowline position. Next, we calculated the velocity profiles of ortho-H2 16 O emission lines from those disks ranging from near-infrared to sub-millimeter wavelengths, and investigated the properties of lines that locate the H2 O snowline position. The method, results, and discussions of the T Tauri disk case (paper I, [66]) and the Herbig Ae disk (paper II, [65]) case are reported in Sects. 2 and 3, respectively. In Sect. 4 (paper III, [64]), we extended our calculations beyond ortho-H2 16 O lines only to sub-millimeter para-H2 16 O and ortho- and para-H2 18 O lines. We discussed the possibility to detect those water lines to locate the H2 O snowline position with future observations with the Atacama Large Millimeter/Submillimeter Array (ALMA). We also investigate the effects of dust emission on velocity profiles of water lines. In Sect. 5 (paper IV, [63]), we also report our ALMA observations of submillimeter water lines (ortho-H2 16 O 321 GHz, para-H2 18 O 322 GHz, and HDO 335 GHz) from the disk around Herbig Ae star HD163296. These lines are considered to be the prime candidate water lines available at sub-millimeter wavelength range in order to locate the H2 O snowline [64–66]. We also report the dust continuum emission from the disk around HD 163296 at a spatial resolution of ∼15 au, that confirms the multi-gapped and ringed structure which was originally detected in previous observations (e.g., Isella et al. [39, 40], Andrews et al. [4], Dent et al. [17]). Most contents of this thesis is based on our refereed papers that have been published [63–66]. In particular, all Figures after Fig. 6 and all Tables are originally reported by these papers. In this thesis, figures, tables, and some texts are reproduced with permission from American Astronomical Society (©AAS) and Astronomy & Astrophysics (A&A), ©ESO.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

Akiyama E, Hasegawa Y, Hayashi M, Iguchi S (2016) ApJ 818:158 Akiyama E, Muto T, Kusakabe N et al (2015) ApJL 802:L17 ALMA Partnership, Brogan CL, Pérez LM et al (2015) ApJL 808:L3 Andrews SM, Huang J, Pérez LM et al (2019) ApJL 869:L41 Andrews SM, Wilner DJ, Zhu Z et al (2016) ApJL 820:L40 Antonellini S, Bremer J, Kamp I et al (2017) A&A 597:A72 Armitage PJ (2011) ARA&A 49:195 Banzatti A, Pinilla P, Ricci L et al (2015) ApJL 815:L1 Banzatti A, Pontoppidan KM, Salyk C et al (2017) ApJ 834:152 Benisty M, Juhasz A, Boccaletti A et al (2015) A&A 578:L6 Blevins SM, Pontoppidan KM, Banzatti A et al (2016) ApJ 818:22 Carr JS, Najita JR (2008) Science 319:1504 Carr JS, Najita JR (2011) ApJ 733:102 Caselli P, Ceccarelli C (2012) A&A Rv 20:56

References 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65.

9

Cieza LA, Casassus S, Tobin J et al (2016) Nature 535:258 Davis SS (2005) ApJ 620:994 Dent WRF, Pinte C, Cortes PC et al (2019) MNRAS 482:L29 Dent WRF, Thi WF, Kamp I et al (2013) PASP 125:477 Du F, Bergin EA (2014) ApJ 792:2 Du F, Bergin EA, Hogerheijde M et al (2017) ApJ 842:98 Fedele D, Bruderer S, van Dishoeck EF et al (2012) A&A 544:LL9 Fedele D, Bruderer S, van Dishoeck EF et al (2013) A&A 559:AA77 Fedele D, Pascucci I, Brittain S et al (2011) ApJ 732:106 Fukagawa M, Tsukagoshi T, Momose M et al (2013) PASJ 65:L14 Garaud P, Lin DNC (2007) ApJ 654:606 Goto M, Usuda T, Dullemond CP et al (2006) ApJ 652:758 Harsono D, Bruderer S, van Dishoeck EF (2015) A&A 582:A41 Hayashi C (1981) Prog Theoret Phys Suppl 70:35 Hayashi C, Nakazawa K, Nakagawa Y (1985) In: Black DC, Matthews MS (eds) Protostars and planets II. University of Arizona Press, Tucson, AZ, p 1100 Henning T, Semenov D (2013) Chem Rev 113:9016 Hirota T, Kim MK, Kurono Y, Honma M (2014) ApJL 782:L28 Hogerheijde MR, Bergin EA, Brinch C et al (2011) Science 334:338 Honda M, Inoue AK, Fukagawa M et al (2009) ApJL 690:L110 Honda M, Kudo T, Takatsuki S et al (2016) ApJ 821:2 Huang J, Andrews SM, Dullemond CP et al (2018) ApJL 869:L42 Huang J, Andrews SM, Pérez LM et al (2018) ApJL 869:L43 Ida S, Guillot T (2016) A&A 596:L3 Inoue AK, Honda M, Nakamoto T, Oka A (2008) PASJ 60:557 Isella A, Guidi G, Testi L et al (2016) Phys Rev Lett 117:251101 Isella A, Huang J, Andrews SM et al (2019) ApJL 869:L49 Kamp I, Thi W-F, Meeus G et al (2013) A&A 559:A24 Kanagawa KD, Muto T, Tanaka H et al (2015) ApJL 806:L15 Kanagawa KD, Tanaka H, Muto T, Tanigawa T, Takeuchi T (2015) MNRAS 448:994 Mandell AM, Bast J, van Dishoeck EF et al (2012) ApJ 747:92 Martin RG, Livio M (2012) MNRAS 425:L6 Martin RG, Livio M (2013) MNRAS 434:633 Mathews GS, Klaassen PD, Juhász A et al (2013) A&A 557:A132 Matsumura S, Brasser R, Ida S (2016) ApJ 818:15 McClure MK, Espaillat C, Calvet N et al (2015) ApJ 799:162 McClure MK, Manoj P, Calvet N et al (2012) ApJL 759:LL10 Meeus G, Montesinos B, Mendigutía I et al (2012) A&A 544:AA78 Min M, Dullemond CP, Kama M, Dominik C (2011) Icarus 212:416 Min M, Bouwman J, Dominik C et al (2016) A&A 593:A11 Morbidelli A, Bitsch B, Crida A et al (2016) Icarus 267:368 Morbidelli A, Chambers J, Lunine JI et al (2000) Meteorit Planet Sci 35:1309 Morbidelli A, Karato S-I, Ikoma M et al (2018) SSRv 214:110 Morbidelli A, Lunine JI, O’Brien DP, Raymond SN, Walsh KJ (2012) Annu Rev Earth Planet Sci 40:251 Mulders GD, Ciesla FJ, Min M, Pascucci I (2015) ApJ 807:9 Muto T, Grady CA, Hashimoto J et al (2012) ApJL 748:LL22 Muto T, Tsukagoshi T, Momose M et al (2015) PASJ 67:122 Najita JR, Carr JS, Pontoppidan KM et al (2013) ApJ 766:134 Nomura H, Tsukagoshi T, Kawabe R et al (2016) ApJL 819:L7 Notsu S, Nomura H, Walsh C et al (2019) ApJ 875:96 (paper IV) Notsu S, Nomura H, Walsh C et al (2018) ApJ 855:62 (paper III) Notsu S, Nomura H, Ishimoto D, Walsh C, Honda M, Hirota T, Millar TJ (2017) ApJ 836:118 (paper II)

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66. Notsu S, Nomura H, Ishimoto D, Walsh C, Honda M, Hirota T, Millar TJ (2016) ApJ 827:113 (paper I) 67. Öberg KI, Furuya K, Loomis R et al (2015) ApJ 810:112 68. Öberg KI, Murray-Clay R, Bergin EA (2011) ApJL 743:L16 69. Oka A, Nakamoto T, Ida S (2011) ApJ 738:141 70. Okuzumi S, Momose M, Sirono S-I, Kobayashi H, Tanaka H (2016) ApJ 821:82 71. Okuzumi S, Tanaka H, Kobayashi H, Wada K (2012) ApJ 752:106 72. Persson MV, Jørgensen JK, van Dishoeck EF (2013) A&A 549:L3 73. Pinilla P, Pohl A, Stammler SM, Birnstiel T (2017) ApJ 845:68 74. Pinte C, Dent WRF, Ménard F et al (2016) ApJ 816:25 75. Piso A-MA, Öberg KI, Birnstiel T, Murray-Clay RA (2015) ApJ 815:109 76. Piso A-MA, Pegues J, Öberg KI (2016) ApJ 833:203 77. Podio L, Kamp I, Codella C et al (2013) ApJL 766:L5 78. Pontoppidan KM, Blake GA, Smette A (2011) ApJ 733:84 79. Pontoppidan KM, Blake GA, van Dishoeck EF et al (2008) ApJ 684:1323 80. Pontoppidan KM, Dullemond CP, van Dishoeck EF et al (2005) ApJ 622:463 81. Pontoppidan KM, Salyk C, Bergin EA et al (2014) Protostars and planets VI, p 363 82. Pontoppidan KM, Salyk C, Blake GA et al (2010) ApJ 720:887 83. Pontoppidan KM, Salyk C, Blake GA, Käufl HU (2010) ApJL 722:L173 84. Qi C, Öberg KI, Andrews SM et al (2015) ApJ 813:128 85. Qi C, Öberg KI, Espaillat CC et al (2019) ApJ 882:160 86. Qi C, Öberg KI, Wilner DJ (2013) ApJ 765:34 87. Qi C, Öberg KI, Wilner DJ et al (2013) Science 341:630 88. Rapson VA, Kastner JH, Millar-Blanchaer MA, Dong R (2015) ApJL 815:L26 89. Raymond SN, Izidoro A (2017) Icarus 297:134 90. Riviere-Marichalar P, Ménard F, Thi WF et al (2012) A&A 538:LL3 91. Ros K, Johansen A (2013) A&A 552:A137 92. Salyk C, Lacy JH, Richter MJ et al (2015) ApJL 810:L24 93. Salyk C, Lacy J, Richter M et al (2019) ApJ 874:24 94. Salyk C, Pontoppidan KM, Blake GA et al (2008) ApJL 676:L49 95. Salyk C, Pontoppidan KM, Blake GA, Najita JR, Carr JS (2011) ApJ 731:130 96. Sato T, Okuzumi S, Ida S (2016) A&A 589:A15 97. Schoonenberg D, Okuzumi S, Ormel CW (2017) A&A 605:L28 98. Schwarz KR, Bergin EA, Cleeves LI et al (2016) ApJ 823:91 99. Takahashi SZ, Inutsuka S-I (2014) ApJ 794:55 100. Takahashi SZ, Inutsuka S-I (2016) AJ 152:184 101. Terada H, Tokunaga AT (2017) ApJ 834:115 102. Terada H, Tokunaga AT, Kobayashi N et al (2007) ApJ 667:303 103. Tominaga RT, Inutsuka S-I, Takahashi SZ (2018) PASJ 70:3 104. van der Marel N, van Dishoeck EF, Bruderer S et al (2013) Science 340:1199 105. van der Marel N, van Dishoeck EF, Bruderer S et al (2016) A&A 585:A58 106. van Dishoeck EF, Bergin EA, Lis DC, Lunine JI (2014) In: Beuther H et al (ed) Protostars and planets VI. University of Arizona Press, Tucson, AZ, p 835 107. van Dishoeck EF, Herbst E, Neufeld DA (2013) Chem Rev 113:9043 108. Wada K, Tanaka H, Okuzumi S et al (2013) A&A 559:AA62 109. Walsh C, Juhász A, Pinilla P et al (2014) ApJL 791:L6 110. Walsh KJ, Morbidelli A, Raymond SN, O’Brien DP, Mandell AM (2011) Nature 475:206 111. Zhang K, Bergin EA, Blake GA, Cleeves LI, Schwarz KR (2017) Nat Astron 1:0130 112. Zhang K, Blake GA, Bergin EA (2015) ApJL 806:L7 113. Zhang K, Pontoppidan KM, Salyk C, Blake GA (2013) ApJ 766:82

Chapter 2

Modeling Studies I. The Case of the T Tauri Star

Abstract We found candidate water lines to locate the H2 O snowline position through future high-dispersion spectroscopic observations. As a first step, we calculated chemical structures of the disk using the self-consistent physical models of a typical T Tauri disk. We confirmed that the water gas abundance is high not only in the hot disk midplane within the H2 O snowline, but also in the outer hot surface and photodesorption region. Next, we calculated the profiles of water lines, and find the lines which are best to locate the position of the H2 O snowline. The lines we identified are those with high upper state energies and small Einstein A coefficients. The wavelengths of the candidate water lines range from mid-infrared to sub-millimeter, and they overlap with the wavelength coverages of ALMA and future mid-infrared high dispersion spectrographs (e.g., TMT/MICHI, SPICA). Most contents of this chapter is based on our refereed paper that has been published (Notsu et al. 2016, ApJ, 827, 113). Keywords Protoplanetary disks · Astrochemistry · Snowline · Planet formation · T Tauri star

