Disk Instabilities and Cooling Fronts

更新时间:2023-08-28 12:22:01 阅读量: 教育文库 文档下载

说明:文章内容仅供预览,部分内容可能不全。下载后的文档,内容与下面显示的完全一致。下载之前请确认下面内容是否您想要的,是否完整无缺。

Accretion disk outbursts, and their subsequent decline, offer a unique opportunity to constrain the physics of angular momentum transport in hot accretion disks. Recent work has centered on the claim by Cannizzo et al. that the exponential decay of luminos

DiskInstabilitiesandCoolingFronts

EthanT.Vishniac

Dept.ofAstronomy,UniversityofTexas,Austin,TX78712

arXiv:astro-ph/9802232v1 18 Feb 1998Abstract.Accretiondiskoutbursts,andtheirsubsequentdecline,o erauniqueopportunitytoconstrainthephysicsofangularmomentumtransportinhotaccretiondisks.RecentworkhascenteredontheclaimbyCannizzoetal.thattheexponentialdecayofluminosityfollowinganoutburstinblackholeaccretiondisksystemsisonlyconsistentwithaparticularformforthedimensionlessviscosity,α=35(cs/r )3/2.Thisresultcanbeunderstoodintermsofasimplemodeloftheevolutionofcoolingfrontsinaccretiondisks.Inparticular,thecoolingfrontspeedduringdeclineis~αFcs,F(cs,F/r )n,whereFdenotesthepositionofthecoolingfront,andtheexactvalueofndependsonthehotstateopacity,(althoughgenerallyn≈1/2).Settingthisspeedproportionaltorconstrainsthefunctionalformofαinthehotphaseofthedisk,whichsetsitapartfrompreviousargumentsbasedontherelativedurationsofoutburstandquiescence.However,itremainsuncertainhowwellweknowtheexponentn.Inaddition,moreworkisneededtoclarifytheroleofirradiationinthesesystemsanditse ectonthecoolingfrontevolution.INTRODUCTIONThemostpopularmodelforsoftX-raytransientsanddwarfnovaeisthatbothareduetothermalinstabilitiesintheaccretiondisksaroundcollapsedobjects.Thespeci cmechanismthoughttodrivethethermalinstabilityisthechangeinopacityassociatedwiththeionizationofhydrogen(forarecentreviewseeCannizzo1993[1],orOsaki1996[2]).Inthesesystemstheaccretiondiskscanbemodeled

asgeometricallythin,H r,andwithverticalgravitysuppliedbythecentralobject.Asaresultthesoundspeedtoorbitalvelocityratio,cs/(r )scaleswiththethicknesstoradiusratio,H/r,andtheorbitalfrequency (r)isproportionaltor 3/2.

Theoutburstcycleinthesesystemsconsistsofalternatingperiodsofquiescenceandoutburst.Duringquiescencethediskluminosityislowandgasisaccretedfromthecompanionwithoutbeingtransferredthroughthedisk.Inthisstatethediskismostlyneutralandcold.Eventuallytheaccumulationofmaterialatlargeradiileadstotherunawayionizationofhydrogenandthediskmaterialjumpstoahotstate.Themasstransferrateincreasesdramaticallyandaheatingwavepropagatesinwardatthethermalspeed,~αcs,whereαisthedimensionlessdiskviscosityandcsisthemidplanesoundspeed.Inashorttimetheentirediskisionizedandhot,

Accretion disk outbursts, and their subsequent decline, offer a unique opportunity to constrain the physics of angular momentum transport in hot accretion disks. Recent work has centered on the claim by Cannizzo et al. that the exponential decay of luminos

andremainsinthatstateuntilthesteadydepletionofmaterialmakesitimpossibletosustaintheoutburst.Atthispointthediskstartstofallbackintothecoldstate,usuallystartingatsomelargeradius,andacoolingwavesweepsinwardwhiletheluminosityofthediskdecreases.Thedurationoftheoutburstandquiescentphasesisconsistentwithanoutburstvalueofαcloseto0.1andacoldstatevalueseveraltimessmaller.

