Accretion onto Black Holes and Neutron Stars Differences and Similarities

RashidSunyaev

1Max-Planck-Institutf¨urAstrophysik,Garching,Germany2

SpaceResearchInstitute,Moscow,Russia

Abstract.Accretingblackholesandneutronstarsatluminositiesabove0.01ofthecriticalEddingtonluminosityhavealotofsimilarities,butalsodrasticdifferencesintheirradiationandpowerdensityspectra.Theefficiencyofenergyreleaseduetoaccretionontoarotatingneutronstarusuallyishigherthaninthecaseofablackhole.Thetheoryofthespreadinglayeronthesurfaceofanaccretingneutronstarisdiscussed.Itpredictstheappearanceoftwobrightbeltsequidistantfromtheequator.Thislayerisunstableanditsradiationfluxmustvarywithhighfrequencies.

1Introduction

OneofthemostimportantpropertiesofaccretingblackholesinourGalaxywasdiscoveredbyRiccardoGiacconiandtheUhuruTeamin1971,whentheydiscoveredthespectraltransitionofCygX-1fromthesofttothehardstate(Tananbaumetal.1972).Simultaneously,aradiosourceappearedinthevicinityofCygX-1.RadioobservationspermitteditslocalizationwithhighaccuracyandtheidentificationoftheX-raysourcewithabrightstarofthe9thmagnitude.Immediatelythereafter,measurementsofitsopticalspectrumshowedthatthisstarismemberofa5.6-daynon-eclipsingbinarywithanopticallyinvisiblecompanion(Bolton1972).Lyutyetal.(1973)interpretedtheobservedellipsoidalvariationsinthebrightnessoftheopticalstarasaresultofthegravitationalinfluenceofanearbyblackholeinvisibleinopticallight.TodayCygX-1isthebest-knownsteadilyaccretingblackholeinourGalaxy.Nowwehavealistwithmorethan12excellentblack-holecandidatesandmanyofthemshowsimilarsoft-tohardstatetransitions(Tanaka&Shibazaki1996).Recently,CygX-1experiencedthethirdtransitionfromahardtoasoftstatein18years(Fig.1).

Suchtransitionsbecameasignatureofblackholes.Todayweknowthatallgalacticblack-holecandidatesshowaverysoftX-rayspectrum.Aspredictedbystandardaccretiontheory,thisisamulticolordiskspectrum(cf.Shakura&Sunyaev1973)orapower-lawhardX-rayspectrumwithaWien-typedecayathighenergiesformedduetocomptonization(Sunyaev&Tr¨umper1979,Sunyaev&Titarchuk1980).Sometimeswedonotevenseethehighfrequencydecayyet.Therefore,usuallywhenanewlydiscoveredX-raytransientshowsanextremelyhottailinitsX-rayspectrum,weimmediatelyrefertoitasablack-holecandidate.

114RashidSunyaev

Fig.1.ThespectralenergydistributionofCygX-1inthesoft(filledcircles)andhard(opencircles)spectralstate.DataareshownofnearlysimultaneousASCAandRXTEobservationsonMarch26,1996(hardstate)andMay30,1996(softstate);cf.Gilfanov,Churazov&Revnivtsev(2000).

Neutronstarswithoutmagneticfieldsandblackholeshavepracticallythesamegravitationalpotentialandmustshowmanysimilarities.Nevertheless,weknownowthattheyhaveverydifferentX-rayspectraandvariabilitycharacteristics.Oneofthegreatsurprisesofthelast15yearsofobservationsisthediscoverythatneutronstarsalsoexhibitsoft-tohard-statetransitions(Fig.2).

Neutronstarswithsmallmagneticfieldsusuallyhavespectrawhicharesignificantlyharderthanthespectraofmulticoloraccretiondisksaroundblack-holecandidatesinahigh/softstate.Buttheirspectraareusuallymuchsofterthanthespectraofblack-holecandidatesinthehard/lowstate.Some-timesweobservehottailsinthepersistentfluxofX-raybursters.However,

AccretionontoBlackHolesandNeutronStars115

Fig.2.TheenergyspectraofthreeX-raybinaries.TheneutronstarinGX354-0(4U1728-34)isshownintwospectralstates–low/hardandhigh/soft.Eveninthehardstatetheneutron-starspectraaremuchsofterthanthespectrumofCygX-1(accretingblackhole).AdaptedfromRevnivtsev&Sunyaev(2000).