2.1 Methods 2.1.1 The Disk Physical Model We derived the physical structure of a protoplanetary disk model by using the methods in Nomura and Millar [56] including X-ray heating [57]. We provide a brief summary of our adopted disk physical model in this subsection. Original papers [56, 57] explained the background theory and computation of this physical model in detail. Some previous papers (e.g., Walsh et al. [88–91], Heinzeller et al. [33], Furuya et al. [24]) used the same physical model to study various effects of disk physics and chemistry, The physical structure treatment are also explained in such papers in detail. We used the a steady, axisymmetric Keplarian disk model surrounding a T Tauri star with effective temperature T∗ = 4000 K, radius R∗ = 2.0 R , and mass © Springer Nature Singapore Pte Ltd. 2020 S. Notsu, Water Snowline in Protoplanetary Disks, Springer Theses, https://doi.org/10.1007/978-981-15-7439-9_2

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M∗ = 0.5 M [40]. The α-disk model [80] is used in order to get the radial surface density, assuming an accretion rate M˙ = 10−8 M yr−1 and a viscous parameter α = 10−2 . By solving the equations of hydrostatic equilibrium in the vertical direction and the local thermal balance between cooling and heating of the gas, the steady distributions of disk density and gas temperature are calculated self-consistently. The gas heating sources are heating due to hydrogen ionization by X-rays and grain photoelectric heating by UV photons. The cooling mechanisms are line emission and gas-grain collisional interactions. The dust temperature is derived by assuming radiative equilibrium between dust grain absorption and remission. The adopted heating sources of dust grains are the central star irradiation and viscous dissipation heating (α-disk model) at the disk midplane. The calculated radial range is r ∼ 0.04 au to 305 au. The dust properties are crucial, since they affect the disk physical and chemical structures in many ways. Dust grains are the dominant opacity source, and the UV radiation field and dust temperature profiles in the disk are strongly influenced on dust grains. The UV radiation field affects processes of photoionization, photodissociation, photodesorption. The properties of dust grains also influence on the distributions of the disk gas temperature, because photoelectric heating is the dominant gas heating source in the disk surface. The total surface area of dust grains affect the molecular abundances through the ice and gas balance. We used the T Tauri star X-ray spectrum model obtained by fitting the observed TW Hya’s XMM-Newton spectrum [39], with a two-temperature thin thermal plasma model (MEKAL model; see, e.g., Liedahl et al. [43]). The best-fit parameters are NH = 2.7 × 1020 cm−2 for the column density of foreground interstellar hydrogen and kT1 = 0.8 keV and kT2 = 0.2 keV for the plasma temperatures. Nomura et al. [57] also adopted the same model. The adopted model of stellar UV radiation field is based on the observational data of TW Hya, which has three components: emission of the Lyα line, optically thin hydrogenic bremsstrahlung radiation, and photospheric blackbody radiation (for details, see Appendix C of Nomura and Millar [56], Walsh et al. [91]). We included scattering and absorption by dust grains for the extinction of UV radiation. The interstellar UV radiation field is also included, but it has negligible contribution since the stellar UV irradiation is much stronger. We adopted the same dust grain model as Nomura and Millar [56]. In that model, the compact and spherical water ices, carbonaceous grains, and silicate grains are assumed. The continuous distribution of PAH-like properties in smallest sizes and graphite-like properties for larger sizes is assumed for the optical properties of the carbonaceous dust grains [42]. The mass fractional abundances are adopted to be consistent with the solar elemental abundances: ζice = 0.0094, ζcarbon = 0.0030, and ζsilicate = 0.0043 [6]. Their bulk densities are assumed to be ρice = 0.92 g cm−3 , ρgraphite = 2.24 g cm−3 , and ρsilicate = 3.5 g cm−3 . The assumed sublimation temperatures of grains are Tice = 150K, Tcarbon = 2300K, and Tsilicate = 1500K, based on Adams and Shu [1]. The gas and dust grains are assumed to be well mixed. The carbonaceous and silicate

2.1 Methods

13

Fig. 2.1 The monochromatic absorption coefficient (thick solid line) of dust grains consisting of carboneceous (dashed line), silicate (thin solid line), and water ice (dot-dashed line). This figure is originally reported in Appendix D of Nomura, H., & Millar, T. J. (2005, A&A, 438, 923, “Molecular hydrogen emission from protoplanetary disks”, DOI: https://doi.org/10.1051/00046361:20052809), and reproduced with permission from Astronomy & Astrophysics (A&A), ©ESO

grain size distributions adopted are obtained by Weingartner and Draine [92]. Such distributions are determined to reproduce the extinction curve in dense clouds with the ratio of visual extinction to reddening RV ≡ A(V )/E(B − V ) = 5.5. The value of bC was assumed to be 3.0×10−5 , which is the total C abundance per H nucleus in the log-normal size dust-grain distribution, This value reproduced the distribution of small hydrocarbon molecules such as PAHs (see also Fig. 6 of Weingartner and Draine [92]). The water ice grains were assumed to have the simple size distribution of dn/da ∝ a −3.5 , where a is the dust particle radius [45]. The maximum dust grain radius is amax is ∼10 µm. The calculated monochromatic absorption coefficient is shown in Fig. 2.1. The number density of gas in cm −3 (top left), the temperature of gas in K (top right, Tg ), the dust-grain temperature in K (bottom left, Td ), and the wavelength-integrated UV flux in erg cm−2 s−1 (bottom right) are shown in Fig. 2.2, as a function of disk radius in au and height (scaled by the radius, z/r ). The density decreases as a function of disk radius and height. The densest region is in the inner disk midplane (∼1014 cm−3 ), and the most diffuse region is in the outer disk surface ∼105 cm−3 ). Almost 10 orders of magnitude are covered in the density range of our adopted disk model. The temperature of gas decreases as a function of disk radius, and it increases as a function of disk height. The coldest area are in the outer disk (∼10 K), and the hottest area are in the disk surface (>103 K). Moreover, the midplane temperature increases within several au from the central T Tauri star, since viscous heating is effective. The gas temperature is more than ten times higher than the dust temperature in the disk surface. Gas-grain collisions become ineffective at low densities, thus in the gas the cooling via radiative line transitions is important. The dust-grain and gas

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2 Modeling Studies I. The Case of the T Tauri Star

Fig. 2.2 The total gas number density in cm−3 (top left), the gas temperature in K (top right), the dust temperature in K (bottom left), and the UV flux in erg cm−2 s−1 (bottom right) of a disk around a T Tauri star as a function of the disk radius in au and height (scaled by the radius, z/r ) up to maximum radii of r = 100 au. This figure is originally reported in Notsu et al. [61], and reproduced by permission from American Astronomical Society (©AAS)

temperatures are similar in the disk midplane. Although the dense disk midplane is effectively shielded over the radial extent of our disk model, the disk surface closest to the central star is influenced on the largest fluxes of both X-ray and UV radiations,

2.1.2 Overview of Disk Chemical Structure To obtain the disk chemical structure, we used a large chemical network which includes gas-grain interactions (thermal and non-thermal desorption from dust grains, and freezeout of gas molecules on dust grains) and gas-phase reactions. Photodesorption and cosmic-ray-induced desorption were included in our adopted networks as non-thermal desorption mechanisms. Similar chemical networks have been adopted to calculate disk chemical structure in previous studies (e.g., Walsh et al. [88–91], Heinzeller et al. [33], Furuya et al. [24], Furuya and Aikawa [25], Ishimoto

2.1 Methods

15

et al. [37], and Du and Bergin [17]) The detailed background theories and procedures are discussed in such papers and the reviews of Henning and Semenov [34] and Dutrey et al. [19]. Here we describe the summary of our adopted chemical network. Adding grain-surface chemistry (e.g., Hasegawa et al. [31], van Dishoeck et al. [83]) would aid the formation of complex organic molecules in the outer disk where significant freezeout has occurred, and grain-surface reactions were included in some previous studies (e.g., Willacy [94], Semenov and Wiebe [79], Walsh et al. [89–91], Furuya et al. [24], Furuya and Aikawa [25], Drozdovskaya et al. [16]). However, our adopted network did not include them, and was equivalent to one of models in Walsh et al. [88], which includes the same desorption and freezeout processes. This is because we are primarily focused on the region of inner hot disk where molecular line emission comes from the thermally desorbed vapor.

2.1.3 Gas-Phase Reactions Our gas-phase chemistry is extracted from the UMIST Database for Astrochemistry (UDfA), henceforth referred to as “Rate06” [98]. Walsh et al. [88, 90], and Heinzeller et al. [33] used Rate06 to obtain the disk chemical structure. We include almost the entire Rate06 gas-phase network, but to reduce computation time, we removed only those species (and thus reactions) which contained phosphorus, P and fluorine. The loss of P- and F-containing species had a minimal impact on the remaining chemistry [33, 88]. Therefore, the chemical network in the gas-phase which we adopted included 375 molecular, atomic, and ionic species (included elements: H, He, C, N, O, Na, Mg, Si, S, Cl, and Fe). The list of these 375 species are shown in Table 2.1 in the online material from Woodall et al. [98]. Our adopted initial elemental fractional abundances (relative to total hydrogen nuclei density) were the oxygen-rich low-metallicity abundance set obtained from Graedel et al. [27], listed in Table 8 of Woodall et al. [98] and also in Table 2.1. We traced the chemical evolution for 106 years. By this time, the chemistry in the inner disk midplane is close to steady state, at which time the chemistry has forgotten its origins. Using initial elemental abundances, instead of considering chemical evolutions in clouds, is thus justified. Our adopted chemical network includes 4336 reactions including 3957 two-body reactions, 11 direct X-ray/cosmic-ray ionization reactions, 154 X-ray/cosmic-rayinduced photoreactions, and 214 photoreactions. In Sect. 2.1 of Woodall et al. [98], our adopted equations which give the reaction rates of two-body reactions, X-ray/cosmic-ray-induced photoreactions, and reactions of X-ray/cosmic-ray ionization are explained In our calculation, instead of the latest version of UDfA, “Rate12” [46], the previous version of the UDfA Rate06 [98] are adopted. There are some updates in Rate12 such as reactions related to some complex molecules. The inclusion of anion reactions is the major difference between Rate06 and Rate12 [46]. It has little effect on the chemistry of main simple molecules like water, although abundances of carbon-chain molecules are affected [46, 87].

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Table 2.1 Initial elemental abundances relative to total hydrogen nuclei Element Abundance He C+ N O Na+ Mg+ Si+ S+ Cl+ Fe+

0.14 7.30 × 10−5 2.14 × 10−5 1.76 × 10−4 3.00 × 10−9 3.00 × 10−9 3.00 × 10−9 2.00 × 10−8 3.00 × 10−9 3.00 × 10−9

This table is originally reported in Notsu et al. [61], and reproduced by permission from American Astronomical Society (©AAS)

In our chemical calculations, we have estimated our photoreaction rates at each point in the disk, k ph (r, z), by scaling the rates of Rate06 which assume the interstellar UV field, k0 , using the wavelength integrated UV flux obtained at each point (see also Fig. 2.2),  G FUV (r, z) =

˚ 2068A(6eV)

˚ 912A(13.6eV)

G FUV (λ, r, z)dλ.

(2.1)

Using this G FUV (r, z) value, the rate for a particular photoreaction at each (r, z) is given by G FUV (r, z) k0 s−1 , (2.2) k ph (r, z) = G0 where G 0 is the interstellar UV flux (2.67 ×10−3 erg cm−2 s−1 , [84]).

2.1.4 Gas-Grain Interactions In our chemical calculations, we included the thermal and non-thermal desorption of molecules from dust grains, and the freezeout of gas-phase molecules on dust grains. In order to occur the thermal desorption, the dust-grain temperature must exceed the sublimation (freezeout) temperature of each molecule. In addition, an input of energy from an external source is required to occur the non-thermal desorptions, and they are thus independent of dust-grain temperature. Photodesorption from UV photons [62, 93, 95] and cosmic-ray-induced desorption [32, 41] are adopted as nonthermal desorption mechanisms. First of all, we introduce our adopted freezeout and

2.1 Methods

17

Table 2.2 Molecular binding energies Species Binding energy E dK (i) [K] CO CO2 H2 O CH4 N2 NH3 HCN H2 CO C2 H2

855 2990 4820 1080 790 2790 4170 1760 2400

References a b c d a e d f d

a Öberg

et al. [65]; [20]; c Sandford and Allamandola [76]; d Yamamoto et al. [99]; e Brown and Bolina [11]; f Hasegawa and Herbst [32] This table is originally reported in Notsu et al. [61], and reproduced by permission from American Astronomical Society (©AAS) b Edridge

thermal desorption mechanisms in detail. Next, we explain our adopted mechanisms of non-thermal desportion. The freezeout (accretion) rate, kia [s−1 ], of species i onto the dust-grain surface is defined using the standard equation (e.g., Hasegawa et al. [31], Woitke et al. [96], Walsh et al. [88]), (2.3) kia = ασd vith n d s−1 , where α is the sticking coefficient. Here we assumed α = 0.4 for all species, which is in the range of high gas temperature cases (Tg ∼ 100–200 K) reported in Veeraghattam et al. [86]). The sticking coefficient were suggested to be lower as the dust-grain and gas temperature become higher (e.g., Masuda et al. [44], Veeraghattam et al. [86]). σd = πa 2 is the dust grain’s geometrical cross section with radius, a, vith  is the thermal velocity of species i with mass m i at gas temperature Tg , n d is the dust grain number density, and k B is the Boltzmann’s constant. We adopt the value of vith  = (k B Tg /m i )1/2 as Walsh et al. [88] adopted. For our gas-grain interactions, a constant grain radius a = 0.1 µm and a fixed dust-grain fractional abundance (xd = n d /n H 1 ) of 2.2 ×10−12 were adopted, as previous studies (e.g., Walsh et al. [90]). This adopted value of xd is consistent with a gas-to-dust ratio of 100 by mass. From the viewpoint of the surface area of dust-grains per unit volume, the value of a constant grain radius a adopted is consistent with the value from the dust-grain size distributions in our adopted disk physical model. 1n

H

is the total gas atomic hydrogen number density.