Oneofthemorestrikingfeaturesofthesesystemsistheextenttowhichtheluminositydeclinecanbemodeledbyanexponentialdecaylaw,inextremecasesstretchingofthreeordersofmagnitudeinX-rayluminosity(Chenetal.1997[3])Mineshigeetal.(1993)[4]notedthatthisimpliesanexponentialdecayofthediskhotphase,andthatthiscanbeachievedinthecontextofthediskinstabilitymodelbyrequiringthecoolingwavevelocitytoscalewiththeradiusofthehotphase.MorerecentlyCannizzo,Chen&Livio(1995)[5]haveexploredthisargumentthroughaseriesofhighresolutionsimulations,andfoundthatthisscalingcanbeobtainedonlyforarestrictedclassofviscositylaws,andthatmodelswithaconstantαcanbestronglyexcluded.Herewewillreviewrecentprogressontheconnectionbetweencoolingwavesandmodelsforangularmomentumtransportinaccretiondisks.

THECOOLINGFRONTSPEED

Ifthehot,innerpartsoftheaccretiondiskareevolvingexponentially,thenthesimplestwaytodrivethisevolutionistohavetheboundaryofthehotphaseofthediskevolveexponentially,thatis

VF

r .(2)

Inotherwords,thatthecoolingfrontspeedisthelocalcoolingrate,α ,timesthelocaldiskheightmodi edbyauniversalspreadingfactor,thoughttobe~0.1.Thisresultre ectstheviewthatthecoolingfrontshouldbethoughtofasapurelylocalphenomena.

However,recentlyCCL[5]showedinsteadthatthecoolingfrontspeedcanbeapproximatedas

Accretion disk outbursts, and their subsequent decline, offer a unique opportunity to constrain the physics of angular momentum transport in hot accretion disks. Recent work has centered on the claim by Cannizzo et al. that the exponential decay of luminos

VF~αFcs,F cs,F

r 3/2,(4)

followingtheformproposedbyMeyerandMeyer-Hofmeister(1983)[8].Thetimescalefortheluminositydecayisthen

τF≈0.4GMBH

7M⊙.(6)

TheyshowedthatthisprescriptionleadstoreasonableagreementwithobservationsofX-raynovae,andwereunableto ndanyothersimpleprescriptionthatdidaswell.Anaddedadvantageofthismodelisapparentfromequation(5).Oneimmediatelyobtainsdramaticallyshortertimescalesfordwarfnovae,inagreementwithobservations.Infact,thesameprescriptioncanbeusedtomodeltheoutburstcycleofSSCygni(Cannizzo1996[9]).

Theseresultsraiseseveralimportantquestions.First,whyisthereafactorof(cs/r )1/2(or(H/r)1/2)inequation(3)?Thereareonlytwoobviousvelocitiesintheproblem,theaccretionvelocity,αc2

s/(r ),andthethermalspeed,αcs.Isthis

somesortofgeometricaverageorisittotallyunrelated?Second,isequation(4)anotherwayofdescribingthedropinalphafromthehotstatetothecoldstate,orisitameasurementofαinthehotstatealone?Third,ifthisisthecorrectformforα,whyistheexponent3/2?Finally,thecoe cientα0ispresumablyaconstantoforderunity.However,35isapeculiarlylargevalueforthenumberone.Wheredoesthisnumbercomefrom?

Toanticipatetherestofthispresentation,wenowhaveananalytictheoryforcoolingwavesinalocallyheateddisk(VishniacandWheeler1996[10],Vishniac1997[11])andthe rsttwoquestionscanbeanswered.Thethirdandfourthquestionsremainconfusing.

Theanalytictheoryofcoolingwavesstartsfromthethreeequationswhichde-scribeaverticallyaverageddiskmodel:

tΣ= 1

Accretion disk outbursts, and their subsequent decline, offer a unique opportunity to constrain the physics of angular momentum transport in hot accretion disks. Recent work has centered on the claim by Cannizzo et al. that the exponential decay of luminos

Vr=2

3c,(9)

followingCCL,wherea=3/7,b=1/7,andc=3/7.Weneedtoaddtheconditionthatbelowsomecriticaltemperature,whichisaveryweakfunctionofradius,coolingbecomesrapid.Atthisradiustheradialthermalgradientbecomesverylarge.Thisinturnimpliesthatalargefractionoftheangularmomentum uxfromsmallerradiiisdeposited,followingequation(8)withinaradialscalelength,rT.Theresultinggasvelocityis

Vr~αFc2

s,F

αF F.(11)

WeconcludethatrTissomeconstanttimesthediskheightandVrisdirectedoutward.