spectraofthesehottailsfromneutronstarsaremuchsteeperthaninthecaseofblackholesandcontainasmallerfractionofthesourceluminosity.Itseemsthatnowweknowthereason.Inthecaseofblack-holeaccretionweonlyseetheradiationofaccretiondisk–plus,maybe,thecoronaaboveit(Galeevetal.1979)ortheadvectionflowwithevensmalleraccretioneffi-ciency(Narayan&Yi1995).Inthecaseofneutronstarswehaveanobjectwithasolidsurface.Therefore,partofthegravitationalenergyoftheac-cretingmattermustbereleasedinanextendedaccretiondisk,andanother

116RashidSunyaev

partinthenarrowboundarylayerinthevicinityoftheneutronstarwhereaccretingmatterisdeceleratingfromtheKeplerianvelocity(oftheorderofhalfthevelocityoflight)tothevelocityofrotationattheequatoroftheneutronstar.Thesurfaceofthestarisabletoproduceenoughsoftprotonsforcomptonizationtocooldownthehotpartsofthediskandboundarylayertotemperaturesbelow20keV(Sunyaev&Titarchuk19).Thephysicsoftheboundarylayerpermitsustoexplainthestrongdifferencesbetweentheradiationspectraofaccretingblackholesandneutronstars.ItalsopredictsastrongdifferenceinthecharacteristicvariabilitytimescalesoftheX-rayfluxfromblackholesandneutronstars(seebelow).

2

EfficiencyofAccretionontoaRapidlyRotatingNeutronStar

Therecentdiscoveryofquasi-periodicoscillations(QPO)withfrequenciesoftheorderof500-600Hzduringthenuclearburstsonthesurfaceofaneutronstarappearstobeverystrongevidenceofneutron-starrotationwiththesamefrequency,orwithperiodsoftheorderof1.6-2ms(Strohmayeretal.1998).Thisinterpretationisnaturalforanuclearburningfrontpropagatingonthesurfaceofarapidlyrotatingneutronstar.AbrightfrontregionmanifestsitselfasahotspotgivingrisetotheQPO.ItisimportantthatforagivenneutronstartheQPOfrequencyremainsthesamefrombursttoburst.

Theefficiencyofaccretionontoneutronstarsishigher(usually)thantheefficiencyofaccretionontoblackholes.Thereasonisobvious:inthecaseofablackholewehaveaneventhorizonandaneffectiveenergyreleaseandthereleaseoftheobservedradiationfluxmightoccuronlyintheaccretionflowwellbeyondtheeventhorizon.Inthecaseofaneutronstarwithoutastrongmagneticfieldpartoftheenergyisreleasedintheextendedaccretiondiskandanotherpartisliberatedinthenarrowboundarylayernearthesurfaceoftheneutronstar.InNewtonianmechanicsenergyreleaseintheboundarylayerisequalto

f1

(1−Ls=

R∗

˙GMM2

thecyclic

keplerianfrequencyneartheitssurface,fisthefrequencyofstellarrotation

˙istheaccretionrate.andM

TheproblembecomesmuchmorecomplicatedinthecaseofGeneralRel-ativity.Kerrmetricsisnotapplicabletothecaseofrapidlyrotatingneutron

2π

R3∗

󰀁

AccretionontoBlackHolesandNeutronStars117

starbecausethemassdistributionwithinthestarisnolongersphericallysymmetric.Thereisastrongquadrupolecomponentinthemassdistribu-tion.Fortunately,thereisanexactsolutionoftheGRequationsforthecasewhenthemassdistributionhasaquadrupolecomponent.Usingthissolution,Sibgatullin&Sunyaev(2000)plottedthedependenceoftheenergyreleaseduetotheaccretionontoaneutronstarasafunctionoftherotationfre-quencyofthatstar(Fig.3).TheexistingGRsolutionpermitsustofindtheefficiencyoftheenergyreleaseonlyinthecasewhenthespindirectionsoftheneutronstarandaccretiondiskareparalleloranti-parallel.Unfortu-nately,theproblemwithanarbitraryanglebetweentheaxesofrotationoftheneutronstarandtheaccretiondiskismuchmorecomplicated.InFig-ure3thepositivevaluesoftherotationalfrequencyfcorrespondtothecaseofcorotationandnegativevaluesdescribethecaseofcounterrotation.Thefigurepresentsthecomputationsfortheequationofstate(EOS)FPSintheclassificationofLorenzetal.(1993)foragravitationalmassoftheneutronstarM=1.4M⊙.

