Astrophysics and Space Science Library 456 C. G. Campbell Magneto- hydrodynamics in Binary Stars Second Edition Magnetohydrodynamics in Binary Stars Astrophysics and Space Science Library SeriesEditor: STEVENN.SHORE,DipartimentodiFisica“EnricoFermi”,UniversitàdiPisa, Pisa,Italy AdvisoryBoard: F.BERTOLA,UniversityofPadua,Italy C.J.CESARSKY,CommissionforAtomicEnergy,Saclay,France P.EHRENFREUND,LeidenUniversity,TheNetherlands O.ENGVOLD,UniversityofOslo,Norway E.P.J.VANDENHEUVEL,UniversityofAmsterdam,TheNetherlands V.M.KASPI,McGillUniversity,Montreal,Canada J.M.E.KUIJPERS,UniversityofNijmegen,TheNetherlands H.VANDERLAAN,UniversityofUtrecht,TheNetherlands P.G.MURDIN,InstituteofAstronomy,Cambridge,UK B.V.SOMOV,AstronomicalInstitute,MoscowStateUniversity,Russia R.A.SUNYAEV,MaxPlanckInstituteforAstrophysics,Garching,Germany Moreinformationaboutthisseriesathttp://www.springer.com/series/5664 C. G. Campbell Magnetohydrodynamics in Binary Stars Second Edition 123 C.G.Campbell SchoolofMathematics StatisticsandPhysics NewcastleUniversity NewcastleuponTyne,UK ISSN0067-0057 ISSN2214-7985 (electronic) AstrophysicsandSpaceScienceLibrary ISBN978-3-319-97645-7 ISBN978-3-319-97646-4 (eBook) https://doi.org/10.1007/978-3-319-97646-4 LibraryofCongressControlNumber:2018951221 ©SpringerNatureSwitzerlandAG1997,2018 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. 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Coverillustration:Thisartist’sconceptshowsaninteractingbinarystarsystemknownasapolar(ora magneticcataclysmicvariable).Thewhitestarisaverydense,highlymagneticwhitedwarfinwhichthe magneticpolesofthestararenotalignedwithitsrotationaxis.Thecool,low-massredstarisdistorted duetothestronggravityofthemuchmoremassivewhitedwarf.Newresearchhasprovidedthefirstdirect observationalevidencethatsignificantstellaractivityintheredstar(suchaslargestarspots,prominences, andflares)canbeinducedbyinteractionswiththestrongmagneticfieldofthewhitedwarf(bluelines), aphenomenondubbedhyperactivity.Credit:P.MarenfeldandNOAO/AURA/NSF ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland To myfamily,Aileen,Graham,Helenaand Barney Preface Sincethepublicationofthefirstedition,theareaofmagneticfieldsinbinarystars has continued to expand. The number of known AM Herculis binaries has more thandoubledinthelast20years,confirmingtheimportanceofthesesystems,and many new intermediate polars have also been discovered. The second edition is a major revision of the first, including new chapters coveringthe stellar magnetic fieldsandaccretiondiscmagneticwinds.Thedevelopmentofnumericalsimulation techniques has enabled much progress to be made in understandingthe nature of magneticallyinfluencedaccretionflows.Thesehavebeenappliedtostudyaccretion streamsinAMHersystems,discdisruptionandcurtainflowsinsystemscontaining strongly magnetic white dwarfs or neutron stars, and for disc magnetic winds. Dynamo simulations in rotating M dwarfs and in accretion discs have also been performed.Analyticandsemi-analyticstudieshavemadesignificantprogress,and, whenresultsarecomparedwiththoseofthesimulations,aclearerpictureemerges forthestructureandbehaviouroftheseimportantsystems. The theme of the book remains the redistribution of angular momentum by magnetic stresses and the associated spin and orbital evolution. A comprehensive description of MHD in binary stars is given, from the pioneering work up to the latestresults. Chapter 1 contains a description of close binary stars and reviews the MHD problemsarising in these systems. Chapter 2 describes the basic theory of MHD, considering the fundamental equations and their applications, including dynamo theory. The descriptions of force-free magnetic fields and those of wave motions havebeenextended.Thetheoryofclosebinarystarsisthenpresented,includingthe Roche model,a new section on tidal theory,mass transfer and the classic viscous