Thisrapidoutwardmotionatthecoolingfrontimpliesthatthecoolingfrontisprecededbyararefactionwave.Thissuggeststhatwecanunderstandtheprogressofthecoolingwavebyconsideringthedynamicsoftherarefactionwave.Ifwelabelapointjustaheadoftherarefactionwavewitha‘p’,thenconservationofmassimpliesthat

ΣpVF≈ΣFαFcs,F,

or

VF≈αFcs,FΣF(12)

r ~αFcs,FΣF

Accretion disk outbursts, and their subsequent decline, offer a unique opportunity to constrain the physics of angular momentum transport in hot accretion disks. Recent work has centered on the claim by Cannizzo et al. that the exponential decay of luminos

coolingwaveplowsthroughit.Thisdecouplesthecoolingwavebehaviorfromthe˙,butitalsoimpliesthatΣpclimbssharplyasthecoolingwavemovesevolutionofM

in.IfwerememberthatTFisnearlyconstant,thenequation(9)impliesthatΣFactuallydropsasatsmallerradii.ThisimpliesasteadydecreaseinΣF/Σp,andaconsequentdropinVF(followingequation(13).Ontheotherhand,ifVFismuchsmallerthantheaccretionvelocityaheadoftherarefactionwave,thenthediskevolvesfasterthanthecoolingwavecanmove.Thisisparadoxicalsincethedrainingoftheinnerdiskautomaticallydropsthediskintothecoldstate.Wecanuseequations(9)and(14)tosolveforVFforanyassumedformforα.If

α=α0 cs

r

where

q 1 q,(16)=1+1+ n

1 (n/2)b.(17)

ForaKramersopacitylaw,theusualchoiceforthediskhotstate,andn=3/2thisgivesq=25/46.Ingeneral,itisverydi culttogetavalueofqwhichisverydi erentfrom1/2foranyoftheusualopacitylaws.

Whathavewelearnedfromthisscalinglawargument?First,thisisanobserva-tionaltestforthefunctionalformofαinthehotstate,inspiteofthefactthatacoolingtransitionisinvolved.Thedynamicsofthewavearecontrolledbytherar-efactionwaveinthehotmaterial,anddonotdependonthestructureoftherapidcoolingregion.Thereisapossibleloopholehere,whichwewillreturntolater.Thecoldmaterialwillpileupafterithas nishedcooling,withacolumndensitynotmuchbelowΣp.Wehaveassumedthatthisisnotmorethanthemaximumcolumndensityonthelowerbranchofthe‘S’curve.Ifthisconditionisnotsatis ed,thengasisnotactuallyejectedataconstantfractionofthethermalspeedacrossthecoolingfrontandwehave,instead,

VF~αFc2s,F

Σcold,maximum 1 1/q.(18)

Asthe‘S’curvecentralbranchbecomesverticalthisgivesacoolingfrontvelocitywhichisclosetotheaccretionspeed.

Second,asatestofthemodelwecanaskhowitbehavesiftheupperbranchofthe‘S’curveisalmosthorizontal,i.e.ifthetemperatureisinsensitivetothecolumndensity.Inthislimit,a=0andconsequentlyq=1.Asexpected,thecoolingfrontmovesattheaccretionvelocity.Intheoppositelimit,whenthehot

Accretion disk outbursts, and their subsequent decline, offer a unique opportunity to constrain the physics of angular momentum transport in hot accretion disks. Recent work has centered on the claim by Cannizzo et al. that the exponential decay of luminos

stateisjustbarelythermallystable,a→∞andq→0.Thatis,thecoolingfrontmovesatclosetothethermalspeed.WecanunderstandtheintermediatebehaviorfoundbyCCLasare ectionofthefactthatrealisticdiskshaveahotstatewhichliesbetweenthesetwoextremecases.

