Table Of Content

Titelei_Rüdiger 21.05.2004 13:08 Uhr Seite 3 Günther Rüdiger and Rainer Hollerbach The Magnetic Universe Geophysical and Astrophysical Dynamo Theory WILEY-VCH Verlag GmbH & Co.KGaA Titelei_Rüdiger 21.05.2004 13:08 Uhr Seite 4 Authors This book was carefully produced.Nevertheless, authors,and publisher do not warrant the infor- Günther Rüdiger mation contained therein to be free of errors. Astrophysical Institute Potsdam Readers are advised to keep in mind that state- [email protected] ments,data,illustrations,procedural details or other items may inadvertently be inaccurate. Rainer Hollerbach Dept.of Mathematics,University of Glasgow Library of Congress Card No.:applied for [email protected] British Library Cataloging-in-Publication Data: A catalogue record for this book is available from the British Library Cover picture Total radio emission and magnetic field vectors of Bibliographic information published by M51,obtained with the Very Large Array and the Die Deutsche Bibliothek Effelsberg 100-m telescope ((cid:1)=6.2 cm,see Beck Die Deutsche Bibliothek lists this publication in 2000).With kind permission of Rainer Beck,Max- the Deutsche Nationalbibliografie;detailed bibli- Planck-Institut für Radioastronomie,Bonn. ographic data is available in the Internet at <http://dnb.ddb.de>. © 2004 WILEY-VCH Verlag GmbH & Co.KGaA, Weinheim All rights reserved (including those of translation into other languages).No part of this book may be reproduced in any form – nor transmitted or translated into machine language without written permission from the publishers.Registered names,trademarks,etc.used in this book,even when not specifically marked as such,are not to be considered unprotected by law. Printed in the Federal Republic of Germany Printed on acid-free paper Printing Strauss GmbH,Mörlenbach Bookbinding Litges & Dopf GmbH , Heppenheim ISBN 3-527-40409-0 Contents Preface XI 1 Introduction 1 2 EarthandPlanets 3 2.1 ObservationalOverview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 Reversals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.2 OtherTime-Variability . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 BasicEquationsandParameters . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.1 AnelasticandBoussinesqEquations . . . . . . . . . . . . . . . . . . 7 2.2.2 Nondimensionalization . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Magnetoconvection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3.1 RotationorMagnetismAlone . . . . . . . . . . . . . . . . . . . . . 14 2.3.2 RotationandMagnetismTogether . . . . . . . . . . . . . . . . . . . 15 2.3.3 WeakversusStrongFields . . . . . . . . . . . . . . . . . . . . . . . 16 2.3.4 OscillatoryConvectionModes . . . . . . . . . . . . . . . . . . . . . 18 2.4 Taylor’sConstraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4.1 Taylor’sOriginalAnalysis . . . . . . . . . . . . . . . . . . . . . . . 19 2.4.2 RelaxationofRo=E=0 . . . . . . . . . . . . . . . . . . . . . . . . 21 2.4.3 TaylorStatesversusEkmanStates . . . . . . . . . . . . . . . . . . . 22 2.4.4 FromEkmanStatestoTaylorStates . . . . . . . . . . . . . . . . . . 24 2.4.5 TorsionalOscillations . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.4.6 αΩ-Dynamos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.4.7 Taylor’sConstraintintheAnelasticApproximation . . . . . . . . . . 30 2.5 HydromagneticWaves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.6 TheInnerCore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.6.1 StewartsonLayersonC . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.6.2 NonaxisymmetricShearLayersonC . . . . . . . . . . . . . . . . . . 33 2.6.3 FiniteConductivityoftheInnerCore . . . . . . . . . . . . . . . . . 36 2.6.4 RotationoftheInnerCore . . . . . . . . . . . . . . . . . . . . . . . 