accretiondisc model.Theessentialsofspindynamicsarereviewed,inconnection withtheresponseofprimarystarstoappliedtorques. Chapter 3 reviews AM Herculis binaries, including tables of all the confirmed systemsandtheirmainparameters.Anextensiverangeofreferencesisgiven,and the associated MHD problems are discussed. Chapter 4 addresses the approach to synchronism, involving inductive magnetic coupling. As well as the case with vii viii Preface vacuum surroundings, the effects of a magnetosphere are now also investigated. Theresultingspin–orbitcouplingcansignificantlyaffectthemasstransferratesand the modificationsare calculatedfor gravitationalwave drivingandmagnetic wind braking.Thetheoreticallypredictedsynchronizationtime-scalesarecomparedwith thosethatcannowbeestimatedfromobservationsofasynchronoussystems,which areintheprocessofevolvingtowardsasynchronousstate. Chapter5considersthenatureoftheaccretionstream,includingthelatestsim- ulationresultsrelatedtothe extentofmagneticchannellingfordifferentmagnetic orientationsoftheprimary.Theaccretiontorqueisconsideredfortotalandpartial magnetic channelling and for synchronous and asynchronous cases. Chapter 6 analyseshownon-dissipativetorquescan balancetheaccretiontorque,in two and threedimensions,toproducesynchronousstates.Magneticandgravitationaltorques are considered. In Chap.7, it is shown that even when a stable synchronousstate exists, certain conditions must be satisfied for the primary to attain such a state. Formulaearegiven,inconvenientforms,thatcanbeused tocomparetheorywith theobservations. Chapter8reviewsbinariescontainingaccretiondiscswhichhavebeenpartially disrupted by the magnetic field of the accretor. These include the intermediate polars, the X-ray binary pulsars and the accreting millisecond pulsars. Detailed tablesofthesesystemsaregiven,togetherwithanextensiverangeofreferences. Chapters 9 and 10 have been completely rewritten. Chapter 9 addresses the mechanism of disc disruption due to the primary’s magnetic field, together with ananalysisoftheaccretioncurtainflowthattransfersmatterfromtheinneredgeof thediscto thestellar surface.Thisincludesareviewfromthepioneeringworkup to the resultsof the latestnumericalsimulations,andthese are comparedwith the resultsofanalyticandsemi-analyticstudies.Chapter10considersthespinevolution oftheaccretingstarduetoitsinteractionwiththediscandcurtainflows,including ananalysisoftorquereversals. Chapter11firstreviewsstandarddynamotheoryinaccretiondiscs.Themagne- torotationalinstability is then discussed together with its non-lineardevelopment, includingMHD dynamos.Theeffectsofa large-scalemagneticfieldonthe radial andverticalstructuresofthediscareinvestigated,usingmorerecentcalculations. Chapter 12 considers the sources of the stellar component magnetic fields, includingdynamooperationinthesecondarystar.Simulationsofdynamosinfully convective stars are outlined. The latest observations relating to the structure and strengthofsurfacemagneticfieldsonrapidlyrotatingMdwarfstarsarediscussed. TheseareparticularlyrelevanttotheoriesofthemaintenanceofsynchronisminAM Herbinaries,andtotheoriesofmagneticwindbraking,togetherwithtidalcoupling, whicharerelevantto masstransferratesabovethe periodgapandinexplanations ofthegap.Thepossibleeffectsofdynamoprocessesoccurringduringthecommon envelopeevolutionaryphaseonwhitedwarfmagneticfieldsaredescribed,andthe effectsofaccretiononthesurfacemagneticfieldsofwhitedwarfsandneutronstars arediscussed. Chapter13describesthebasictheoryofstellarmagneticwinds,withparticular applicationto fast rotators. The theory is used to calculate brakingtorques on the Preface ix secondarystarsinbinariesandhencecalculatemasstransferratesinsystemsabove theperiodgap.Thetheoryoftheperiodgap,andwhyAMHersystemsappearnot tobeaffectedbyit,isdiscussed. Chapter14considersaccretiondiscmagneticwinds,beginningwiththelaunch- ingandfieldsourceproblems.Windstructuremodelsaredescribed,fromtheearly