Third,wenotethatonceweallowforthevariationoftheminimumhotstatetemperaturewithradius,aperfectexponentialdeclineactuallyfollowsforn=1.63.Thishasbeencon rmedbysubsequentnumericaltests(Cannizzo1997[12]).Thisdoesnotimplythatthisisthecorrectvaluefortheexponentn,sincetheobserva-tionsaren’tnecessarilyperfectlyexponential.Instead,thisshouldberegardedastestoftheabilityofthescalinglawtopredicttheresultsofnumericalsimulations.Wecanimproveonthisscalinglawbyconstructingasimilaritysolutionforthediskgasusingtheequationsofcontinuity,torque,andthermalstructure(Vishniac1997[11]).Theresultisonlyanapproximate ttotheactualsolution,sincethe˙atproblemitselfhasabuilt-inscale.TheappropriateboundaryconditionforMthefrontis

˙F=2πrFΣF(αFcs,F ),M(19)

where isaconstantrelatingtheout owspeedatthefronttothethermalspeedatthefront.Theanalytictheorydoesnotconstrainthevalueof soweneedtotakeitfromthesimulationsofCannizzoetal..(Thisgives ≈1/6).Thesecondboundaryconditionlooksabsurd.Itis

ΣF=0.(20)

Inpracticethismeansonlythatthedensitycontrastthroughtherarefactionwaveislarge.

Fromthiswederiveasimilaritysolutionwith

˙inner tM

r q(6 )1/2.(22)

Bothofwhichareconsistentwiththesimulationresults.Atanyonetimemorethanhalfthehotphaseofthediskisactuallymovingoutward,http://www.77cn.com.cnparingthesimilaritysolutiontothenumericalworkwe ndthatthetwodi erbyabout5-10%whichgivesuscon dencethatweunderstandbothofthem.

Accretion disk outbursts, and their subsequent decline, offer a unique opportunity to constrain the physics of angular momentum transport in hot accretion disks. Recent work has centered on the claim by Cannizzo et al. that the exponential decay of luminos

IMPLICATIONSFORATHEORYOFANGULAR

MOMENTUMTRANSPORT

Themodelpresentedherefortheevolutionofthecoolingwaveisbasedonassumingthatthediskisheatedthroughthelocaldissipationoforbitalenergyandthatαcanbedescribedintermsoflocalvariables.Assumingforthemomentthatthisisbasicallycorrect,whataretheimplicationsforafundamentaltheoryofα?Knowingthataparticularfunctionalformofα tstheavailableobservationalevidencefallswellshortofafundamentaltheoryforα.Ontheotherhand,wecanuseourresultstoidentifyparticularlypromisingmodels,ifanyexist.Sinceweareconcernedherewithangularmomentumtransportinthehot,ionizedphasewecanrestrictourattentiontomodelswhicharemoste cientinthisphase.

AllcurrentlypopularmodelsforthisregimemakeuseoftheVelikhov-Chandrasekharinstability(Velikhov1959[13],Chandrasekhar1961[14]), rstiden-ti edbyBalbusandHawley(1991)[15]asthemost,andperhapsonly,promisingmechanismforangularmomentumtransportinconductingaccretiondisks.Thisisaninstabilityofamagnetic eldembeddedinastronglyshearing ow.Thelinearinstabilityhasatypicalgrowthrate~ andatypicallengthscale~VA/ witha22resultantα∝VA/cs.Numericalsimulations(cf.thereviewbyGammie1997[16]andreferencestherein)con rmtheexistenceoftheinstabilityanditssaturationinaturbulentstate.Interestinglyenough,theyalsoindicatethatverticalstructureislargelyirrelevantforthedynamoprocess,whichallowsustoexcludemagneticbuoyancyasadrivingforceforthedynamo.Di erencesamongthemodelsbasedontheseresultsaredueentirelytodi erentproposalsfortheunderlyingdynamomechanism.

First,theturbulencemightsupportaninversecascade,inwhichalargescale eldisgeneratedspontaneouslyfromtheunderlyingturbulencewithoutanyappealtothekindofsymmetrybreakingusedinmean- elddynamotheory(BalbusandHawley1991[15],seealsoGammie1997[16]andreferencestherein).Sincethisisapurelylocalprocess,itproducesanαwhichissomeconstantoforderunity,witharelaxationtimewhichissomeconstanttimestheeddyturnovertime(~ 1).Theavailablesimulationsseemconsistentwiththismodeloveralimitedrangeofboxsizes,buttheresultantαisafunctionofgridresolution(e.g.Brandenburgetal.1996[17]).Periodicshearingboxsizeshavealengthwhichvariesbetween1and4times2πtimestheboxheight,whichisprobablyameasureofthesensitivitytodiskgeometryovertherange1<(r/H)<4inathindisk.However,thismodelisinconsistentwiththecoolingwaveresults.Ifthelatterarecorrect,thenthemodelneedstobemodi edtoallowsomenon-locale ects.

