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Saas-Fee Advanced Courses Saas-Fee Advanced Courses Volume 39 For further volumes: http://www.springer.com/series/4284 Paul Charbonneau Solar and Stellar Dynamos Saas-Fee Advanced Courses 39 Swiss Society for Astrophysics and Astronomy Edited by O. Steiner 123 Paul Charbonneau Département de Physique Université de Montréal Montréal Canada This Series is edited on behalf of the Swiss Society for Astrophysics and Astronomy: Société Suisse d’Astrophysique et d’Astronomie Observatoire de Genève, ch. des Maillettes 51, CH- 1290 Sauverny, Switzerland Cover picture: Snapshot of a global, three-dimensional, numerical simulation of solar magneto- convection. The color scale codes the radial magnetic field at the outer surface of the domain: red-yellow for positive magnetic polarity and blue-cyan for negative. At the given time instant of the magnetic cycle, polarity reversal of the polar cap magnetic field is just taking place. Even though the surface magnetic field is spatiotemporally intermittent, a well-defined axisymmetric component develops with a full magnetic cycle lasting about 78 years in this specific simulation. (From the web-page of the solar physics research group at Montreal University http://www.astro.umontreal.ca/*paulchar/grps/) ISSN 1861-7980 ISSN 1861-8227 (electronic) ISBN 978-3-642-32092-7 ISBN 978-3-642-32093-4 (eBook) DOI 10.1007/978-3-642-32093-4 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2012944388 Ó Springer-Verlag Berlin Heidelberg 2013 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Preface Magnetic fields are seen to interweave the fabric of the universe wherever tele- scopes are directed to. They are observed and measured in such diverse astro- physical objects and scale-sizes as galaxies, interstellar clouds, stars, planets, and compact objects, including the Sun and the Earth. While primordial magnetic fields may have been pre-existent in the early universe, it is believed that most cosmic magnetic fields that we observe nowadays have been, and still are, con- tinuously created by an electromagnetic inductive process known as the dynamo effect. Various types of astrophysical dynamos form the cosmic power plants for the production of magnetic fields. They are a central theme of virtually all kinds of astrophysical research and of planetary physics and geophysics. Here, they are the central topic this book is devoted to. This monograph is a thorough introduction to astrophysical dynamos, leading up to present-day research questions. It is directed at physics students at the intermediate to advanced level with basic knowledge of hydro- and electrody- namics, for self-study or for study in classes. Also, the advanced astrophysicists may learn to appreciate it as an introduction to, or a reference book on, the foundations of astrophysical dynamos. After familiarizing the reader with the concept and meaning of the magnetohydrodynamic equations, it starts with basic examples of kinematic flows and discusses conditions for the onset of dynamo action. The main part of the book is devoted to the solar dynamo, which is the best studied stellar dynamo with the most precise and longest lasting observational record. Different types of stellar dynamos across the H-R diagram and a brief outlook on compact objects, galaxies, and beyond, complete the book. Each chapter is complemented with an annotated bibliography leading the reader to background information including historical matters, as well as to the more advanced literature and present-day research articles. The book is accompanied by a course Web page, which can be found under http://obswww.unige.ch/SSAA/ sf39/dynamos. It contains animations of several figures of Chaps. 2 and 3, to which references are made in the text. Other than ad hoc introduced equations and definitions, all equations can be derived step by step (and should be rederived by the reader for a healthy exercise), often by using the appendices, which contain all v vi Preface the necessary identities and theorems from vector calculus, and operators and fluid equations in the cylindrical and spherical coordinate systems. The present book is an extended and updated version of the lectures delivered under the same title by Paul Charbonneau during the 39th ‘‘Saas-Fee Advanced Course’’, which took place in Les Diablerets (Switzerland) from March 23–28, 2009. The course title was ‘‘Magnetic Fields of Stars: From the Sun to Compact Objects’’ and included additional lectures by Sami K. Solanki (Magnetic fields in the atmospheres of the Sun and stars) and Christopher Thompson (Stellar Magnetofluids). Sixty students from 16 countries attended the course and could benefit from the excellent lectures delivered by these top experts. The Eurotel in Les Diablerets provided much appreciated hospitality. Snow, sunshine, and not least skiing and curling were also appropriately enjoyed by the course participants. The organizers of the course, M. Liebendörfer and F.-K. Thielemann (University of Basel), S. Berdyugina and O. Steiner (Kiepenheuer-Institut, Freiburg i.Br.), and R. Hirschi (Keele University) thank the three speakers for high-standard lectures, Paul Charbonneau for preparing the present lecture notes, and the course students for their active participation and enthusiasm. They also gratefully acknowledge finan- cial assistance provided by the Swiss Society for Astrophysics and Astronomy. Freiburg i. Br., May 2012 Oskar Steiner Acknowledgments The Lecture Notes making up this volume are an expanded and updated version of the notes distributed to attendees of the 39th Saas Fee Advanced School of the Swiss Astronomical Society. These Notes actually have had a long and tortuous genesis. They began as class notes for a graduate course in solar physics which, initially thanks to Fran Bagenal, I had the opportunity co-teach at the University of Colorado in Boulder with my then-HAO-colleague Tom Bogdan. Already with the first instance of the course, we opted to treat a few subjects at great depth, rather than give a broad, necessarily shallower survey of all of solar physics. Our emphasis was on modeling, mathematical and computational, the idea being that a detailed understanding of modeling in the context of a few topics, solidly grounded in the underlying physics, could be transferred to other subject areas and remain useful even if some of the chosen topics were to fall out fashion with time. The solar dynamo was one of these topics (which has not yet fallen out of fashion!), for which I was lead author and lecturer. We did have the privilege to have Fausto Cattaneo and David Galloway contributing lectures and written material, and the 1997 instance of the course also benefited greatly from feedback by Nic Brummell and Steve Tobias, who were attending ex officio. It is truly a pleasure for me to acknowledge here the influence all these individuals—as well as Keith MacGregor and Peter Gilman at HAO/NCAR—have had on my own thinking about dynamos. Tom and I eventually started turning these CU class notes into a book, but as we each went our own way, geographically and professionally, this project has yet to come to fruition. Upon moving to the Université de Montréal, I used the dynamo part of this embryonic book to teach graduate courses on astrophysical magneto- hydrodynamics, adding and modifying much of the material in the process. When I was invited to lecture at Saas-Fee 39 on the topic of astrophysical dynamos, this provided a natural starting point to produce the Lecture Notes the reader now has in hand, with some additional material borrowed from an extensive review article I wrote a few years ago for the online Journal Living Reviews in Solar Physics, and skillful LATEX ing and editing manoeuvres by Oskar Steiner. vii viii Acknowledgments At various points in time, many colleagues have kindly provided numerical data or actual plots that are now included in these Lecture Notes; their contributions are explicitly acknowledged in the captions to the corresponding figures. Many graduate students, too numerous to list here, have also provided useful feedback over the years. I do wish to mention explicitly Michel-André Vallières-Nollet, Étienne Racine, Patrice Beaudoin, Alexandre St-Laurent-Lemerle and Caroline Dubé, who have gone well beyond the call of duty in verifying and/or rederiving mathematical expressions, uncovering a number of significant mistakes (usually minus signs) in the process.
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