18

2 Modeling Studies I. The Case of the T Tauri Star

The thermal desorption rate, kid [s−1 ], of species i from the dust-grain surface is defined by (e.g., Hasegawa et al. [31], Woitke et al. [96], Walsh et al. [88]), 

kid

−E dK (i) = ν0 (i) exp Td



s−1 ,

(2.4)

where E dK (i) is the binding energy of species i to the dust-grain surface in units of K. In Table 2.2, the values of E dK (i) for several important molecules are listed. Most of these values are adopted in Walsh et al. [88, 90]. Td is the dust-grain temperature in units of K. The characteristic vibrational frequency of each adsorbed species i in its surface potential well, ν0 (i), is represented by a harmonic oscillator relation [31],  ν0 (i) =

erg

2n sur f E d (i) −1 s , π2 m i

(2.5)

erg

where, E d (i) is in units of erg here, m i is the mass of each absorbed species i, and n sur f = 1.5 × 1015 cm−2 is the surface density of absorption sites on each dust grain. Next, the overview of our adopted non-thermal desorption mechanisms are described. To obtain the rate of the cosmic-ray-induced desorption for each species, kicrd , we assumed that dust grains with a radius of 0.1 µm are impulsively heated by the impact of relativistic Fe nuclei with energies of 20–70 MeV nucleon−1 which deposit an energy of 0.4 MeV on average into each dust grain [32, 41]. If we assume that the majority of molecules desorb around 70 K, the cosmic-ray-induced desorption rate can be approximated by kicrd = f (70K)kid (70K)

ζCR s−1 , 1.36 × 10−17 s−1

(2.6)

where ζCR is the cosmic-ray ionization rate of H2 , kid (70K) is the thermal desorption energy of species i at a dust temperature of 70 K computed using Eq. (2.4). f (70K) is the fraction of time spent by dust grains around 70 K and is defined as the ratio of the desorption cooling time (10−5 s) to the time interval between successive heatings to 70K. The latter value is estimated to be 3.16 ×1013 s from the Fe cosmic-ray flux, then f (70K) is 3.16 ×10−19 [32, 41]. Here we noted that X-ray photons can penetrate deep in the disk and locally heat dust grains, like cosmic-ray particles. Unlike previous studies (e.g., Walsh et al. [89–91]), X-ray desorption was not yet included in our reaction set. This is because X-ray desorption is the least constrained experimentally or theoretically of all the non-thermal desorption mechanisms, and significant uncertainties are remained in the reaction rates (e.g., Najita et al. [55], Walsh et al. [88]). Absorption of a UV photon by a species in the grain surface can increase the species internal energy enough to induce desorption. The photodesorption rate of

2.1 Methods

19

species i is given by pd

i ki = FUV YUV σd

n d −1 s , n act

(2.7)

where FUV is the wavelength integrated UV flux computed at each (r, z) in units of photons cm−2 s−1 . n act = 4πa 2 n d n sur f N Lay is the number of active surface sites in the ice mantle per unit volume. N Lay is the number of surface layers to be coni sidered as “active”, and we adopt the value of Aikawa et al. [2], N Lay = 2. YUV is −1 the photodesorption yield in units of molecules photon which is determined by pd experiments. The similar method to calculate ki is adopted in Woitke et al. [96] and Heinzeller et al. [33]. FUV is commuted from the dust opacity and the profiles of i densities in the disk physical model we adopted [56, 57, 91]. We assumed that YUV −3 is 3.0 × 10 for all species. This is the same value determined for pure CO ice by Öberg et al. [62] and for pure water ice by Westley et al. [93]. Walsh et al. [88] use i . Photodesorption rates are dependent on ice composition and the same value of YUV the depth of the ice layer on a dust grain, according to recent experiments [63, 64, 66]. Therefore, the total formation rate of ice species i is pd

desorb d n˙ i,ice = n i kia − n i,ice (ki + kicrd + ki ).

(2.8)

desorb is the fraction of where n i,ice denotes the number density of ice species i, and n i,ice n i,ice located in the uppermost active surface layers of the ice mantles. In addition, pd ki is the photodesorption rate for a specific species i, kicrd is the cosmic-ray-induced desorb is given by Aikawa et thermal desorption rate for each species i. The value of n i,ice al. [2], Woitke et al. [96]

 desorb = n i,ice

(n ice < n act ), n i,ice (n ice ≥ n act ), n act nni,ice ice

(2.9)

where n ice is the total number density of all ice species, n act = 4πa 2 n d n sur f N Lay is the number of active surface sites in the ice mantle per volume. N Lay is the number of surface layers to be considered as “active”, and we adopt the value from Aikawa et al. [2], N Lay = 2.

2.1.5 Water Emission Line Profiles Using the distributions of H2 O gas abundance, we obtained the water line profiles ranging from near-infrared to sub-millimeter wavelengths, and investigated the best candidate lines to probe the emission from the thermally desorbed water gas inside the H2 O snowline. We also investigated how the line fluxes and profile shapes depend on the H2 O snowline position. Here we overview the calculation methods we adopted

20

2 Modeling Studies I. The Case of the T Tauri Star

(based on Rybicki and Lightman [74], Hogerheijde and van der Tak [36], and Nomura and Millar [56]). The line transition frequency is νul , where the subscript ul means the transition from the upper level (u) to the lower level (l). The line intensity at the frequency ν, Iul (ν), is obtained by solving the radiative transfer equation in the line-of-sight direction of the disk, dIul (ν) = −χul (ν)(Iul (ν) − Sul (ν)). ds

(2.10)

The source function, Sul (ν), and the total extinction coefficient, χul (ν), are given by Sul (ν) = and

1 hνul n u Aul ul (ν) , χul (ν) 4π

(2.11)

χul (ν) = ρd κul + (n l Blu − n u Bul )ul (ν)

hνul , 4π

(2.12)

where n u and n l are the number densities of the upper and lower levels, respectively. In addition, the symbols Aul and Bul are the Einstein A and B coefficients for the transition u → l, the symbol Blu is the Einstein B coefficient for the transition l → u, h is the Planck constant. The energy difference between the levels u and l corresponds to hνul . κul is dust absorption coefficient at the frequency νul as described in Sect. 2.1.1. ρd is the mass density of dust grains which we calculate from the values of total gas mass density ρg and gas-to-dust mass ratio (ρg /ρd = 100). The symbol ul (ν) is the line profile function at the frequency ν, and we include the effects of thermal broadening and the Doppler shift due to Keplerian rotation, when we calculate the emission line profiles. This function is defined by the following equation,  1 (ν + ν K − νul )2 , (2.13) ul (ν) = √ exp − ν D π ν D2 where m is the mass of a water molecule, k is the Boltzmann constant,

Tg is the gas temperature, c is the speed of light. In addition, ν D = (νul /c)( 2kTg /m) is the Doppler width, and ν K is the Doppler-shift due to projected Keplerian velocity for the line-of-sight direction and is given by, νul νK = c



G M∗ sin φ sin i, r

(2.14)

where r is the distance from the central star, M∗ is the mass of central star, G is the gravitational constant. Moreover, φ is the azimuthal angle between the line and

2.1 Methods

21

semi-major axis which links the point in the disk along the line-of-sight and the center of the disk. The line flux density profiles are given by integrating Eq. (2.8) in the line-of-sight direction and summing up the integrals in the plane of the projected disk, (x, y), as, Ful (ν) =

   1 d dxdy 4πd 2  s∞ jul (s, x, y, ν)ds. ×

(2.15)

−s∞

Here, the distance of the observed disk from the Earth is d. jul (s, x, y, ν) is the emissivity at (s, x, y) and the frequency ν, including the effect of absorption in the upper disk layer. Thus, it is given by, hνul ul (s, x, y, ν) 4π × exp(−τul (s, x, y, ν)),

jul (s, x, y, ν) =n u (s, x, y)Aul

(2.16)

Here, τul (s, x, y, ν) is the optical depth from s to the disk surface s∞ at the frequency ν, and it is given by the following equation, 

s∞

τul (s, x, y, ν) =

χul (s , x, y, ν)ds .

(2.17)

s

Hence, the line total fluxes, Ful , are given by,  Ful =

Ful (ν)dν

(2.18)

We adopted a distance of d = 140 pc for calculating the profiles of water lines, since this is the typical distance to the Taurus molecular cloud. This molecular cloud is the nearest star formation regions which have well-known protoplanetary disks. The code that we made for calculating profiles of emission lines from the protoplanetary disk is a modification of the original 1D code called RATRAN2 [36]. The data for the ortho- and para-H2 16 O energy levels are adopted from Tennyson et al. [81]. We used the radiative rates (Einstein A coefficients Aul ) from the BT2 water line list [10], and the collisional rates, < σv >, for the excitation of H2 O by H2 and by electrons from Faure and Josselin [21]. The collisional rates were used to determine the critical densities of transitions which we were interested in. These data are part of Leiden Atomic and Molecular Database called LAMDA3 [78]. We calculated the level populations of the water molecule (n u and n l ) under the assumption of local thermal equilibrium (LTE). In Sect. 2.3.2, the validity of the assumption 2 http://home.strw.leidenuniv.nl/~michiel/ratran/. 3 http://home.strw.leidenuniv.nl/~moldata/.

22

2 Modeling Studies I. The Case of the T Tauri Star

of LTE in our work are discussed. Emission from disk winds and jet components is not included in our calculations. In this subsection, we do not include dust-grain emission, too. As described above, the effects of the absorption of line emission by dust grains are included. The nuclear spins of the two hydrogen atoms in each H2 O molecule can be either parallel or anti-parallel, and thus the H2 O energy levels are divided into ladders of ortho (K a + K c = odd) and para (K a + K c = even) molecules. The ortho to para ratio (OPR) of gas-phase water molecules will depend on the formation and thermal conditions of water molecules in disks and comets (e.g., Mumma and Charnley [53], van Dishoeck et al. [82, 83]). An another method to explain the OPR is through the “spin temperature”, defined as the temperature which characterizes the observed OPR under thermal equilibrium conditions. The OPR becomes 3 in the higher temperature region (60 K) and zero in the lowest temperature limit. [54] describes the original OPR definition of gas-phase water in thermal equilibrium. Here we defined the OPR = 3 in the whole region of the disk in order to calculate n u and n l values. Our calculated water lines which will trace the H2 O snowline position mainly locate the gas-phase hot water for which the temperature is higher than the sublimation temperature of water molecules (∼150–160 K). Our adopted disk physical model is steady, and chemical and thermal equilibrium is almost achieved in the whole region of the disk. According to the previous observations at mid-infrared wavelengths, OPR is 3 in the inner warm water of disks (e.g., Pontoppidan et al. [71]). Hama et al. [29] discussed that water molecules desorbed from the surfaces of icy dust-grains at 10 K have the OPR of 3, which is not consist with the assumed relation between the water formation temperature and the OPR. According to their discussions, though the detailed mechanism is not yet clarified, the role of gas-phase processes that convert the OPR to a lower value in low temperature regions will be important,

2.2 Results 2.2.1 The Distributions of H2 O Gas and Ice The fractional abundances (relative to the density of total gas hydrogen nuclei, n H ) of H2 O gas and H2 O ice in a disk around a T Tauri star are shown in Fig. 2.3. The chemistry is computed between r ∼0.5 au and 100 au in order to reduce computation time. In the inner disk, due to the midplane’s high densities, a significant column density of material is shielded from the intense stellar UV and X-ray radiations. Thus, molecules including water are expected to exist in the inner disk midplane within ∼0.1 au, unless in some disks cavities are also existed in gas and dust. Therefore, the actual total amount of molecular gas may be larger than that of our chemical calculation results.

