This page intentionally left blank STELLAR ASTROPHYSICAL FLUID DYNAMICS In all phases of the life of a star, hydrodynamical processes play a major role. This volume gives a comprehensive overview of the current state of knowledge in stellar astrophysical fluid dynamics, and marks the 60th birthday of Douglas Gough,ProfessorofTheoreticalAstrophysicsattheUniversityofCambridgeand leadingcontributortostellarastrophysicalfluiddynamics.Topicsincludeproper- tiesofpulsatingstars,helioseismology,convectionandmixinginstellarinteriors, dynamics of stellar rotation, planet formation, and the generation of stellar and planetary magnetic fields. Each chapter is written by leading experts in the field, andthebookprovidesanoverviewthatiscentraltoanyattempttounderstandthe properties of stars and their evolution. With extensive references to the technical literature, this is a valuable text for researchers and graduate students in stellar astrophysics. michael thompson is Professor of Physics at the Imperial College of Science, TechnologyandMedicine,London. jørgen christensen-dalsgaardisProfessorofHelio-andAsteroseismology intheDepartmentofPhysicsandAstronomy,UniversityofAarhus,Denmark. STELLAR ASTROPHYSICAL FLUID DYNAMICS Editedby MICHAEL J. THOMPSON ImperialCollegeLondon JØRGEN CHRISTENSEN-DALSGAARD UniversityofAarhus    Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge  , United Kingdom Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521818094 © Cambridge University Press 2003 This book is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2003 -  isbn-13 978-0-511-06972-7 eBook (EBL) -  isbn-10 0-511-06972-3 eBook (EBL) -  isbn-13 978-0-521-81809-4 hardback -  isbn-10 0-521-81809-5 hardback Cambridge University Press has no responsibility for the persistence or accuracy of s for external or third-party internet websites referred to in this book, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents Preface pageix 1 Aselectiveoverview 1 JørgenChristensen-DalsgaardandMichaelJ.Thompson I Stellarconvectionandoscillations 2 Onthediversityofstellarpulsations 23 WojciechA.Dziembowski 3 Acousticradiationandmodeexcitationbyturbulentconvection 39 Gu¨nterHoudek 4 UnderstandingroApstars 51 MargaridaS.Cunha 5 Wavesinthemagnetisedsolaratmosphere 63 ColinS.Rosenthal II Stellarrotationandmagneticfields 6 Stellarrotation:ahistoricalsurvey 75 LeonMestel 7 Theoscillationsofrapidlyrotatingstars 99 MichelRieutord 8 Solartachoclinedynamics:eddyviscosity,anti-friction,or somethinginbetween? 111 MichaelE.McIntyre 9 Dynamicsofthesolartachocline 131 PascaleGaraud 10 Dynamoprocesses:theinteractionofturbulenceand magneticfields 143 MichaelProctor 11 Dynamosinplanets 159 ChrisJones v vi Contents III Physicsandstructureofstellarinteriors 12 Solarconstraintsontheequationofstate 179 WernerDa¨ppen 13 3Hetransportandthesolarneutrinoproblem 193 ChrisJordinson 14 Mixinginstellarradiationzones 205 Jean-PaulZahn 15 Elementsettlingandrotation-inducedmixinginslowly rotatingstars 219 SylvieVauclair IV Helio-andasteroseismology 16 Solarstructureandtheneutrinoproblem 231 HiromotoShibahashi 17 Helioseismicdataanalysis 247 JesperSchou 18 Seismologyofsolarrotation 263 TakashiSekii 19 Telechronohelioseismology 279 AlexanderKosovichev V Large-scalenumericalexperiments 20 Bridgesbetweenhelioseismologyandmodelsofconvection zonedynamics 299 JuriToomre 21 Numericalsimulationsofthesolarconvectionzone 315 JulianR.Elliott 22 Modellingsolarandstellarmagnetoconvection 329 NigelWeiss 23 Nonlinearmagnetoconvectioninthepresenceofastrong obliquefield 345 KeithJulien,EdgarKnoblochandStevenM.Tobias 24 Simulationsofastrophysicalfluids 357 MarcusBru¨ggen VI Dynamics 25 Amagicelectromagneticfield 369 DonaldLynden-Bell 26 Continuumequationsforstellardynamics 377 EdwardA.SpiegelandJean-LucThiffeault Contents vii 27 Formationofplanetarysystems 393 DouglasN.C.Lin 28 Thesolar-cycleglobalwarmingasinferredfromsky brightnessvariation 411 WasaburoUnnoandHiromotoShibahashi