Second,thereistheinternalwave-drivendynamo(Vishniac&Diamond1992

[18],andreferencestherein)inwhichtidallygeneratedwavesdriveadynamowithagrowthrate~(H/r)n,wherenisabitlessthan1.5inastationarydisk.Balancingdissipationwithgrowthgivesα~Γ/ .Thisistherightscaling,butthisdynamomodelisinherentlynonlocalinabadsense.Thedependenceoninternalwaves

Accretion disk outbursts, and their subsequent decline, offer a unique opportunity to constrain the physics of angular momentum transport in hot accretion disks. Recent work has centered on the claim by Cannizzo et al. that the exponential decay of luminos

propagatingthroughthecoolregionshouldmakethisdynamoveryweakjustinsidethecoolingfront,wipingoutthe‘S’curvee ectandcompletelychangingtheevolutionofthecoolingfront.Althoughnodetailedcalculationofthesee ectsexist,itseemslikelythatthiswouldleadtoabroadcoolingfront,propagatingattheviscousspeed,withadependenceon(H/r)whichistoosteep.

Finally,therehasbeenanattempttoconstructamean elddynamotheorywithnosymmetrybreaking,theincoherentmean elddynamo(VishniacandBranden-burg1997[19]).Inthismodelthehelicitynecessaryforgeneratinglargescaleradialmagnetic eldemergesfromtherandom uctuationsprovidedbythesmallscaleinstabilitiesofthemagnetic eld.Itcanbeshownthatthisprocesswilldrivetheexponentialgrowthoflargescale,axisymmetricmagnetic elddomainsinthepresenceofstrongshearing.However,thisprocessbecomeslesse cientasthenumberofeddiesperannulusincreases,i.e.thisdynamorunsmoreslowlyasH/rdecreases(or,insimulations,astheheighttolengthratiooftheperiodicshearingboxdecreases).Inasense,thisisanattempttoimplementageometrydependentinversecascadeinthecontextofthe rstmodel.Unfortunately,whilethismodelseemsqualitativelypromising,itpredicts

α~ VA

r 2,(23)

whichistoosteep.Moreover,thenumericalsimulationsdonotshowtheexpectedsensitivitytogeometry.Thismaybebecausethelargevalueofα0restrictstheasymptoticregime,wherethescalinglawgiveninequation(23)isvalid,toboxesconsiderablylongerandthinnerthantherangeexploredtodate.Inanycase,inordertoreconcilethismodeltothecoolingwavecalculations,werequiredwarfnovaeandX-raynovaediskstobesu cientlythickthatsmallcorrectionstothedynamogrowthsoftenthesaturatedvalueofα.Moredetailedmodelingofthisdynamoprocesswillbenecessarytojudgewhetherornotthisisarealistichope.Weconcludethatnocurrentmodelisfullyconsistentwiththecoolingwaveresults,althoughthereissomechancethatamorerealisticversionoftheincoherentdynamomodelwillproveadequate.

FUTUREPROSPECTS

Whatcanweexpectbywayofprogressinthisarea?Ourabilitytosetlimitsontheallowedformsofαislimitedbytherangeofluminositieswecanobserveandthepresenceofnon-exponentialfeaturesinaccretiondisklightcurves,e.g.re aresandsecondarymaxima.Aslongasthesefeaturesremainpoorlyunderstooditwillbedi culttopindowntherequiredformofα.However,evenwithinthelimitsimposedbyourcurrentstateofunderstandingthecomputationalmodelscouldbemadetoyieldsigni cantlymoreinformation.Forexample,wehavenopreciseideaoftheappropriateerrorbarsareontheparametersoftheproposedfunctionalformofα.CCLoriginallyestimatedthatthevalueofnallowedbyobservational

Accretion disk outbursts, and their subsequent decline, offer a unique opportunity to constrain the physics of angular momentum transport in hot accretion disks. Recent work has centered on the claim by Cannizzo et al. that the exponential decay of luminos

constraintswasprobablywithin15%ofthe‘exponential’valueof1.5,butthevalueofnwhichactuallyyieldsaperfectexponentialdecayis10%higher,andtheavailablegridofmodelshasnotyetnaileddowntheallowedrangeofn.