2.2 Results

23

Fig. 2.3 The fractional abundance (relative to total hydrogen nuclei density) distributions of H2 O gas (left panel) and H2 O ice (right panel) of a disk around a T Tauri star as a function of disk radius and height (scaled by the radius, z/r ) up to maximum radii of r = 100 au. This figure is originally reported in Notsu et al. [61], and reproduced by permission from American Astronomical Society (©AAS)

The H2 O gas fractional abundance is high (∼10−4 ) in the disk midplane within the H2 O snowline, and in the disk midplane beyond the H2 O snowline it is low (10−12 ). The H2 O ice fractional abundance has the opposite distribution. In the disk midplane, It is high (∼10−5 ) outside the H2 O snowline, and low (10−9 ) within the H2 O snowline. In our adopted T Tauri disk model, the H2 O snowline position in the disk midplane is at a radius of ∼1.6 au (Tg ∼ 150–160 K), consistent with our adopted value of the binding energy. The temperature is larger than the sublimation temperature under the pressure conditions of the disk midplane (Tg ∼ 150–160 K) within the H2 O snowline and most water molecules are in the gas-phase because of thermal desorption. Moreover, this region has a high temperature (>150 K) and large total gas particle number density (> 1011 cm−3 ), is almost shielded from the interstellar and intense stellar UV and X-ray radiations ([56, 57], see also Fig. 2 of Walsh et al. [90]). Thermal and thermochemical equilibrium between the dust and gas is also achieved (Tg ∼ Td ), and thus most of the oxygen atoms will be included in CO and H2 O molecules (e.g., Glassgold et al. [28], Woitke et al. [96, 97], Walsh et al. [88, 90, 91], van Dishoeck et al. [82, 83], Du and Bergin [17], Antonellini et al. [7]). Therefore, the gas-phase abundances of H2 O molecules are approximately given by the elemental abundance of oxygen (1.76 × 10−4 , [98]) minus those of CO molecules. Moreover, the H2 O gas fractional abundances are relatively high in the outer disk hot surface layer. The H2 O gas fractional abundance is ∼10−8 –10−7 at z/r of 0.1– 0.3 between r ∼ 0.5–100 au. This region can be considered as the photodesorption (sublimation) front of H2 O molecules, so-called photodesorbed layer [15], which is driven by the relatively intense UV radiation from central protostars. In this region, H2 O will survive in the gas phase where it would otherwise be frozen out on the surfaces of dust-grains. The abundance and extent of gas-phase H2 O in this layer is

24

2 Modeling Studies I. The Case of the T Tauri Star

mediated by absorption back onto the dust grains, destruction by the intense stellar UV photons and by chemical reactions with other species. At z/r of 0.15–0.7 between r ∼ 0.5–100 au, the abundance of H2 O molecules are relatively high (∼10−7 ) compared with the outer cold midplane region (10−12 – 10−10 ). In this region, the dust temperature is significantly lower than the gas temperature (typically Tg ∼ 200–2000 K) and the gas density is low compared to the disk midplane. Thus, the water chemistry in the gas-phase is controlled by chemical kinetics as opposed to thermodynamic (or chemical) equilibrium. Because of the very high gas temperature (>200 K), the dominant neutral-neutral two-body reactions (such as O+H2 →OH+H and OH+H2 →H2 O+H) will become efficient, and gas-phase H2 O molecules are produced rapidly. By these reactions, all the available oxygen atoms in the gas-phase will be included in H2 O molecules, unless high atomic hydrogen abundance or intense UV ares able to convert some water molecules back to O and OH (e.g., Glassgold et al. [28], Woitke et al. [97], Meijerink et al. [48], van Dishoeck et al. [82, 83], Walsh et al. [91]). Water is even more rapidly destroyed by reactions with atomic hydrogen atoms and photodissociation in the uppermost surface layers. Thus, there are few water molecules in those regions. The gas-phase abundance of OH molecules in our calculations and others (e.g., Walsh et al. [90]) are also high in the hot disk surface. It is consistent with the discussions above that reactions with H2 O and OH [90, 91]. The H2 O gas (red solid line) and ice (blue dashed line) radial column density profiles are shown in Fig. 2.4. In the disk midplane, the H2 O gas and ice column densities flips across the H2 O snowline (∼1.6 au). The H2 O gas column density is high (∼1021 cm−2 ) within the H2 O snowline, and it is low outside the H2 O snowline (∼1014 –1015 cm−2 ). The H2 O ice column density profile is roughly opposite. In the outer disk, it is ∼1020 –1021 cm−2 . According to previous chemical modeling studies (e.g., Walsh et al. [90, 91], Du and Bergin [17]), the H2 O gas column density within the H2 O snowline is ∼1021 –1022 cm−2 . This value is slightly higher than that in our calculations, possibly because they included grain surface reactions. In the disk

1022

Column Density (cm-2)

Fig. 2.4 The vertically integrated radial column density profiles of cm−2 of H2 O gas (red solid line) and ice (blue dashed line). This figure is originally reported in Notsu et al. [61], and reproduced by permission from American Astronomical Society (©AAS)

H2O gas H2O ice

1021 1020 10

19

1018 1017 10

16

1015 1014

10

1

r [AU]

2.2 Results

25

midplane gas-phase H2 O is almost obscured by dust grains at near- to mid-infrared wavelengths [91], thus at these wavelengths the “visible” column density of the H2 O gas is much smaller than the actual value. In Walsh et al. [91], the visible value of the H2 O gas column density is on the order of a few times 1019 cm−2 inside the H2 O snowline. According to previous infrared spectroscopic observations with low spectral resolutions which were conducted by Spit zer /IRS, the column densities of H2 O gas in classical T Tauri disks were ranging from 4 ×1017 to 7.9 ×1020 cm−2 [12, 75]. Although the model T Tauri disk model is a generic model which is not representative of any particular source, however, there is an overlap between these observed values and the calculated “visible” column densities. According to previous numerical and analytical modelings, the H2 O snowline positions in optically thick disks were derived for given parameters, such as the average dust opacity and grain size a, a gas-to-dust mass ratio g/d, a viscous parameter ˙ central star temperature (T∗ ) and mass (M∗ ) (e.g., Davis [13], α, an accretion rate M, Garaud and Lin [26], Min et al. [51], Oka et al. [67], Du and Bergin [17], Harsono et al. [30], Mulders et al. [52], Piso et al. [70], Sato et al. [77]), and the H2 O snowline position are considered to be changed, as these parameters change. In T Tauri disk cases with a ∼ 0.1 µm, M˙ ∼ 10−8 M yr−1 , M∗ ∼ 0.5 − 1M , the H2 O snowline ˙ M∗ , and the position is around 1.5–2 au. We adopted similar parameters for a, M, H2 O snowline position in the disk midplane is around 1.6 au (Tg ∼ 150–160 K), which is in the range of previous studies. The physical mass transport effects in the radial direction by viscous accretion and in the vertical direction by disk winds and diffusive turbulent mixing were discussed in Heinzeller et al. [33]. According to that paper, the gas-phase abundance of H2 O is enhanced in the warm surface layer because of the vertical mixing effects. In the disk midplane within the H2 O snowline, however, the accretion flow does not affected the gas-phase H2 O abundance, since in this region the chemical reactions will be fast enough to compensate for the accretion flow effects.

2.2.2 The Overview of Ortho-H2 16 O Lines from the T Tauri Disk We investigate the H2 16 O emission line profiles for a protoplanetary disk in Keplerian rotation, as explained in Sect. 2.1.5 and next paragraph. The pure rotational and rovibrational ortho- and para- H2 16 O lines at sub-millimeter and near-, mid-, and farinfrared wavelengths are included. We find that in order to trace emission from the hot water gas inside the H2 O snowline, water lines with relatively high upper energy levels (E up ∼ 1000 K) and small Einstein A coefficients (Aul ∼ 10−3 –10−6 s−1 ) are suitable. Here we explain how we find around fifty candidate ortho-H2 16 O transition lines selected from the LAMDA database. First, we select around twenty ortho-H2 16 O lines from the database with various upper state energies (E up < 3000 K), Einstein

26

2 Modeling Studies I. The Case of the T Tauri Star

A coefficients (Aul ∼ 10−1 –10−7 s−1 ), and wavelengths (from near-infrared to submillimeter). In this initial selection, water lines with very high upper state energies and very small Einstein A coefficients are ignored, since the line emission fluxes are likely to weak to detect. Through these calculations, we found that H2 16 O lines with relatively large upper state energies (E up ∼ 700–2100 K) and small Einstein A coefficients (Aul ∼ 10−3 –10−6 s−1 ) are the best candidate lines to probe emission from the innermost hot water gas inside the H2 O snowline. The number of these candidate lines is 10 lines within originally selected 20 lines. Thus, we calculated all other ortho-H2 16 O lines which satisfy these conditions, and found an additional 40 ortho-H2 16 O candidate lines. In the reminder parts of this thesis, we sometimes describe the H2 16 O lines as H2 O lines. The detailed properties of three characteristic pure rotational ortho-H2 16 O lines (λ = 682.93, 63.37, 538.66 µm) with different values of Aul and E up are explained in the remaining part of this section. The H2 16 O 682.93 µm line falls in ALMA Band 8, and it is a candidate line to trace the emission from the hot water gas inside the H2 O snowline. The other two lines are examples of less suited lines, and are used in order to check the validity of our model calculations, since these two lines are observed from disks with H er schel (see Sects. 2.2.4 and 2.2.5). The lists and properties of many other candidate water lines from mid-infrared (Q band) to submillimeter wavelengths, especially the variation in line fluxes with wavelength, are described in next Section (paper II, [60], see also Sect. 3).

2.2.3 The Case of a Candidate Ortho-H2 16 O Emission Line The top panels in Fig. 2.5 show three pure rotational ortho-H2 16 O line profiles at λ = 682.93 µm (JK a K c = 643 -550 , top left), 63.37 µm (JK a K c = 818 -707 , top middle), and 538.66 µm (JK a K c = 110 -101 , top right), which have various Einstein A coefficients (Aul ) and upper state energies (E up ). The detailed line parameters, such as Aul , E up , frequency, transitions (JK a K c ), wavelength, total line fluxes, critical density n cr , are listed in Table 2.3. The distance to the object d = 140 pc (∼the distance of Taurus molecular cloud), and the inclination angle of the disk i = 30 deg are assumed in these line profiles. The total line fluxes (λ = 682.93, 63.37, 538.66 µm) are 3.12 × 10−22 , 5.66 × 10−18 , 1.13 × 10−20 W m−2 , respectively. The bottom panels in Fig. 2.5 show the ortho-H2 16 O 63.37 µm line (bottom left) and the 538.66 µm line (bottom right) profiles, which enlarge the components from the inner disks. Since the ortho-H2 16 O 682.93 µm line and 63.37 µm line have large upper state energies (E up = 1088.7 K and 1070.6 K), these lines trace the hot water gas (Tg  a few hundred K). According to the discussions in previous subsections, the H2 O gas abundance is high in the disk midplane within the H2 O snowline (Tg > 150 K) and in the disk outer hot surface layer. In the top left panel of Fig. 2.5, we show the H2 16 O 682.93 µm line profile. The contribution from the optically thick region in the inner disk midplane (red solid line, 0–2 au, “in” component) is dominant compared with that from the outer optically

2.2 Results

27

Table 2.3 Calculated ortho-H2 16 O line parameters and total line fluxes JK a K c λ Freq. Aul E up n cr (µm) (GHz) (s−1 ) (K) (cm−3 ) 643 -550

682.926

439.286

818 -707

63.371

4733.995

110 -101

538.664

556.933

2.816 ×10−5 1.772 3.497 ×10−3

1088.7

1.0 × 106

1070.6

1.5 × 1010

61.0

2.9 × 107

Total flux1 (W m−2 ) 3.12 × 10−22 5.66 × 10−18 1.13 × 10−20

2 O lines, we use a distance d = 140 pc and the inclination angle of the disk i = 30 deg This table is originally reported in Notsu et al. [61], and reproduced by permission from American Astronomical Society (©AAS)

a In calculating total flux of these H

Fig. 2.5 Top: three characteristic pure rotational ortho-H2 16 O line profiles at λ = 682.93 µm (JK a K c = 643 –550 , top left), 63.37 µm (JK a K c = 818 –707 , top middle), and 538.66 µm (JK a K c = 110 –101 , top right), with upper state energies E up and various Einstein A coefficients Aul . Bottom: the ortho-H2 16 O 63.37 µm line (bottom left) and 538.66 µm line (bottom right) profiles, which enlarge the inner components. Red solid lines are the line profiles within inside 2 au (∼inside the H2 O snowline), black dashed lines are those from 2–30 au (∼outside the H2 O snowline), and blue dotted lines are those from the total area inside 30 au. When we calculate these line profiles, we assume the distance to the object d = 140 pc (∼ the distance of Taurus molecular cloud), and the inclination angle of the disk i = 30 deg. This figure is originally reported in Notsu et al. [61], and reproduced by permission from American Astronomical Society (©AAS)

thin surface layer (black dashed line, 2–30 au, “out” component), since this line has a small Aul (=2.816 × 10−5 s−1 ). On the basis of Eqs. (2.13)–(2.16), the flux density is computed by summing up the emissivity at each point ( jul (s, x, y, ν)) in the line-of-sight direction. In the optically thin (τul 170K, r < 7–8 au). In the T Tauri disk midplane, the radial temperature profile is steeper than that in the Herbig Ae disk midplane. This will be another reason why the T Tauri disk does not have such a region which have a relatively large H2 O gas abundance (∼10−8 ). In Fig. 1 of Woitke et al. [91], the similar distribution of gaseous H2 O molecules in the Herbig Ae disk is discussed. In Eistrup et al. [21, 22], the chemical evolution in the disk midplane are calculated under both atomic and molecular initial abundances. In the former atomic scenario, the abundance of H2 O gas and ice around the H2 O snowline (∼10−6 ) is smaller than that for molecular initial abundances (∼10−4 ). This is because O2 is formed in the gas-phase via O+OH→O2 +H and remains in the gas phase. The sublimation temperature of O2 is much lower than that of other molecules like H2 O. The gas-phase H2 O formation is competed with this reaction route. As also shown in the T Tauri disk case, the H2 O gas abundance is also relatively high (∼10−8 –10−7 ) in the outer hot surface layer and at the H2 O sublimation (photodesorption) layer compared with the outer cold disk midplane (10−12 –10−10 ). Unlike the T Tauri disk model, In the inner disk midplane with a high H2 O gas abundance (∼10−4 ) extends to a larger radius (r ∼10 au) at z/r  0.1 than at z/r ∼ 0 (r ∼ 7–8 au) in the Herbig Ae disk model. This is because the scale height of the T Tauri disk (e.g., H/r ∼ 1.7 at r = 5 au) is larger than that of the Herbig Ae disk (e.g., H/r ∼ 1.2 at r = 5 au), and the stellar radiation is stronger in the Herbig Ae model than that in the T Tauri model, and thus the gas temperature around z/r ∼ 0.1 in the Herbig Ae disk is higher. The disk scale height in the T Tauri disk is larger than that in Herbig Ae disk, and thus the disk gas temperature values in the T Tauri disk between z/r ∼ 0–0.1 is constant. The water gas and ice radial column density profiles for both the T Tauri disk and the Herbig Ae disk are shown in the left panel of Fig. 3.3. As expected, the water gas