37 2.7 NumericalSimulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.8 MagneticInstabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.9 OtherPlanets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.9.1 Mercury,VenusandMars . . . . . . . . . . . . . . . . . . . . . . . 42 VI Contents 2.9.2 Jupiter’sMoons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.9.3 JupiterandSaturn . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.9.4 UranusandNeptune . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3 DifferentialRotationTheory 47 3.1 TheSolarRotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.1.1 TorsionalOscillations . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.1.2 MeridionalFlow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.1.3 Ward’sCorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.1.4 StellarObservations . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.2 AngularMomentumTransportinConvectionZones . . . . . . . . . . . . . . 57 3.2.1 TheTaylorNumberPuzzle . . . . . . . . . . . . . . . . . . . . . . . 63 3.2.2 TheΛ-Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.2.3 TheEddyViscosityTensor . . . . . . . . . . . . . . . . . . . . . . . 72 3.2.4 Mean-FieldThermodynamics . . . . . . . . . . . . . . . . . . . . . 74 3.3 DifferentialRotationandMeridionalCirculationforSolar-TypeStars . . . . 77 3.4 KineticHelicityandtheDIV-CURL-Correlation . . . . . . . . . . . . . . . . 81 3.5 OvershootRegionandtheTachocline . . . . . . . . . . . . . . . . . . . . . 84 3.5.1 TheNIRVANACode . . . . . . . . . . . . . . . . . . . . . . . . . . 85 3.5.2 PenetrationintotheStableLayer . . . . . . . . . . . . . . . . . . . . 86 3.5.3 AMagneticTheoryoftheSolarTachocline . . . . . . . . . . . . . . 89 4 TheStellarDynamo 95 4.1 TheSolar-StellarConnection . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.1.1 ThePhaseRelation . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.1.2 TheNonlinearCycle . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.1.3 Parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 4.1.4 Dynamo-relatedStellarObservations . . . . . . . . . . . . . . . . . 101 4.1.5 TheFlip-FlopPhenomenon . . . . . . . . . . . . . . . . . . . . . . 104 4.1.6 MoreCyclicities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 4.2 Theα-Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.2.1 TheMagnetic-FieldAdvection . . . . . . . . . . . . . . . . . . . . . 112 4.2.2 TheHighlyAnisotropicα-Effect . . . . . . . . . . . . . . . . . . . 116 4.2.3 TheMagneticQuenchingoftheα-Effect . . . . . . . . . . . . . . . 122 4.2.4 Weak-CompressibleTurbulence . . . . . . . . . . . . . . . . . . . . 125 4.3 Magnetic-DiffusivityTensorandη-Quenching . . . . . . . . . . . . . . . . 129 4.3.1 TheEddyDiffusivityTensor . . . . . . . . . . . . . . . . . . . . . . 129 4.3.2 SunspotDecay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 4.4 Mean-FieldStellarDynamoModels . . . . . . . . . . . . . . . . . . . . . . 135 4.4.1 Theα2-Dynamo . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 4.4.2 TheαΩ-DynamoforSlowRotation . . . . . . . . . . . . . . . . . . 142 4.4.3 MeridionalFlowInfluence . . . . . . . . . . . . . . . . . . . . . . . 146 4.5 TheSolarDynamo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 4.5.1 TheOvershootDynamo . . . . . . . . . . . . . . . . . . . . . . . . 146 4.5.2 TheAdvection-DominatedDynamo . . . . . . . . . . . . . . . . . . 149 Contents VII 4.6 DynamoswithRandomα . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 4.6.1 ATurbulenceModel . . . . . . . . . . . . . . . . . . . . . . . . . . 155 4.6.2 DynamoModelswithFluctuatingα-Effect . . . . . . . . . . . . . . 155 4.7 NonlinearDynamoModels . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 4.7.1 Malkus-ProctorMechanism . . . . . . . . . . . . . . . . . . . . . . 159 4.7.2 α-Quenching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 4.7.3 MagneticSaturationbyTurbulentPumping . . . . . . . . . . . . . . 