Fig.3.Efficiencyoftheenergyreleaseinthedisk(Ld)andonthestellarsurface(Ls)asafunctionofthestellarrotationfrequencyf.Negativefvaluescorrespondtothecaseofcounterrotationofdiskandstar.Thesolidlineandthenumbers

˙2.Thedashedlineandthevaluesonontheleftaxisgivethevalue(Ls+Ld)/Mc

therightaxisgivetheratioLd/Ls.Agapbetweenthemarginallystableorbitandthestellarsurfaceexistsintheregionleftsideofthetwoasterisksonthesolidanddashedcurves.Thereisnosuchgapinthecaseofrapidcorotationofstaranddisk(f>550Hz).AdaptedfromSibgatullin&Sunyaev(2000).

118RashidSunyaev

Weseethattheenergyreleaseefficiencydropsrapidlywithincreasingfrequencyinthecaseofcorotationandincreasesrapidlytowardshighfre-quenciesofcounterrotation.Theratioofthediskluminositytotheluminosityintheboundarylayerorinthespreadinglayernearthesurfaceofthestaralsostronglydependsonthefrequencyofrotation.Itiscloseto1forthecaseofcorotationwithf=600Hzanddecreasesupto0.2inthecaseofcounterrotationwiththesamefrequency.

TheasterisksinFigure3giveinformationontheexistenceofagapbetweenthemarginallystableorbitintheaccretiondiskandtheradiusofthestar.Forfrequenciesofcorotationhigherthan550Hzsuchagapdoesnotexist;thenthediskisincontactwiththesurfaceoftheneu-tronstar.ForlowerfrequenciesofcorotationandinthecaseofcounterrotationfortheEOSFPSandM=1.4M⊙thereisagapRm−R∗≈[1.44−3.06(f/kHz)+0.843(f/kHz)2+0.6(f/kHz)3−0.22(f/kHz)4]km.Inthemostinterestingcaseofcorotationthegapisverynarrowandthethick-nessoftheboundarylayerorthehightofthespreadinglayerusuallyexceedsthedimensionofthegap.However,inthecaseofcounterrotation(negativevaluesoff)thegapcouldbesufficientlylargethatithastobetakenintoaccount.

Theenergyreleaseefficiencyduetoaccretionontoacounter-rotating

˙c2forthecaseofaneutronstarmayreachverylargevaluesupto0.67M

neutronstarwithbaryonicmassm=2.1M⊙forf=1.5kHzandtheEOSFPS.Obviously,suchahighenergyreleaseefficiencyisconnectedwiththespindownoftherapidly(counter)rotatingstar.ThisefficiencyismuchhigherthanthatofdiskaccretionontoaKerrblackhole.Inthecaseofcorotationtheenergyreleaseefficiency,duetoaccretionontoaKerrblackhole,ishigherthaninthecaseofcounterrotation.Thisisreversedinthecaseofaccretionontoaneutronstar.

3StructureoftheBoundaryLayer

Theproblemofdiskaccretionontoaneutronstarwithoutamagneticfieldistwo-dimensional.Theheightofanaccretiondiskatlowaccretionratesandluminosities(0.014πGMmp

radiusoftheneutronstar.HereandbelowLEdd=

AccretionontoBlackHolesandNeutronStars119

accretiondiskorwecouldconsiderthemotionofmatterinthespreadinglayerasbelongingtothesurfaceoftheneutronstar.Wetriedtoinvestigatebothoftheseapproachesinone-dimensionalapproximations.InthepaperbyPopham&Sunyaev(2000)wecomputedthestructureandpropertiesoftheboundarylayerconsideringitasapartofthedisk.Figure4showshowtheheightoftheboundarylayerdependsonthedistancefromthestellarsurfacefordifferentaccretionrates.InthecaseofalowaccretionrateorL∼0.01LEdd,theheightofthediskinthe“neck”betweentheaccretiondiskandtheboundarylayerisclosetoonly40metersandtheextensionoftheboundarylayerabout1.5km.ThesituationdrasticallychangeswhenwegotothecaseofhighaccretionrateswithaluminosityclosetothecriticalEddingtonluminosity.Theheightoftheneckbetweentheboundarylayerandtheaccretiondiskinthiscaseexceeds2kmandtheboundarylayerextendsupto2neutron-starradii.