22

22

10

−2

Column Density [cm ]

−2

Column Density [cm ]

10

20

10

1018 16

10

14

10

1012

H2O gas T Tauri H2O ice T Tauri H2O gas Herbig Ae H2O ice Herbig Ae

1010

1

10

r [AU]

20

10

1018 16

10

14

10

H2O gas Total H2O ice Total H2O gas τ(17.75μm)=1 H2O gas τ(61.32μm)=1 H2O gas τ(682.66μm)=1

1012 1010

100

1

10

100

r [AU]

Fig. 3.3 Left panel: The radial profiles of the vertically integrated column density in cm−2 of H2 O gas and ice in the T Tauri disk (green dotted line and black dashed dotted line) and the Herbig Ae disk (red solid line and blue dashed line). Right panel: The radial profiles of the column density in cm−2 of H2 O ice (blue dashed line) and gas in the Herbig Ae disk, which are vertically integrated from z = ∞ to −∞ (red solid line), to z(τ17.75µm = 1) (black bold solid line), to z(τ61.32µm = 1) (green dotted line), and to z(τ682.66µm = 1) (orange dashed dotted line). Since τ682.66µm at z = −∞ is lower than unity at r  10 au, the radial profile of this case is plotted only r 10 au. This figure is originally reported in Notsu et al. [64], and reproduced by permission from American Astronomical Society (©AAS)

50

3 Modeling Studies II. The Case of the Herbig Ae Star

column density of H2 O gas and ice in the Herbig Ae disk midplane flips across the H2 O snowline (r ∼ 14 au). The water gas column density of H2 O gas is low outside the H2 O snowline (4 are listed in Table 3.1. The values of the total fluxes from both the T Tauri disk and the Herbig Ae disk (see also Notsu et al. [65]) are shown in Table 3.1. The same method as in Sect. 2 are adopted to calculate the values from the T Tauri disk model (see also paper I, Notsu et al. [65]). When we calculate all profiles of water lines in this section (see Figs. 3.4, 3.8, 3.11, and 3.12), the inclination angle of the disk i = 30 deg and the distant to the object d = 140 pc (∼the distance of Taurus molecular cloud) are adopted. The contributions for line emission from the inner disk midplane (r < 14 au) are much larger thant those from the outer surface layer (r = 14–30 au), and the characteristic double-peaked profile due to Keplerian rotation are displayed (see Fig. 3.4). This is because these lines with relatively large values of upper state energies (Eup ∼ 1000 K) and small values of Einstein A coefficients (Aul ∼ 10−3 –10−6 s−1 ) mainly trace the hot H2 O gas within the H2 O snowline. In Sects. 2.1.5 and 2.2.3 of this thesis [65], the detailed reasons are explained. Almost all of the line fluxes (>95%) emitted from the innermost region with a high H2 O gas abundance (∼10−4 , r < 8 au) except the cases of 482.99 µm and 682.66 µm lines (see Fig. 3.4), and using the two peak positions and the rapid drop in flux density between the line peaks the outer edge position of this region will be constrained. In the cases of the 482.99 µm and 682.66 µm lines (see Fig. 3.4), however, some line fluxes (∼10–20%) are emitted from the region with a relatively high H2 O gas abundance (∼10−8 , r = 8–14 au), and most of the emission fluxes (∼80–90%) are coming from the innermost region with a high H2 O gas abundance (∼10−4 , r < 8 au), and. In these cases, the two peak positions and the rapid drop 4
is the collisional rates for the excitation of H2 O by H2 and electrons for an adopted collisional temperature of 200 K from Faure and Josselin [23].

52

3 Modeling Studies II. The Case of the Herbig Ae Star

Table 3.1 Calculated representative ortho-H2 16 O line parameters and total line fluxes JK a K c λ1 Freq. Aul E up n cr HAe TT flux3,4 flux2,3 (µm) (s−1 ) (cm−3 ) (W m−2 ) (GHz) (K) (W m−2 ) 652 -505

17.754

550 -505

23.996

541 -616

61.316

652 -725

94.172

532 -441

482.990

643 -550

682.664

1029 -936

933.277

818 -707 110 -101

1067.7

8.3 × 1010 1.9 × 109

878.1

4.1 × 108

1278.5

3.1 × 108

732.1

3.3 × 106

1088.7

1.0 × 106

1861.2

4.7 × 106

1070.6

1.5 × 1010 2.9 × 107

63.324

16885.840 2.909 ×10−3 12493.205 2.696 ×10−4 4889.280 2.686 ×10−4 3183.464 3.387 ×10−4 620.701 1.106 ×10−4 439.151 2.816 ×10−5 321.226 6.165 ×10−6 4734.296 1.772

538.289

556.936

61.0

17413 12.396 16314 1376 -1249 12.453

1278.5

3.497 ×10−3 24184.126 7.728

5780.8

24073.032 1.053

4212.6

761 -652

4.958

60463.186 3.260

4180.4

761 -634

4.432

67646.817 2.080 ×10−4

4180.4

1.1 × 1011 1.1 × 1013 1.6 × 1013 6.5 × 1011

4.1 × 10−17 9.4 × 10−18 5.9 × 10−18 1.8 × 10−18 5.3 × 10−20 1.4 × 10−20 2.3 × 10−21 1.1 × 10−16 7.2 × 10−20 6.7 × 10−17 6.9 × 10−17 2.2 × 10−16 5.0 × 10−20

2.3 × 10−20 6.4 × 10−21 3.5 × 10−20 1.6 × 10−20 1.1 × 10−21 3.1 × 10−22 7.8 × 10−23 5.7 × 10−18 1.1 × 10−20 5.3 × 10−19 2.5 × 10−19 1.1 × 10−18 8.1 × 10−23

1 In

calculating the value of line wavelength from the value of line frequency, we use the value of speed of light c = 2.99792458 × 108 m s−1 2 The total flux of each emission line from the Herbig Ae disk 3 When we calculate these line profiles, we assume the distance to the object d = 140 pc, and the inclination angle of the disk i = 30 deg 4 The total flux of each emission line from the T Tauri disk (see also paper I, Notsu et al. [65]) This table is originally reported in Notsu et al. [64], and reproduced by permission from American Astronomical Society (©AAS)

in flux density between the peaks contains information on the radial hot H2 O gas distribution within the H2 O snowline. The distributions of the line-of-sight emissivity (emissivity times extinction, ηul e−τul ; see Eq. (16)) and the total optical depth, τul (including dust and gas components) of the seven ortho-H2 16 O lines are shown in Figs. 3.5 and 3.6, respectively. The inclination angle, i, of the disk is assumed to be 0 deg in making these figures (see Figs. 3.5, 3.6, 3.9, 3.10, and 3.7), and the line-of-sight direction is from z = +∞

3.2 Results

53

Fig. 3.4 Seven characteristic ortho-H2 16 O 17.75 µm (top left), 24.00 µm (top center), 61.32 µm (top right), 94.17 µm (middle left), 482.99 µm (middle center), 682.66 µm (middle right), and 933.28 µm (bottom) line profiles, with large E up and small Aul , from the Herbig Ae disk. These lines are considered to be candidate H2 O lines to locate the H2 O snowline positions. When we calculate the line profiles in this work (see Figs. 3.4, 3.8, 3.11, and 3.12), we assume the distance to the object d is 140pc (∼the distance of Taurus molecular cloud), and the inclination angle of the disk, i, is 30 degree. The parameters and total fluxes of these lines are listed in Tables 3.1 and 3.2. Red solid lines are the emission line profiles from inside 8 au (=the inner high temperature region), blue dashed lines are those from inside 14 au (∼inside the H2 O snowline), green dotted lines are those from 14–30 au (∼outside the H2 O snowline), and black dashed dotted lines are those from the total area inside 30 au. This figure is originally reported in Notsu et al. [64], and reproduced by permission from American Astronomical Society (©AAS)

to −∞ at each disk radius. In the left panels of Fig. 3.5, the total optical depth contours (τul = 0.1, 1, and 10) are plotted on top of these line emissivity panels (see also Fig. 3.6). In the right panels, the contours of gas temperature Tg (Tg = 120, 170, and 300K, see also Fig. 3.1) are also plotted. The normalized cumulative line emissivities at r = 5 au (top two panels), r = 10 au (middle two panels), and r = 30 au (bottom two panels), and the gas temperature Tg plots in the vertically directions are shown in Fig. 3.7. The distributions for these seven lines are displayed in the left three panels. We normalize the cumulative emissivity of each line using the values at z = −∞. The emissivities at r  14 au (=the H2 O snowline position), z/r ∼ 0.05–0.12, Tg  120 K are larger than those of the disk outer optically thin hot surface and the photodesorbed region, on the basis of Figs. 3.5, 3.6, and 3.7. In particular, those in the innermost disk midplane with a higher H2 O gas abundance (∼10−4 , r < 7–8 au, and

54

3 Modeling Studies II. The Case of the Herbig Ae Star

Fig. 3.5  Fig. 3.5 a The line-of-sight emissivity distributions of the ortho-H2 16 O 17.75 µm (top left and right), 24.00 µm (middle left and right), 61.32 µm (bottom left and right) lines with large E up and small Aul , from the Herbig Ae disk. In the left panels, we overplot the total optical depth contours (τul = 0.1 (red cross points), 1 (cyan circle points), and 10 (orange square points)) on top of these line emissivity panels (see also Fig. 3.6). In the right panels, we overplot the gas temperature Tg contours (Tg =120K (red cross points), 170 K (blue circle points), and 300K (cyan square points), see also Fig. 3.1). The inclination angle, i, of the disk is assumed to be 0 deg in making these figures in this work (see Figs. 3.5, and 3.9), and the emissivity is calculated along the line from z = +∞ to −∞ at each disk radius. The units are W m−2 Hz−1 sr −1 . This figure is originally reported in Notsu et al. [64], and reproduced by permission from American Astronomical Society (©AAS). b The line-of-sight emissivity distributions of the ortho-H2 16 O 94.17 µm (top left and right), 482.99 µm (second line left and right), 682.66 µm (third line left and right), and 933.28 µm (bottom left and right) lines with large E up small Aul , from the Herbig Ae disk. This figure is originally reported in Notsu et al. [64], and reproduced by permission from American Astronomical Society (©AAS)

3.2 Results

Fig. 3.5 (continued)

55

56

Fig. 3.6

3 Modeling Studies II. The Case of the Herbig Ae Star

3.2 Results

57

Fig. 3.6 The line-of-sight total optical depth τul (s, x, y, ν) (gas emission and dust) distributions of the ortho-H2 16 O 17.75 µm (top left), 24.00 µm (top right), 61.32 µm (second line left), 94.17 µm (second line right), 482.99 µm (third line left), 682.66 µm (third line right), and 933.28 µm (bottom) lines from the Herbig Ae disk. The inclination angle, i, of the disk is assumed to be 0 deg in making these figures in this work (see Figs. 3.6 and 3.10), and thus the optical depth is calculated along the line from z = +∞ to −∞ at each disk radius. In calculating the values of τul (s, x, y, ν), we consider the contributions of both absorption by dust grains and the line absorption by the H2 O gas. This figure is originally reported in Notsu et al. [64], and reproduced by permission from American Astronomical Society (©AAS)

Tg  170 K) and z/r ∼ 0.05–0.12 are much larger. Emission from z ∼ 0 at r  7 au is not possible to detect. This is because the optical depth in the inner disk midplane is high due to absorption by excited water molecules and dust grains in the upper disk layer. Nevertheless, the information of the radial hot H2 O gas distributions within the H2 O snowline are expected to extract, because within r < 14 au (=the position of the H2 O snowline), the H2 O gas abundance is relatively constant over z/r ∼ 0–0.1 for the same disk radius r (see also Fig. 3.2). Strictly speaking, as we explained in Sect. 3.2.1, the high H2 O gas abundance region (∼10−4 ) extends to a radius of r ∼ 10 au at z/r ∼ 0.1 compared with that at z ∼ 0 (r ∼ 7–8 au), and is reflected in the emissivity distribution. Its influence is not so serious to obtain information on the general trend of the water gas distribution in the inner disk inside the H2 O snowline, since the radial shift in the distribution is small (a few au). The differences in the line profiles (see Figs. 3.4, 3.5, 3.6, and 3.7) come from the differences in line parameters, such as wavelengths, Aul , and E up . For the lines with similar wavelengths, since the absorption by excited H2 O molecules decreases, the optical depth values tend to be smaller as values of Aul of the lines become smaller. The optical depth values become smaller as values of E up become larger. This is because the line absorption become weaker in the disk surfaces. The dust grain opacity becomes smaller for the lines with larger wavelengths [60]. In the shorter wavelength lines (mid- and far-infrared), the absorption by the dust grains mainly determine the total optical depths (including components of gas and dust grains) and line emitting regions throughout the disk. In contrast, In the longer wavelength lines, the values of the line absorption by excited molecules become larger (see also Eq. (12)) even if the values of E up and Aul are similar. In the lines with longer wavelengths (sub-millimeter lines), the line emitting regions and the total optical depth profiles in the inner disk midplane are mainly determined by the line absorption by excited molecules, although the absorption by dust grains mainly determines those in the disk surface and outer colder disk midplane. The ortho-H2 16 O 482.99 µm and 682.66 µm lines have relatively smaller E up values (400 µm) compared with other lines, thus the dust opacity is smaller and they can trace the regions closer to the midplane in the outer disk. Therefore, line fluxes from the region with a relatively high H2 O gas abundance (∼10−8 , r = 8–14 au) are not so small (∼10–20% of total emission fluxes) compared to the region with a high H2 O