162 4.7.4 η-Quenching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 4.8 Λ-QuenchingandMaunderMinimum . . . . . . . . . . . . . . . . . . . . . 163 5 TheMagnetorotationalInstability(MRI) 167 5.1 StarFormation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 5.1.1 MolecularClouds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 5.1.2 TheAngularMomentumProblem . . . . . . . . . . . . . . . . . . . 171 5.1.3 TurbulenceandPlanetFormation . . . . . . . . . . . . . . . . . . . 174 5.2 StabilityofDifferentialRotationinHydrodynamics . . . . . . . . . . . . . . 174 5.2.1 CombinedStabilityConditions . . . . . . . . . . . . . . . . . . . . . 176 5.2.2 SufficientConditionforStability . . . . . . . . . . . . . . . . . . . . 178 5.2.3 NumericalSimulations . . . . . . . . . . . . . . . . . . . . . . . . . 179 5.2.4 VerticalShear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 5.3 StabilityofDifferentialRotationinHydromagnetics. . . . . . . . . . . . . . 181 5.3.1 IdealMHD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 5.3.2 BaroclinicInstability . . . . . . . . . . . . . . . . . . . . . . . . . . 183 5.4 StabilityofDifferentialRotationwithStrongHallEffect . . . . . . . . . . . 184 5.4.1 CriteriaofInstabilityofProtostellarDisks . . . . . . . . . . . . . . . 184 5.4.2 GrowthRates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 5.5 GlobalModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 5.5.1 ASphericalModelwithShear . . . . . . . . . . . . . . . . . . . . . 187 5.5.2 AGlobalDiskModel. . . . . . . . . . . . . . . . . . . . . . . . . . 192 5.6 MRIofDifferentialStellarRotation . . . . . . . . . . . . . . . . . . . . . . 194 5.6.1 TTauriStars(TTS) . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 5.6.2 TheAp-StarMagnetism . . . . . . . . . . . . . . . . . . . . . . . . 195 5.6.3 DecayofDifferentialRotation . . . . . . . . . . . . . . . . . . . . . 198 5.7 Circulation-DrivenStellarDynamos . . . . . . . . . . . . . . . . . . . . . . 199 5.7.1 TheGailitisDynamo . . . . . . . . . . . . . . . . . . . . . . . . . . 200 5.7.2 MeridionalCirculationplusShear . . . . . . . . . . . . . . . . . . . 201 5.8 MRIinKeplerDisks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 5.8.1 TheShearingBoxModel . . . . . . . . . . . . . . . . . . . . . . . . 202 5.8.2 AGlobalDiskDynamo? . . . . . . . . . . . . . . . . . . . . . . . . 205 5.9 Accretion-DiskDynamoandJet-LaunchingTheory . . . . . . . . . . . . . . 207 5.9.1 Accretion-DiskDynamoModels . . . . . . . . . . . . . . . . . . . . 207 5.9.2 Jet-Launching. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 5.9.3 Accretion-DiskOutflows . . . . . . . . . . . . . . . . . . . . . . . . 212 5.9.4 Disk-DynamoInteraction. . . . . . . . . . . . . . . . . . . . . . . . 213 VIII Contents 6 TheGalacticDynamo 215 6.1 MagneticFieldsofGalaxies . . . . . . . . . . . . . . . . . . . . . . . . . . 215 6.1.1 FieldStrength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 6.1.2 PitchAngles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 6.1.3 Axisymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 6.1.4 TwoExceptions: MagneticTorusandVerticalHaloFields . . . . . . 221 6.1.5 TheDiskGeometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 6.2 NonlinearWindingandtheSeedFieldProblem . . . . . . . . . . . . . . . . 224 6.2.1 UniformInitialField . . . . . . . . . . . . . . . . . . . . . . . . . . 224 6.2.2 SeedFieldAmplitudeandGeometry. . . . . . . . . . . . . . . . . . 226 6.3 InterstellarTurbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 6.3.1 TheAdvectionProblem . . . . . . . . . . . . . . . . . . . . . . . . 228 6.3.2 HydrostaticEquilibriumandInterstellarTurbulence . . . . . . . . . 229 6.4 FromSpherestoDisks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 6.4.1 1DDynamoWaves . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 6.4.2 Oscillatoryvs. SteadySolutions . . . . . . . . . . . . . . . . . . . . 235 6.5 Linear3DModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 6.6 TheNonlinearGalacticDynamowithUniformDensity . . . . . . . . . . . . 238 6.6.1 TheModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 6.6.2 TheInfluencesofGeometryandTurbulenceField. . . . . . . . . . . 240 6.7 DensityWaveTheoryandSwingExcitation . . . . . . . . . . . . . . . . . . 242 6.7.1 DensityWaveTheory. . . . . . . . . . . . . . . . . . . . . . . . . . 242 6.7.2 TheShort-WaveApproximation . . . . . . . . . . . . . . . . . . . . 243 6.7.3 SwingExcitationinMagneticSpirals . . . . . . . . . . . . . . . . . 244 6.7.4 NonlocalDensityWaveTheoryinKeplerDisks . . . . . . . . . . . . 248 6.8 Mean-FieldDynamoswithStrongHaloTurbulence . . . . . . . . . . . . . . 251 6.8.1 Nonlinear 2D Dynamo Model with Magnetic Supported Vertical Stratification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 6.8.2 Nonlinear3DDynamoModelsforSpiralGalaxies . . . . . . . . . . 253 6.9 NewSimulations: MacroscaleandMicroscale . . . . . . . . . . . . . . . . . 255 6.9.1 Particle-HydrodynamicsfortheMacroscale . . . . . . . . . . . . . . 256 6.9.2 MHDfortheMicroscale . . . . . . . . . . . . . . . . . . . . . . . . 258 6.10 MRIinGalaxies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 7 NeutronStarMagnetism 265 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 7.2 Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 7.3 WithoutStratification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 7.4 WithStratification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 7.5 Magnetic-DominatedHeatTransport . . . . . . . . . . . . . . . . . . . . . . 276 7.6 WhiteDwarfs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 8 TheMagneticTaylor–CouetteFlow 281 8.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 8.2 TheEquations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 Contents IX 8.3 ResultswithoutHallEffect . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 8.3.1 SubcriticalExcitationforLargePm . . . . . . . . . . . . . . . . . . 286 8.3.2 TheRayleighLine(a=0)andBeyond . . . . . . . . . . . . . . . . 286 8.3.3 ExcitationofNonaxisymmetricorOscillatoryModes . . . . . . . . . 290 8.3.4 WaveNumberandDriftFrequencies. . . . . . . . . . . . . . . . . . 291 8.4 ResultswithHallEffect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 8.4.1 HallEffectwithPositiveShear . . . . . . . . . . . . . . . . . . . . . 293 8.4.2 HallEffectwithNegativeShear . . . . . . . . . . . . . . . . . . . . 294 8.4.3 AHall-DrivenDisk-Dynamo? . . . . . . . . . . . . . . . . . . . . . 295 8.5 Endplateeffects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 8.6 WaterExperiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 8.7 Taylor–CouetteFlowasKinematicDynamo . . . . . . . . . . . . . . . . . . 299 9 Bibliography 301 Index 327 Preface Itisnow85yearssinceSirJosephLarmorfirstproposedthatelectromagneticinductionmight betheoriginoftheSun’smagneticfield(Larmor1919). Todaythisso-calleddynamoeffectis believedtogeneratethemagneticfieldsofnotonlytheSunandotherstars,butalsotheEarth andotherplanets,andevenentiregalaxies. Indeed,mostoftheobjectsintheUniversehave associatedmagneticfields,andmostofthesearebelievedtobeduetodynamoaction. Quite animpressiverecordforapaperthatisonlytwopageslong,andwaswrittenbeforegalaxies otherthantheMilkyWaywereevenknown! However, despite this impressive list of objects to which Larmor’s idea has now been applied, in no case can we say that we fully understand all the details. Enormous progress has undoubtedly been made, particularly with the huge increase in computational resources availableinrecentdecades,butconsiderableprogressremainstobemadebeforewecansay thatweunderstandthemagneticfieldsevenjustoftheSunortheEarth,letalonesomeofthe