Fig.4.TheverticalpressurescaleheightH(top)andtheangularvelocityΩ(bot-˙=10−10(longdash),10−9(solid)and10−8M⊙yr−1tom),forsolutionswithM

˙=10−9M⊙yr−1anda(dotted),allforanon-rotatingneutronstar,andforM

neutronstarrotationfrequencyf∗=636Hz(dashed),allwithstandardviscosityandα=0.1.NotetheverysmallvaluesofHatthe“neck”betweenthediskand

˙solutions,andtherapidincreaseinHinthetheboundarylayerinthelowerM

boundarylayer.AdaptedfromPopham&Sunyaev(2000).

120RashidSunyaev

AmorenaturalapproachwasconsideredbyInogamov&Sunyaev(1999).Thisapproachusestheshallowwaterorhydraulicapproximation.Itassumesthatthethicknessofthespreadinglayeronthesurfaceoftheneutronstarislessthanthecircumferenceoftheneutron-starequatorH<<2πR∗.Thisapproachassumesthatmatterenteringtheequatorialringwithaveryhighrotationalvelocityoftheorderof0.5c,wherecisthevelocityoflight.Thenthematterbeginstospiralslowlytowardsthepoleslosingitskineticrotationenergyduetoturbulentfrictionwiththedenseunderlyinglayer(Fig.5andFig.6).

Fig.5.Rotationofmatterinthediskandonthestellarsurfaceinthespreadinglayermodel;Sisthestellarsurface,Pisthepole,andeistheequator.

Fig.6.Spreadingoftherotatingplasmafromthedisk,D,overtheneutronstarsurface,S.Here,Iistheintermediatezonenearthediskneck,θ∗correspondstothepositionofthehotbelt,andθ>θ∗isthecoldpartofthespreadinglayer.Therotationvelocityvφ(filledcircle)isdirectedalongthenormaltotheplaneofthefigure.Theslowlycirculatingdenseunderlyinglayersofmatterbeneaththespreadinglayerareindicatedbythedashes.BothfiguresareadaptedfromInogamov&Sunyaev(1999).

Thethicknessofthespreadinglayerishighestinthevicinityoftheequatoranddecreasestowardsthepoles.Thismeansthatmatterismovingdownthehillundertheinfluenceofgravity,thecentrifugalforceandthelightpressureforce.Theproblemisextremelyinteresting.Wearedealingwithradiationdominatedplasmawhentheradiationpressurestronglyexceedsthematterpressure.Thesoundspeediscloseto0.1−0.15c.Radiativeviscosityisalsomuchstrongerthantheviscosityofplasma.Thesolutionofthesetofhydrodynamicequationsresultsinthefollowingpicture(seeInogamov&Sunyaev1999fordetails).Twobrightbeltsequidistantfromtheequator

AccretionontoBlackHolesandNeutronStars121

appearonthesurfaceoftheneutronstarduetodiskaccretion.Figure7givesthedistanceofthebrightbeltsfromtheequatorfor4luminositiesoftheneutronstar:0.01,0.04,0.20and0.80LEdd.Thedistancefromtheequatorincreaseswithluminosity.

Fig.7.Dependenceofthesurfacebrightnessasafunctionofdistancefromtheequator.Labels1,2,3and4refertoLSL/LEdd=0.01,0.04,0.2,and0.8,respec-tively;qoisthecriticalEddingtonflux.AdaptedfromInogamov&andSunyaev(1999).

Theenergyreleaseinthevicinityoftheequatorisverylowbecausetherecentrifugalforcescompensategravitywithhighprecision.Therefore,anysub-stantialradiationfluxcoulddestroythestructureofthethinspreadinglayer.Fortunately,advectiontakestheradiationenergydensityandtransportsittothebrightbeltsaboveandbelowtheequator(Fig.8).

Inthesebrightbeltstherotationalvelocityofthespreadingmatterbe-comeslowenoughtopermittheexistenceofalargeradiationfluxcomparable

mc3222W

tothecriticalEddingtonfluxq0=p

R∗)=10

122RashidSunyaev

Fig.8.Thedynamicsofthespreadinglayerisdeterminedinmanywaysbythehydrodynamictransferofradiativeenergy.Theratiooftheenergyflux,q,emittedperunitareaoftheradiatinglayertothefrictionalenergyreleaseQ+perunitareaofthecontactsurfacebetweenthespreadinglayerandthestar.TheenergyistransferredfromzoneAintozoneBthroughmeridionaladvection.ThiscalculationisforLSL/LEdd=0.2.