10000

1 0.8 0.6

0 -0.4

-0.2

0

0.2

100 0.4

1 0.8 0.6 0.4 0.2

1000 Tgas 682.66 μm 63.32 μm 538.29 μm 12.40 μm 12.45 μm 4.96 μm 4.43 μm

0 -0.4

-0.2

1 0.8 0.6

0.2

1000 Tgas 17.75 μm 24.00 μm 61.32 μm 94.17 μm 482.99 μm 682.66 μm 933.28 μm

0 -0.4

-0.2

0

0.2

100 0.4

Normalized Cumulative Emissivity

10000 Gas Temperature [K]

Normalized Cumulative Emissivity

1.2

0.4

0.8

1000

0.6 Tgas 17.75 μm 24.00 μm 61.32 μm 94.17 μm 482.99 μm 682.66 μm 933.28 μm

100

-0.2

0

z/r

0.2

10 0.4

Normalized Cumulative Emissivity

1

Gas Temperature [K]

Normalized Cumulative Emissivity

10000

0 -0.4

100 0.4 10000

1 0.8 0.6 0.4 0.2

1000 Tgas 682.66 μm 63.32 μm 538.29 μm 12.40 μm 12.45 μm 4.96 μm 4.43 μm

0 -0.4

-0.2

0

0.2

100 0.4

z/r

1.2

0.2

0.2

1.2

z/r

0.4

0

z/r

z/r

Gas Temperature [K]

0.2

10000

1.2

10000

1 0.8

1000

0.6 0.4 0.2

Tgas 682.66 μm 63.32 μm 538.29 μm 12.40 μm 12.45 μm 4.96 μm 4.43 μm

0 -0.4

100

-0.2

0

0.2

Gas Temperature [K]

0.4

1000 Tgas 17.75 μm 24.00 μm 61.32 μm 94.17 μm 482.99 μm 682.66 μm 933.28 μm

1.2

Gas Temperature [K]

1.2

Normalized Cumulative Emissivity

3 Modeling Studies II. The Case of the Herbig Ae Star

Gas Temperature [K]

Normalized Cumulative Emissivity

58

10 0.4

z/r

Fig. 3.7 The normalized cumulative line emissivities at r = 5 au (top two panels), r = 10 au (middle two panels), and r = 30 au (bottom two panels), and the gas temperature Tg plots at Kelvin (gray dotted line) in the vertical direction. The left three panels show the distributions for seven ortho-H2 16 O 17.75 µm (red solid line), 24.00 µm (black long dashed line), 61.32 µm (blue dashed line), 94.17 µm (brown dashed two dotted line), 482.99 µm (green dashed dotted line), 682.66 µm (violet long dashed dotted line), and 933.28 µm (orange dotted line) lines. The right three panels show the distributions for seven ortho-H2 16 O 682.66 µm (violet long dashed dotted line), 63.32 µm (red solid line), 538.29 µm (black long dashed line), 12.40 µm (blue dashed line), 12.45 µm (brown dashed two dotted line), 4.96 µm (green dashed dotted line), and 4.43 µm (orange dotted line) lines. We normalized the cumulative emissivity of each line using the values at z = −∞. The inclination angle of the disk i is assume to be 0 degree in making these figures. This figure is originally reported in Notsu et al. [64], and reproduced by permission from American Astronomical Society (©AAS)

3.2 Results

59

gas abundance (∼10−4 , r < 8 au). Although the ortho-H2 16 O 933.28 µm line resides in the sub-millimeter region, this line has a larger E up (=1861.2 K) than other lines, and thus most of the emission flux is emitted from the region with high temperature and a high H2 O gas abundance (∼10−4 , r < 8 au). The radial difference of the positions between the outer edge of the hot H2 O gas region and the exact location of the water snowline is not so large (several au), and thus when we want to constrain the overall H2 O distribution of the inner disk and roughly estimate the H2 O snowline position, the influence is not so serious. However, if we observe several candidate ortho-H2 16 O lines at various wavelengths between mid-infrared and sub-millimeter, with small Aul (∼10−6 –10−3 ) and various Eup (e.g., ∼700–2100 K), there is the possibility to confine the detailed distribution in the disk midplane, not only the position of the H2 O snowline, but also the H2 O gas abundance and the gas temperature. As adopted in previous works to get the H2 O distributions (e.g., Zhang et al. [95], Blevins et al. [12]), the water reservoir inside the H2 O snowline can be traced from the Keplerian profiles of lines independently regardless of the assumption of the relation between disk radius and the gas temperature. The emission from the disk surface is mainly traced by the previous water line observations with very high E up (>3000 K) and large Aul (∼10−1 –100 s−1 ) (e.g., Salyk et al. [77], Pontoppidan et al. [73, 74], Fedele et al. [26], Mandell et al. [52], van Dishoeck et al. [84], Banzatti et al. [9], Blevins et al. [12], see also Sect. 3.2.4). On the basis of results and discussions above, in the remainder part of this section (and basically of this thesis), we consider that these water lines with small Aul and relatively larger values of E up are candidates to trace the H2 O snowline positions in disks.

3.2.4 The Case of the Less Suited Ortho-H2 16 O Emission Lines The line profile for the ortho-H2 16 O 63.32 µm line is shown in the top left panel of Fig. 3.8. The contribution from the outer optically thin surface layer (r = 14–30 au) is large (three times larger in flux density) compared with that of the inner disk midplane (r 15 au, e.g., Fedele et al. [24, 25]). From the HD163296 disk (at a inclination i of 44 deg and distance d of ∼122 pc), the H2 O 63.32 µm line flux is observed to be (2.0 ± 0.6) × 10−17 W m−2 , and the values of the other lines (e.g., ortho-H2 16 O 56.82 µm and 71.95 µm lines) are roughly similar (e.g., Fedele et al. [24], Meeus et al. [53]). The upper limits of such water emission line fluxes, including the 63.32 µm from other Herbig Ae disks (d ∼ 100–150 pc), are considered to be between a few 10−18 and a few 10−17 W m−2 [25, 53]. If the difference in the distances from the solar system is considered, the values of water line fluxes in our modeling for the Herbig Ae disk (see also Table 3.1, d = 140 pc) are roig;u several tens of time larger than these observed upper limit values. Our model disk is not intended to be representative of any particular source. In Sect. 3.3.3, we explain this issue further. The line profile for the ortho-H2 16 O line at 538.29 µm is shown in the top right panel of Fig. 3.8. The contribution from the outer disk (r = 14–30 au) is large compared to that from the optically thick inner disk midplane (r < 14 au) and the width between the double peaks of the line profile is around two times narrower than those of candidate water lines to trace the position of the H2 O snowline, although the Aul is not so high (=3.497 ×10−3 s−1 ). This is because this 538.29 µm line is the groundstate rotational transition. In addition, compared with the other lines discussed in this work, it has a low E up (=61.0 K). This line flux comes mainly from the outer cold water vapor in the photodesorbed region. The emissivity value of the ortho-H2 16 O 538.29 µm line at each (r, z) in the photodesorbed layer is comparable inside and outside the H2 O snowline (see Figs. 3.7 and 3.9) However, most disk-integrated emission from this line arises from the outer disk, because of the larger surface area of the outer disk. The midplane opacity of this line (see Fig. 3.10) in the outer disk is around 103 –104 times higher than those of the candidate water lines to trace the position of the H2 O snowline, although the wavelength and thus the dust opacity are similar. This is because this line has a small value of E up and the level population for this water line is very high at the outer cold disk midplane. Thus, this line is not suited to trace the H2 O snowline position in the Herbig Ae disk, as also disk in the T Tauri disk [65]. This ortho-H2 16 O 538.29 µm line has been detected from disks around two T Tauri stars DG Tau and TW Hya, and one Herbig Ae star HD100546 (e.g., Hogerheijde et al. [41], Podio et al. [72], van Dishoeck et al. [84], Salinas et al. [76]), by previous space high-dispersion spectroscopic observations with H er schel/HIFI. The number of detections is small because the line flux is low compared with the sensitivity of

3.2 Results

65

that instrument [6]. According to observational and modeling studies (e.g., Meijerink et al. [55], Woitke et al. [91], Antonellini et al. [6]), the emitting region arises in the cold outer disk, consistent with the results of our model calculations. In this study we define OPR = 3 (=the value in the high temperature region) throughout the disk, thus we may be overestimating the line flux of the ortho-H2 16 O 538.29 µm line (for more details, see Sect. 2.1.5 of this thesis and paper I, Notsu et al. [65]). Moreover, for accurate determination of the gas phase H2 O abundance in this region, it also may be necessary to include grain-surface reactions (e.g., Hasegawa et al. [36], Walsh et al. [90]). This is because this line flux is controlled by the amount of outer cold H2 O gas which is desorbed from the cold dust-grain surfaces. The profiles for the mid-infrared ortho-H2 16 O12.40 µm (middle left) and 12.45 µm (middle right) lines from the Herbig Ae disk are shown in the middle two panels of Fig. 3.8. The line-of-sight emissivities the total optical depths (dust and gas emission), and the vertical normalized cumulative emissivities of these two mid-infrared ortho-H2 16 O lines from the Herbig Ae disk are shown in Figs. 3.7, 3.9, and 3.10, respectively. Both lines have much larger E up (>4000 K) and Aul (>1 s−1 ) values than those of the candidate mid-infrared water lines to probe the H2 O snowline positions in the disk midplane (see Tables 3.1 and 3.2), and emission from the disk inner and outer hot surface region are mainly traced by those lines. By previous ground-based mid-infrared spectroscopic observations of VLT/VISIR [74], the two lines profiles were obtained from bright T Tauri disks (RNO 90 and AS 205N). The Keplerian double-peaked or flat-topped (for low inclination objects) profiles are shown, and the line emitting region is the hot disk surface. The profiles of pure rotational near-infrared ortho-H2 16 O 4.96 µm (bottom left), 4.43 µm (bottom right) lines from the Herbig Ae disk are shown in the bottom two panels of Fig. 3.8. The line-of-sight emissivities, the total optical depths (dust and gas emission), and the vertical normalized cumulative emissivities of these near-infrared lines for the Herbig Ae disk, are shown in Figs. 3.9, 3.10, and 3.7, respectively. Both lines have the same much larger values of E up (=4180.4 K), the former line has a larger value of Aul (=3.260 s−1 ) and the latter has a smaller value of Aul (= 2.080 × 10−4 s−1 ). For the former case, the emission from the hot surface of the inner and outer disk is mainly traced. This is because it has much larger E up and Aul values than those of the candidate ortho-H2 16 O lines (see Tables 3.1 and 3.2). This line has similar E up and Aul values with the observed near-infrared rovibrational water lines in L band [52]. For the latter smaller Aul line case, it only traces the very innermost region (r < 3 au for the 4.43 µm line case). This is because the value of E up in this near-infrared line is much larger (>4000 K) than those of the candidate water lines to probe the water snowline positions from sub-millimeter to mid-infrared wavelengths. Moreover, the widths between the two peaks of the profiles of these near- and mid-infrared lines with large E up are larger than those of candidate water lines to probe the H2 O snowline positions (see Figs. 3.4, 3.8, and 3.12). These are because they trace the innermost hot region compared with the region around the H2 O snowline. Any water lines have not been detected regardless of the value of Aul (For more details, see Sect. 3.3.3) by previous spectroscopic observations at near- and mid-

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3 Modeling Studies II. The Case of the Herbig Ae Star

infrared wavelengths using VLT/CRIRES and Spit zer /IRS for Herbig Ae disks (e.g., Pontoppidan et al. [73], Fedele et al. [26], Salyk et al. [78]). In addition, the level populations of the water molecule are calculated under LTE, as opposed to nonLTE (see also Sect. 3.1 of this paper). However, as found in previous studies (e.g., Meijerink et al. [56], Woitke et al. Woitke et al. [91], Banzatti et al. [7], Antonellini et al. [6]), in our LTE calculations there is a possibility that we have overestimated the emission fluxes of strong H2 O lines with large Aul which trace the hot surface layer.