work up to the latest results. A detailed solution is presented for the structure of the disc and the well sub-Alfvénic region of the wind. It is shown that the spin rateoftheaccretorcanaffectthewindmasslossrateinthe innerpartofthedisc, leading to significantly enhanced values near the star. Finally, wind flow stability is analysed, particularly in relation to potential field bending instabilities and the possiblequenchingeffectsofturbulentviscosity. Anappendixisincludedcontainingbasicdata,vectoridentities,vectoroperators incoordinatesystems,specialfunctionsandderivationsrelatedtoviscousforceand gravitationaltorques. SIunitsareemployed,butmagneticfieldvaluesareoftenquotedinGausssince manyastronomersandastrophysicistshavea moreimmediatefeelformagnitudes expressedintheseunits.Itshouldberememberedthat1Tesla=104Gauss. The book should be of interest to observers as well as to theorists, with many usefulformulaebeingincludedwhichcanbecomparedtoobservations,andthereis awiderangeofreferences.Althoughthemainfocusisonbinarystars,muchofthe materialonaccretiondiscs,stellarwindsanddiscwindshasmoregeneralrelevance. The text is mainly aimed at research workers, but some material (particularly in Chap.2)couldbeusefulforpostgraduatecoursesinmagneticstellarastrophysics. IamgratefultoMichaelBeatyforinvaluablehelpwiththeLaTeXproductionof themanuscript.IshouldliketothankthePhysicsDepartmentatDurhamUniversity for affording me the use of its facilities and for warm hospitality, with particular thankstoChrisDone,CarlosFrenk,AlanLottsandMartinWard.Iamindebtedto RamonKhannaandChristinaFehlingatSpringerNaturefortheirkindsupportand adviceduringthepublicationprocess. Newcastle,UK ChrisCampbell Contents 1 MagnetisminBinaryStars................................................ 1 1.1 CloseBinaries........................................................ 1 1.2 MagneticFieldsinBinaries.......................................... 4 1.3 Magnetohydrodynamics ............................................. 6 1.4 TypesofProblems.................................................... 6 References.................................................................... 8 2 TheoreticalPrerequisites .................................................. 9 2.1 Introduction........................................................... 9 2.2 BehaviourofBFieldsinPlasmas ................................... 10 2.2.1 PlasmaFluids............................................... 10 2.2.2 Maxwell’sEquations....................................... 15 2.2.3 TheInductionEquation .................................... 17 2.2.4 MagneticForce ............................................. 24 2.2.5 TheMagneto-FluidEquations ............................. 27 2.2.6 MagnetohydrodynamicWaves............................. 35 2.2.7 MachNumbers.............................................. 42 2.2.8 TheFree-FallAlfvénRadius............................... 43 2.2.9 PoloidalandToroidalRepresentationsofB............... 44 2.2.10 DecayModesofBinaConductor......................... 46 2.2.11 MagneticDiffusivity ....................................... 48 2.3 BasicDynamoTheory ............................................... 51 2.3.1 FieldGeneration............................................ 51 2.3.2 TypesofMean-FieldDynamos............................ 55 2.4 CloseBinaryStars.................................................... 57 2.4.1 TheRocheModel........................................... 57 2.4.2 TidalTheory................................................ 63 2.4.3 MassTransfer............................................... 67 2.4.4 AccretionDiscs............................................. 70 2.5 SpinDynamics ....................................................... 84 References.................................................................... 89 xi