moreexoticobjectstowhichdynamotheoryhasbeenapplied. Our goal in writing this book was therefore to present an overview of these various ap- plicationsofdynamotheory, andineachcasediscusswhatisknownsofar, butalsowhatis stillunknown.Wespecificallyincludebothgeophysicalandastrophysicalapplications.There is anunfortunate tendencyin the literature to regardstellar andplanetary magnetic fields as somehowquitedistinct. Howthisstateofaffairscameaboutisnotclear,althoughitismost likelysimplyduetothefactthatgeophysicsandastrophysicsaretraditionallyseparatedepart- ments. Regardlessofitscause,itiscertainlyregrettable. Webelievethetwohaveenoughin commonthatresearchersineitherfieldwouldbenefitfromacertainfamiliaritywiththeother areaaswell. Itisourhopethereforethatthisbookwillnotonlybeofinteresttoworkersin bothfields,butthattheywillfindnewideasonthe‘othersideofthefence’tostimulatefurther developmentsontheirside(andmaybetherebyhelpteardownthefenceentirely). Muchofthefinalwritingwasdoneinthe2nd halfof2003. Withoutthetechnicalsupport ofMrs. A.TrettinandM.SchultzfromtheAstrophysicalInstitutePotsdamitwouldnothave beenpossibletofinishtheworkintime. Wegratefullyacknowledgetheirkindandconstant help. Many thanks also go to Axel Brandenburg, Detlef Elstner, and Manfred Schu¨ssler – tonameonlythreeofthevastdynamocommunity–fortheirindispensablesuggestionsand never-endingdiscussions. PotsdamandGlasgow,2004 1 Introduction MagnetismisoneofthemostpervasivefeaturesoftheUniverse,withplanets,starsandentire galaxiesallhavingassociatedmagneticfields. Allofthesefieldsaregeneratedbythemotion ofelectricallyconductingfluids,viatheso-calleddynamoeffect. Thebasicsofthiseffectare almosttrivialtoexplain: movinganelectricalconductorthroughamagneticfieldinducesan emf (Faraday’s law), which generates electric currents (Ohm’s law), which have associated magnetic fields (Ampere’s law). The hope is then that with the right combination of flows and fields the induced field will reinforce the original field, leading to (exponential) field amplification. Ofcourse,thedetailsarerathermorecomplicatedthanthat. Thebasicphysicalprinciples may date back to the 19th century, but it was not until the middle of the 20th century that Backus(1958)andHerzenberg(1958)rigorouslyprovedthatthisprocesscanactuallywork, that is, that it is possible to find ‘the right combination of flows and fields.’ And even then their flows were carefullychosentomake the problemmathematically tractable, rather than physicallyrealistic.Formostofthesemagnetizedobjectsmentionedaboveitisthusonlynow, atthestartofthe21st century,thatwearebeginningtounravelthedetailsofhowtheirfields aregenerated. Thepurposeofthisbookistoexaminesomeofthiswork.Wewillnotdiscussthebasicsof dynamotheoryassuch;forthatwerefertothebooksbyRoberts(1967),Moffatt(1978)and Krause&Ra¨dler(1980), whicharestillhighlyrelevanttoday. Instead, wewishtofocus on someofthedetailsspecifictoeachparticularapplication,andexploresomeofthesimilarities anddifferences. Forexample,whatisthemechanismthatdrivesthefluidflowinthefirstplace,andhence ultimatelysuppliestheenergyforthefield? Inplanetsandstarsitturnsouttobeconvection, whereasinaccretiondisksitisthedifferentialrotationintheunderlyingKeplerianmotion. In galaxiesitcouldbeeitherthedifferentialrotation,orsupernova-inducedturbulence,orsome combinationofthetwo. Next,whatisthemechanismthatultimatelyequilibratesthefield,andatwhatamplitude? Thebasicphysicsisagainquitestraightforward;whatequilibratesthefieldistheLorentzforce inthemomentumequation,whichalterstheflow,atleastjustenoughtostopitamplifyingthe field anyfurther. But again, the details are considerablymore complicated, and againdiffer widelybetweendifferentobjects. Another interesting question to ask concerns the nature of the initial field. In particular, doweneedtoworryaboutthisatall,orcanwealwayscountonsomemoreorlessarbitrarily