3.2.5 The Candidate Ortho-H2 16 O Line Fluxes The total fluxes of the various ortho-H2 16 O lines to trace the H2 O snowline positions are shown in Fig. 3.11, for a T Tauri disk (right panel) and for a Herbig Ae disk (left panel). Those lines are selected from the LAMDA database (see Sect. 2.1.5 of this thesis and Notsu et al. [65]) with both relatively large vE up values (700 < E up < 2100 K) and small Aul values (10−6 < Aul < 10−2 s−1 ). The wavelengths of these lines range from mid-infrared to sub-millimeter, λ ∼ 11–1000 µm. This is because on the basis of our criteria for E up and Aul , there are not candidate lines with wavelengths λ < 10µm to trace the positions of the H2 O snowline. The opacity of the dust grains for wavelengths λ < 10µm is expected to be too large, and the values of E up of lines for wavelengths λ < 10 µm are too large (3000 K), to trace the emission from the disk midplane (see Sects. 3.2.2 and 3.3.4). The detailed line parameters of E up , Aul , frequency, wavelength, transitions (JK a K c ), and total line fluxes of these candidate ortho-H2 16 O lines shown in Fig. 3.11 are listed in Table 3.2. Both values for the total fluxes from the Herbig Ae disk and the T Tauri disk

Fig. 3.11 The total fluxes of the ortho-H2 16 O lines which are best candidates to trace the emission from the water vapor within the H2 O snowline, for a Herbig Ae disk (left panel) and a T Tauri disk (right panel). We select these lines based on their small Einstein A coefficients of 10−6 < Aul < 10−2 s−1 and relatively large excitation energies of 700 < E up < 2100K. The wavelengths of these lines range from mid-infrared to sub-millimeter, λ ∼11–1000 µm. This figure is originally reported in Notsu et al. [64], and reproduced by permission from American Astronomical Society (©AAS)

3.2 Results

67

are shown in Fig. 3.11 and Table 3.2. Moreover, Fig. 3.12 shows the profiles of midinfrared candidate lines (λ ∼ 11–25 µm) for the Herbig Ae disk. All lines in this figure are listed in Table 3.2. These line fluxes from the Herbig Ae disk are around 102 –103 larger than those of the T Tauri disk (see Figs. 3.11, 3.12, and Tables 3.1, 3.2). This is because the H2 O snowline position in the Herbig Ae disk exists at a larger radius from the central star than that in the T Tauri disk. As the Eup values become smaller and the Aul values become larger, the line peak fluxes become larger. In addition, as the wavelengths of these water lines become shorter, the total flux values tend to be larger. This is because the peak wavelengths of the Planck function at the gas temperatures around the H2 O snowline (Tg ∼ 100–200 K) are at mid-infrared wavelengths. The total fluxes of the mid-infrared candidate water lines to trace H2 O snowline positions are ∼101 – 102 times larger in the T Tauri disk and ∼102 –104 times larger in the Herbig Ae disk case than those of sub-millimeter lines, respectively, and there are differences in the line flux ratio of mid-infrared lines to sub-millimeter lines between the Herbig Ae and the T Tauri disks. These are because the amount of hot H2 O vapor around the region at τul  1 in mid-infrared lines and within the H2 O snowline are higher in the Herbig Ae disk model than that in the T Tauri disk model. Most of the emission flux from these mid-infrared lines comes from the region with a high H2 O gas abundance (∼10−4 , r < 8 au), and the two peaks positions and the rapid drop in flux density between the peaks contains information on the position of the outer edge of this region (see Fig. 3.12). This is because they have relatively larger values of E up (∼1500–2000 K except for the ortho-H2 16 O 17.75 and 24.00 µm lines) and shorter wavelengths (λ ∼ 11–25 µm) among all candidate water lines to trace the H2 O snowline position (see Table 3.2).

3.2.6 The Radial Distributions of Normalized Cumulative Line Fluxes The normalized radial cumulative fluxes for seven H2 16 O 682.66 µm, 63.32 µm, 538.29 µm, 12.40 µm, 12.45 µm, 4.96 µm, and 4.43 µm lines are shown in Fig. 3.13. The properties of these seven lines are discussed in Sects. 3.2.3 and 3.2.4. On the basis of these figures, around 90% of the flux of the 682.66 µm line is emitted from the region within the H2 O snowline (r < 14 au). In contrast, mostly from the region outside the H2 O snowline, emission from the 538.29 µm and the 63.32 µm lines is emitted. The 538.29 µm line is mainly emitted from a region with r ∼ 50–300 au, and the 63.32 µm line is mainly emitted from the region between r ∼ 25–200 au. The properties of these three lines for the Herbig Ae disk are similar to those for the T Tauri disk which we discussed in Sects. 2.2.3–2.2.5 in this thesis (see also paper I, Notsu et al. [65]). Both from the regions within 3 au and outside the H2 O snowline (r > 14 au) the 4.96 µm, 12.40 µm, and 12.45 µm lines are mainly emitted. The emission from the

68

3 Modeling Studies II. The Case of the Herbig Ae Star

Fig. 3.12 a The velocity profiles of mid-infrared ortho-H2 16 O lines at λ = 11.88 µm (top left), 13.01 µm (top right), 15.49 µm (middle left), 16.33 µm (middle right), 16.73 µm (bottom left), and 17.75 µm (bottom right), from the Herbig Ae disk. These exist between 11–25 µm and are also the best mid-infrared candidate ortho-H2 O lines to trace the hot water vapor within the H2 O snowline. The parameters and total fluxes of these ortho-H2 O lines are reported in Table 3.2. Red solid lines are the emission line profiles from inside 8 au (=the inner high temperature region), blue dashed lines are those from inside 14 au (∼inside the H2 O snowline), green dotted lines are those from 14–30 au (∼outside the H2 O snowline), and black dashed dotted lines are those from the total area inside 30 au. This figure is originally reported in Notsu et al. [64], and reproduced by permission from American Astronomical Society (©AAS). b The velocity profiles of mid-infrared ortho-H2 16 O lines at λ = 19.53 µm (top left), 19.64 µm (top right), 21.12 µm (middle left), 21.19 µm (middle right), 21.57 µm (bottom left), and 24.00 µm (bottom right), from the Herbig Ae disk. This figure is originally reported in Notsu et al. [64], and reproduced by permission from American Astronomical Society (©AAS)

3.2 Results

69

Fig. 3.12 (continued)

region between 3–14 au (=the H2 O snowline) is much smaller. The 4.43 µm line is mainly emitted from the innermost region of the disk (r < 3 au). These are because these four lines have much larger values of E up (>4000 K) than both the candidate ortho-H2 16 O lines that trace the hot water vapor within the H2 O snowline and the 63.32 µm line. Therefore, the values of flux densities from the hot surface layer of the inner disk are larger. The 4.43 µm line has a smaller value of Aul (=2.080 × 10−4 s−1 ), and thus the flux density values from the hot surface layer of the outer disk are much smaller, but the other three lines have larger values of Aul (>1 s−1 ) and thus the values of flux densities from the hot surface layer of the outer disk are larger. Figure 3.14 shows The normalized radial cumulative fluxes for above seven candidate ortho-H2 16 O lines to trace the H2 O snowline positions. The properties of these

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3 Modeling Studies II. The Case of the Herbig Ae Star

Table 3.2 Candidate ortho-H2 16 O line parameters and total line fluxes (11–1000 µm) JK a K c λ1 Freq. Aul E up HAe flux2,3 TT flux3,4 (µm) (s−1 ) (W m−2 ) (W m−2 ) (GHz) (K) 770 -625

11.878

25239.615

761 -616

13.005

23052.310

661 -514

15.489

19354.618

770 -725

16.329

18359.435

661 -616

16.728

17921.765

652 -505

17.754

16885.840

761 -716

19.532

15348.791

770 -827

19.638

15265.853

752 -707

21.115

14197.932

761 -818

21.185

14151.161

770 -743

21.571

13897.693

550 -505

23.996

12493.205

661 -634

25.247

11874.160

661 -716

29.339

10218.246

854 -909

29.851

10043.001

652 -707

33.074

9064.381

550 -523

33.833

8860.835

770 -845

36.750

8157.523

441 -414

37.984

7892.616

945 -10110

40.702

7365.464

761 -836

47.601

6297.997

661 -734

49.334

6076.834

6.653 ×10−3 2.585 ×10−4 4.138 ×10−4 7.756 ×10−5 2.153 ×10−5 2.909 ×10−3 1.269 ×10−3 1.900 ×10−6 2.078 ×10−3 6.154 ×10−6 3.474 ×10−3 2.696 ×10−4 3.803 ×10−3 1.859 ×10−5 1.605 ×10−4 5.942 ×10−5 4.552 ×10−3 1.123 ×10−4 2.629 ×10−3 4.815 ×10−4 4.268 ×10−4 1.195 ×10−4

2006.8

3.4 × 10−19 1.8 × 10−22

1749.8

2.9 × 10−18 1.1 × 10−21

1503.6

6.9 × 10−18 2.6 × 10−21

2006.8

3.8 × 10−19 1.6 × 10−22

1503.6

3.2 × 10−19 1.1 × 10−22

1278.5

4.1 × 10−17 2.3 × 10−20

1749.8

8.3 × 10−18 3.5 × 10−21

2006.8

7.6 × 10−21 3.1 × 10−24

1524.8

2.0 × 10−17 9.9 × 10−21

1749.8

4.8 × 10−20 1.7 × 10−23

2006.8

1.1 × 10−17 5.5 × 10−21

1067.7

9.4 × 10−18 6.4 × 10−21

1503.6

2.6 × 10−17 1.9 × 10−20

1503.6

2.5 × 10−19 1.3 × 10−22

1805.9

1.2 × 10−18 4.7 × 10−22

1278.5

1.4 × 10−18 1.3 × 10−21

1067.7

3.2 × 10−17 7.1 × 10−20

2006.8

4.3 × 10−19 1.6 × 10−22

702.3

3.1 × 10−17 1.0 × 10−19

1957.1

2.1 × 10−18 1.1 × 10−21

1749.8

2.3 × 10−18 2.2 × 10−21

1503.6

1.3 × 10−18 1.8 × 10−21 (continued)

3.2 Results

71

Table 3.2 (continued) JK a K c λ1 (µm)

Freq. (GHz)

Aul (s−1 )

E up (K)

HAe flux2,3 TT flux3,4 (W m−2 ) (W m−2 )

1.442 ×10−4 5.030 ×10−4 7.203 ×10−4 2.686 ×10−4 3.387 ×10−4 1.670 ×10−4 6.768 ×10−4 7.255 ×10−4 7.403 ×10−3 3.911 ×10−4 2.947 ×10−4 2.927 ×10−4 2.334 ×10−3 2.599 ×10−4 1.074 ×10−3 1.552 ×10−3 9.459 ×10−4 1.417 ×10−3 1.087 ×10−4 1.106 ×10−4 2.231 ×10−5

1067.7

3.7 × 10−18 1.4 × 10−20

1339.8

5.2 × 10−18 1.6 × 10−20

1524.8

4.1 × 10−18 1.1 × 10−20

878.1

5.9 × 10−18 3.5 × 10−20

1278.5

1.8 × 10−18 1.6 × 10−20

702.3

1.8 × 10−18 2.3 × 10−20

1729.3

1.0 × 10−18 8.1 × 10−21

1447.5

1.4 × 10−18 1.5 × 10−20

1615.3

1.1 × 10−18 1.7 × 10−20

933.7

9.0 × 10−19 1.5 × 10−20

1805.9

2.5 × 10−19 3.8 × 10−21

1088.7

4.9 × 10−19 8.9 × 10−21

795.5

6.0 × 10−19 1.2 × 10−20

1615.3

2.0 × 10−19 3.9 × 10−21

1274.1

3.7 × 10−19 6.8 × 10−21

1399.8

3.6 × 10−19 6.7 × 10−21

1805.9

1.8 × 10−19 3.5 × 10−21

933.7

3.5 × 10−19 7.0 × 10−21

1125.7

1.9 × 10−19 3.9 × 10−21

732.1

5.3 × 10−20 1.1 × 10−21

1524.8

9.4 × 10−21 2.6 × 10−22

550 -625

52.864

5671.021

743 -818

53.455

5608.351

752 -827

57.394

5223.441

541 -616

61.316

4889.280

652 -725

94.172

3183.464

441 -514

112.803

2657.666

927 -10110

114.454

2619.334

836 -909

116.350

2576.644

845 -752

159.051

1884.888

634 -707

159.400

1880.753

854 -927

187.810

1595.252

643 -716

190.437

1574.232

625 -532

226.761

1322.065

845 -918

229.206

1307.963

827 -734

231.248

1296.411

743 -652

234.531

1278.266

854 -761

256.593

1168.358

634 -541

258.816

1158.324

725 -818

261.457

1147.621

532 -441

482.990

620.701

752 -661

676.704

443.018

(continued)

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3 Modeling Studies II. The Case of the Herbig Ae Star

Table 3.2 (continued) JK a K c λ1 (µm)

Freq. (GHz)

Aul (s−1 )

E up (K)

HAe flux2,3 TT flux3,4 (W m−2 ) (W m−2 )

2.816 ×10−5 6.165 ×10−6

1088.7

1.4 × 10−20 3.1 × 10−22

1861.2

2.3 × 10−21 7.8 × 10−23

643 -550

682.664

439.151

1029 -936

933.277

321.226

1 In

calculating the value of line wavelength from the value of line frequency, we use the value of speed of light c = 2.99792458 × 108 m s−1 2 The total flux of each emission line from the Herbig Ae disk 3 When we calculate these line profiles, we assume the distance to the object d = 140 pc, and the inclination angle of the disk i = 30 deg 4 The total flux of each emission line from the T Tauri disk (see also paper I, Notsu et al. [65]) This table is originally reported in Notsu et al. [64], and reproduced by permission from American Astronomical Society (©AAS)

seven lines are also discussed in Sects. 3.2.3 and 3.2.5. In the cases of the 682.66 µm and 482.99 µm lines, some emission flux is emitted from the region with a relatively high H2 O gas abundance (∼10−8 , r = 8–14 au), and most of the flux is emitted from the region with a high H2 O gas abundance (∼10−4 , r < 8 au). On the other hand, for the other lines, almost all of the emission flux comes from the region with a high H2 O gas abundance (∼10−4 , r 400 µm) and relatively smaller values of E up ( tends to be smaller [23], if the line wavelength is shorter. However, emission from these lines mainly comes from the hot water vapor inside the H2 O snowline where total gas density is much larger (∼1011 –1014 cm−3 ) than the values of n cr , and thus it is valid to use LTE to calculate their fluxes.