Amoreseriousdangeristhepossibilityisthatthecoolingwavemodelusedhereneglectssomeimportantphysicale ects.Therelaxationofthemagnetic eldasthecoolingwaveapproachesisdi culttocalculate,sincetheactualdynamomechanismis,asnotedabove,acontroversialtopic.However,weexpectthetypicalrateforthisrelaxationtobecomparabletothedynamogrowthrate,whichshouldbe~α .Thisisalsothethermalrelaxationrateinanopticallythickdisk.Thediskstructurewillevolveatslowerratesuntiltheonsetofrapidcooling,whichistoolatetoa ectthecoolingwavearguments.Moreover,evenifweassumethatthemagnetic eldisfrozenintotheplasmafromtheverybeginningoftherarefactionwavewecanshowthatithasnoperceptiblee ectonourresults.

Another,andpotentiallymoreseriousproblemisthatthistreatmentassumesthatthedisktemperatureisdeterminedbylocaldissipation,thatis,itignoresirradiation.AttemptstoaccountfortheopticallightfromBHsystemssuggestthatirradiationmaybeassigni cantaslocalenergydissipation(Cannizzo1997

[12]),althoughitprobablydoesnotdominatebyalargefactor.Ifwerestrictourattentiontodwarfnovaesystems,whereirradiationislessimportant,thenwe ndsimilar,butlessprecise,constraintsonα(Canizzo1996[9]).Inanycase,thee ectofmoderateirradiationonthecoolingwavestructureneedstobeexplored.

Arethereacceptablealternativestothecoolingwavemodelforthethesesystems,perhapsonesthatnotinvolveavaryingα?Atpresenttheanswerisno,althoughathoroughsearchhasnotyetbeendone.Ifwewishtoconsideralternativeex-planationsfortheexponentialdecayofX-rayemissionfromblackholeaccretiondisksystems,weneedmodelsthatmaintainaconstantaccretiontimescaleintherelevantmassreservoir,thatis

1τacc=αc2

s

Accretion disk outbursts, and their subsequent decline, offer a unique opportunity to constrain the physics of angular momentum transport in hot accretion disks. Recent work has centered on the claim by Cannizzo et al. that the exponential decay of luminos

anddensityincreasessmoothlyasLxdecreases.Itremainstobeseenwhetherornotaphysicallyreasonablemodelcanbeconstructedalongtheselines.ThisworkhasbeensupportedinpartbyNASAgrantNAG5-2773.

REFERENCES

1.Cannizzo,J.K.1993,inAccretionDisksinCompactStellarSystems,ed.J.C.Wheeler(Singapore:WorldScienti c),p.6

2.Osaki,Y.1996,Pub.Astr.Soc.J.,108,39

3.Chen,W.,Shrader,C.R.,&Livio,M.1997,ApJ,491,312

4.Mineshige,S.,Yamasaki,T.,&Ishizaka,C.1993,Pub.Astr.Soc.J.,45,707

5.Cannizzo,J.K.,Chen,W.,andLivio,M.1995,ApJ,454,880(CCL)

6.Cannizzo,J.K.,Shafter,A.W.,andWheeler,J.C.1988,ApJ,333,227

7.Mineshige,S.1987,Astrophys.Sp.Sci.,130,331

8.Meyer,F.&Meyer-Hofmeister,E.1983,A&A,1218,420

9.Cannizzo,J.K.1996,ApJLett.,473,L51

10.Vishniac,E.T.,&Wheeler,J.C.1996,ApJ,471,921

11.Vishniac,E.T.1997,ApJ,482,414

12.Cannizzo,J.K.1997,ApJ,inpress

13.Velikhov,E.P.1959,SovietPhys.-JETPLett.,35,1398

14.Chandrasekhar,S.1961,HydrodynamicandMagnetohydrodynamicStability(Ox-

ford:OxfordUniv.Press)

15.Balbus,S.A.,&Hawley,J.F.1991,ApJ,376,214

16.Gammie,C.1997,astro-ph/9712233

17.Brandenburg,A.,Nordlund,A.,Stein,R.F.,&Torkelsson,U.1996,ApJLett.,458,

L45

18.Vishniac,E.T.,&Diamond,P.H.1992,ApJ,398,561

19.Vishniac,E.T.,&Brandenburg,A.1997,ApJ,477,516

本文来源:https://www.bwwdw.com/article/odhi.html

微信扫码分享

《Disk Instabilities and Cooling Fronts.doc》
将本文的Word文档下载到电脑,方便收藏和打印
推荐度:
点击下载文档
下载全文
范文搜索
下载文档
Top