Table Of ContentAstrophysics 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
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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
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