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3 Modeling Studies II. The Case of the Herbig Ae Star

3.3.3 Previous Water Line Observations in Herbig Ae Disks The “visible” H2 O gas column density at these wavelengths is smaller than the total H2 O column density integrated over the disk in the vertical direction, since water line emission from the disk midplane is likely obscured by dust grains at near- to mid-infrared wavelengths (see e.g., Fig. 3.3). For example, in Walsh et al. [90], inside the H2 O snowline the visible column density at 14 µm in the Herbig Ae disk case is ∼1019 –1020 cm−2 . The visible H2 O gas column densities at 17.75, 61.32, and 682.66 µm in the Herbig Ae disk are ∼1018 –1019 cm−2 within the H2 O snowline, which are lower than those of Walsh et al. [90] (see the bottom panel of Fig. 3.3). This is because the total integrated column density of water vapor in our model (∼1020 –1022 cm−2 ) is lower than that of Walsh et al. [90] (∼1021 –1023 cm−2 ), and because absorption by dust grains is dominant in the disk midplane and the disk surface (τul  1) compared to that by excited gas molecules, especially remarkable in the cases of infrared lines (see also Sect. 3.2.3). Only upper limits values of H2 O gas column densities (1018 cm−2 ) using near- and mid-infrared water lines have not been detected by previous spectroscopic observations using instruments on space and ground telescopes (e.g., Spit zer /IRS and VLT/CRIRES) for Herbig Ae disks [26, 73, 78]. In contrast, those near- and mid-infrared water lines are observed in many T Tauri disks (e.g., Pontoppidan et al. [73]). Water lines at far-infrared wavelengths have been detected with H er schel/PACS only in the disk around HD163296, although this emission originates in the hot surface layer of the outer disk (r > 15 au), and it is farther out than that expected for emission at shorter wavelengths [24, 25, 53]. From these observational results, there is an important question as to why the detection rate for near- and mid-infrared water lines for Herbig Ae disks is lower than that for T Tauri disks. Some answers to the above question have been discussed in previous studies (e.g., Woitke et al. [91], Pontoppidan et al. [73], Fedele et al. [26], Meeus et al. [53], Walsh et al. [90], Antonellini et al. [5, 6]). Here we introduce some important answers (see also Sect. 3.2.4). First, dust-graindust-grain growth and settling can reduce the total dust-grain surface area and possibly increase the UV irradiation rates in the upper disk (e.g., Vasyunin et al. [85], Akimkin et al. [2]), which can push the molecular layer deeper into the disk atmosphere. Thus, a higher fraction of the gas-phase water may be hidden from view (e.g., Walsh et al. [90], Krijt et al. [48]). We note that HD100546, for which far-infrared water lines have not been detected, has very high UV flux from the central star and even at 30 au the UV field is expected to be too strong for gasphase water to survive [53]. Tilling et al. [82] modeled the disk of HD163296, and they pointed out that the dust material is settled. Meanwhile, dust-grain growth and the dust-grain shape also affect the UV field through scattering efficiency in the disk atmosphere. If the dust-grain radius is large enough compared with the wavelength of radiation from the central star, forward scattering by dust grains becomes efficient and the UV field decreases in the disk atmosphere (e.g., Bethell and Bergin [11]). The gas temperature in the disk atmosphere, which affects the water line fluxes, is also controlled by the UV radiation field. The gas temperature in the disk atmosphere will

3.3 Discussions

77

become lower/higher if the UV radiation field decreases/increases The isotropic dust scattering and the grain size distribution of the dark cloud model with compact and spherical dust grains are assumed in our calculations (For more details, see Nomura and Millar [60] and paper I, Notsu et al. [65]), and these assumptions will affect the resulting H2 O line fluxes. Second, if the disk is transitional and has a significant gap/hole in the inner disk (e.g., HD100546), the fluxes of lines from the inner disk atmosphere will be decreased (e.g., Banzatti et al. [9], see also Sect. 3.3.1). Third, there may be additional destruction routes for gas-phase water in the inner disk atmosphere, not yet included in the chemical networks we have adopted, for example the reaction to produce OH via photodissociation of H2 O by Lyman-α photons [90]. Fourth, in Herbig Ae disks the strong infrared excess of dust emission might veil the faint emission of molecular lines at infrared wavelengths (e.g., Lahuis et al. [50], Pontoppidan et al. [73], Fedele et al. [26], Antonellini et al. [5, 6]). According to previous line modeling calculations (e.g., Du and Bergin [17] and Antonellini et al. [5, 6]) the infrared and sub-millimeter water line fluxes would be affected by disk physical structures, such as maximum size of dust grains, disk gas mass. dust-to-gas mass ratio, dust-grain size distribution, and luminosity of the central star. According to Antonellini et al. [5, 6], the spectral resolution and sensitivity of previous midinfrared observations (by e.g., Spit zer /IRS) were not sufficient to detect the detailed profiles of even strong H2 O lines (with large Aul ) in many protoplanetary disks, especially disks around high-mass Herbig Ae/Be stars. This was because of the presence of noise in the spectra which can mask the line emission, combined with the high dust continuum flux (the noise level is proportional to the dust continuum flux).

3.3.4 Requirement for the Observations of Candidate Ortho-H2 16 O Lines Since the velocity width between the eine peaks is ∼20 km s−1 , high-dispersion spectroscopic observations (R = λ/δλ> tens of thousands) of the water lines in Table 3.2 are needed to trace emission from the hot water vapor within the H2 O snowline. Their profiles will be used to locate the H2 O snowline position. Compared with the total disk size, the emitting region area are small (r < 2 au for a T Tauri disk and r < 14 au for a Herbig Ae disk). The sensitivity and spectral resolution (of many instruments)used for previous sub-millimeter, far-infrared, and mid-infrared observations (e.g., H er schel/HIFI, H er schel/PACS, Spit zer /IRS) were not sufficient to detect and resolve the profiles of candidate water lines identified in Table 3.2 which trace emission from the hot water vapor inside the water snowline. Among the various water lines in ALMA Band 8, the ortho-H2 16 O 682.66 µm line is the most suitable o locate the H2 O snowline positon. Other candidate submillimeter H2 O lines o locate the H2 O snowline positon, having the same order-of-

78

3 Modeling Studies II. The Case of the Herbig Ae Star

magnitude fluxes, exist in ALMA Bands 7, 9 and 10 (∼300–1000 µm). The orthoH2 16 O 482.99 µm and 933.28 µm lines are the most suitable lines in ALMA Bands 7 and 9, respectively. Here we note that although there is no candidate ortho-H2 16 O line in ALMA Band 10, some candidate para-H2 16 O lines do fall in this band. Highdispersion (R > 100,000), high sensitivity (∼10−21 –10−20 W m−2 (5σ, 1 h)), and even high spatial resolution ( is the collisional rates for the excitation of H2 O molecules by electrons and H2 molecules for an adopted value of the collisional temperature of 200 K [11].

86

4 Modeling Studies III. Sub-millimeter H2 16 O and H2 18 O Lines

layer of the outer disk (∼107 –108 cm−3 ) and in the photodesorption region (∼108 – 1010 cm−3 ). Non-LTE effects are important for strong water lines with large Aul (∼10−1 –100 s−1 ) which trace the inner/outer hot surface layers (e.g., the ortho-H2 16 O 63.32 µm line) or the cold photodesorbed region (e.g., the ortho-H2 16 O 1113 GHz and the para-H2 16 O 557 GHz lines, see e.g., Meijerink et al. [34], Woitke et al. [70], Banzatti et al. [5], Antonellini et al. [3, 4]).

4.2 Results 4.2.1 The Profiles of Sub-millimeter Water Emission Lines The profiles for representative para-H2 16 O183 GHz (top left) and 1113 GHz (bottom left) lines, and para-H2 18 O 203 GHz (top right) and 1102 GHz (bottom right) lines from the Herbig Ae disk and the T Tauri disk are shown in Figs. 4.1 and 4.2, respectively. The para-H2 16 O 183 GHz line and the para-H2 18 O 203 GHz line are the same transition levels and they fall in ALMA Band 5 [25, 26]. In Tables 4.3 and 4.4, The detailed line parameters are listed. We do not include dust emission when we the line profiles in Figs. 4.1 and 4.2 (also Figs. 4.7 and 4.8, see Sect. 4.2.4), and total fluxes in Tables 4.3 and 4.4, although we do include both gas and dust absorption. We discuss the effects of dust emission in Sect. 4.3.1. The inclination angle of the disk is assumed to be i = 30 deg and the distance to the object is assumed to be d = 140 pc (∼the distance of Taurus molecular cloud), when we calculate line profiles and total fluxes in this work (see Figs. 4.1, 4.2, 4.7, 4.8, 4.9 and 4.10, and Tables 4.3 and 4.4), The position of the H2 O snowline position in the Herbig Ae disk (r ∼ 14 au, Tg ∼ 120 K, see paper II) is at a larger radius to the central star than that in the T Tauri disk (r ∼ 1.6 au, Tg ∼ 150 K, see paper I), in agreement with previous studies (e.g., Woitke et al. [70], Walsh et al. [67]). The regional classifications in the disk midplane with different fractional abundances of water molecules are shown in Table 4.2 (for more details, see also papers I and II). The temperature exceeds the sublimation temperature within the H2 O snowline (regions ATT , AHA and BHA , see also Table 4.2), and most of the H2 O molecules are released into the gas-phase through thermal desorption. Therefore, the column densities of water vapor become larger (>1016 cm−2 , see Fig. 3 of paper II) than those of the outer disk (∼1014 cm−2 ). The gas-phase chemistry to form water molecules is efficient in the inner region at a higher temperature (region AHA , see Table 4.2) in the case of Herbig Ae disks, and the column densities of gaseous water molecules become much larger (∼1020 – 1022 cm−2 ). The radial temperature profile in the T Tauri disk midplane is steeper than that in the Herbig Ae disk midplane, thus the T Tauri disk does not have BHA like transition region with relatively large fractional abundance of water vapor (∼10−8 ). Therefore, in the cases of candidate water lines with relatively high upper state energies (Eup ∼ 1000 K) and smaller Einstein A coefficients (Aul = 10−6 ∼ 10−3 s−1 ),

4.2 Results

87 0.005

0.004

0.003

0−8 au 0−14 au 14−30 au 0−30 au

16

para−H2 O 183 GHz

0−8 au 0−14 au 14−30 au 0−30 au

18

Flux Density [Jy]

Flux Density [Jy]

0.0035

0.0025 0.002 0.0015 0.001

0.004

para−H2 O 203 GHz

0.003

0.002

0.001 0.0005 0

−30

−20

−10

0

10

20

0

30

−30

−20

−10

0.3

Flux Density [Jy]

Flux Density [Jy]

0−8 au 0−14 au 14−30 au 0−30 au

para−H216O 1113 GHz

5 4 3 2

−30

20

30

0−8 au 0−14 au 14−30 au 0−30 au

para−H218O 1102 GHz

0.25 0.2 0.15 0.1 0.05

1 0

10

0.35

7 6

0

v−v0 [km/s]

v−v0 [km/s]

−20

−10

0

v−v0 [km/s]

10

20

30

0

−30

−20

−10

0

10

20

30

v−v0 [km/s]

Fig. 4.1 The profiles of para-H2 16 O183 GHz (top left) and 1113 GHz (bottom left) lines, and paraH2 18 O 203 GHz (top right), and 1102 GHz (bottom right) lines for the Herbig Ae disk. In these line profiles, the dust emission componets are ignored, and a disk inclination is assumed to be i = 30 deg and the distance to the object is assumed to be d = 140 pc. The line profiles from inside 8 au (=the inner high temperature region) are displayed with red solid lines, those from within 14 au (∼within the H2 O snowline) are blue dashed lines, those from 14 to 30 au (∼outside the H2 O snowline) are green dotted lines, and those from the total area inside 30 au are black dashed dotted lines. In the top two panels, the flux densities outside the H2 O snowline (green dotted lines, 150

∼10−5 –10−4

2–30

170

∼10−5 –10−4

BHA

8–14

120–170

∼10−8

CHA

14–30