smallstrayfieldtostartthisdynamoprocessoff? Andyetagain,theanswerisverydifferent for different objects. For planets we do not need to consider the initial field, since both the TheMagneticUniverse:GeophysicalandAstrophysicalDynamoTheory. Gu¨ntherRu¨diger,RainerHollerbach Copyright(cid:1)c 2004Wiley-VCHVerlagGmbH&Co.KGaA ISBN:3-527-40409-0 2 1 Introduction advective and diffusive timescales are so short compared with the age that any memory of thepreciseinitialconditionsislostveryquickly. Incontrast,instarstheadvectivetimescale is still short, but the diffusive timescale is long, so so-called fossil fields may play a role in certainaspectsofstellarmagnetism. Andfinally, ingalaxieseventheadvectivetimescaleis relativelylongcomparedwiththeage,sotherewedoneedtoconsidertheinitialfield. Accretion disks provide another interesting twist to this question of whether we need to considerthe initialcondition. The issuehereis notwhetherthedynamoactsona timescale shortorlongcomparedwiththeage, butwhetheritcanactatallifthefieldistooweak. In particular,thisKepleriandifferentialrotationbyitselfcannotactasadynamo,sosomething must be perturbing it. It is believed that this perturbation is due to the Lorentz force itself, viatheso-calledmagnetorotationalinstability. Inotherwords, thedynamocanonlyoperate at finite field strengths, but cannot amplify an infinitesimal seed field. One must therefore considerwhethersufficientlystrongseedfieldsareavailableinthesesystems. Accretion disks also illustrate the effect that an object’s magnetic field may have on its entire structure andevolution. As we saw above, the magnetic field always affects the flow, andhencetheinternalstructure,insomeway,butinaccretiondiskstheeffectisparticularly dramatic. It turns out that the transport of angular momentum outward – which of course determinestherateatwhichmassmovesinward–isdominatedbytheLorentzforce. Some- thingasfundamentalasthecollapseofagascloudintoaproto-stellardiskandultimatelyinto a star is thus magnetically controlled. That is, magnetism is not only pervasive throughout theUniverse,itisalsoacrucialingredientinformingstars,themostcommonobjectsfound withinit. Wehopethereforethatthisbookwillbeofinterestnotjusttogeophysicistsandastrophysi- cists,buttogeneralphysicistsaswell. Thegeneraloutlineisasfollows: Chapter2presents the theory of planetary dynamos. Chapters 3 and 4 deal with stellar dynamos. We consider only those aspectsof stellar hydrodynamics and magnetohydrodynamics that are relevant to thebasicdynamoprocess;seeforexampleMestel(1999)forotheraspectssuchasmagnetic braking. Chapter5discussesthismagnetorotationalinstabilityinKepleriandisks. Chapter6 considers galaxies, in which the magnetorotational instability may also play a role. Chap- ter7,concerningneutronstars,isslightlydifferentfromtheothers. Inparticular,whereasthe otherchaptersdealwiththeoriginoftheparticularbody’smagneticfield,inChapt.7wetake the neutron star’s initial field as given, and consider the details of its subsequentdecay. We consideronlythefieldintheneutronstaritselfthough; seeMestel(1999)forthephysicsof pulsarmagnetospheres. Lastly,Chapt.8discussesthemagnetorotationalinstabilityincylin- dricalCouetteflow. Thisgeometryisnotonlyparticularlyamenabletotheoreticalanalysis,it isalsothebasisofaplannedexperiment. However,wealsopointoutsomeofthedifficulties onewouldhavetoovercomeinanyrealcylinder,whichwouldnecessarilybeboundedinz. Whererelevant,individualchaptersofcourserefertooneanother,topointoutthevarious similarities anddifferences. However, mostchapters canalsobe readmore or lessindepen- dentlyoftheothers. Mostchaptersalsopresentbothnumericalaswellasanalytic/asymptotic results,andasmuchaspossiblewetrytoconnectthetwo,showinghowtheymutuallysup- porteachother. Finally,wediscussfieldsoccurringonlengthscalesfromkilometerstomega- parsecs,andrangingfrom10−20to1015G–trulythemagneticUniverse.