Fig.9.Columndensityofmatterinthespreadinglayerasafunctionofthedistancefromtheequator.AstrongincreaseofΣoccurswhentheflowcoolsdownandbeginstomoveveryslowly.BrightbeltscorrespondtotheregionsofminimalΣ.Labels1,2,3and4refertoLSL/LEdd=0.01,0.04,0.2and0.8,respectively.BothfiguresareadaptedfromInogamov&Sunyaev(1999).

Thematterinthespreadinglayerispracticallylevitating.Thedifferencebetweenthegravitationalforceandthecentrifugal-andradiationpressureforceiscloseto(1−3)×10−3ofgravity.Athigherlongitudestherotationalvelocityofmatterandthevelocityoftheflowalongthemeridiandecreasesandtheflowbecomessubsonic,cool,denseandveryslow.

Oneofthemostinterestingpredictionsofthetheoryofthespreadinglayeristhestrongdependenceofthemattercolumndensityinthespread-inglayerontheaccretionrateortheluminosityoftheneutronstar(seeFig.9).InthecaseofalowluminositythelevitatinglayerinthebrightbeltsisopticallythinagainstThompsonscatteringτT∼2.Underthesecircum-stancesitisimpossibletoradiatetheenergyreleasedduetoaccretionatlowtemperatures.Comptonizationformshardtails.Inthecaseofahighlumi-nositythebrightbelthasalargecolumndensity(upto10kg/cm2).Thenfree-freeprocessesandcomptonizationformBose-Einsteintypespectrain-sidethespreadinglayerandtheresultingspectrumismuchsofterthaninthecaseoflowluminosity.

AccretionontoBlackHolesandNeutronStars123

4

TimeVariabilityintheAccretionDiskandintheBoundaryLayer

Allinstabilitiesexistingintheaccretiondiskmodulatetheflowofmatterontotheneutron-starsurface.Therefore,wecouldexpectthatthemajorityofthetypesofvariabilityweobserveinaccretingblackholesmustmanifestthemselvesinaccretingneutronstarswithcharacteristictimescalespropor-tionaltothemassoftheaccretingobject(seee.g.Shakura&Sunyaev1976,Wijnands&vanderKlis1999).Thespreadinglayeronthesurfaceoftheneutronstaristhesourceofadditionalhigh-frequencyinstabilities(seethediscussioninSunyaev&Revnivtsev2000).Theiroriginisobvious–themat-terinthebrightbeltsisradiationdominated,levitating,theheightissmallerthanintheregionofthemainenergyreleaseintheaccretiondisk,thesoundvelocityishugeandcorrespondingsoundfrequenciesareveryhigh.

Fig.10.Comparisonofthepowerspectraofablackhole(CygX-1)andaneu-tronstar(Terzan2).ThedashedlineshowsthepowerspectrumofCygX-1scaled

scaled

accordingtothemassratiowithTerzan2(fCygX−1×7→fCygX−1.Thissim-plescalingisimportantbutinsufficienttoexplainfullythedifferenceinthehighfrequencyvariabilityofTerzan‘2andCygX-1.NotethattheslopesofthepowerdensityspectraofTerzan2andCygX-1inthehighandlowfrequencylimitsaresimilar,butthatthepowerspectrumofTerzan2issignificantlybroaderthanthatofCygX-1.AdaptedfromSunyaev&Revnivtsev(2000).

Sunyaev&Revnivtsev(2000)comparedthepowerdensityspectraof9blackholesand9neutronstarsobservedbyRXTEintheirlow/hardstate.

124RashidSunyaev

Thereisaverystrongdifference.InthepowerdensityspectraofaccretingneutronstarswithaweakmagneticfieldsignificantpoweriscontainedatfrequenciesclosetoonekHz.Atthesametime,mostGalacticaccretingblackholesdemonstrateastrongdeclineinthepowerspectraatthefrequencieshigherthan10-50Hz.InprinciplethismightopenanadditionalwaytodistinguishtheaccretingneutronstarsfromblackholesinX-raytransients(wedonotmentioninthispaperthewell-knowndifferences:X-rayburstsorX-raypulsations).Fig.10comparesthepowerdensityspectrumofCygX-1withthepowerdensityspectrumoftheX-raybursterinTerzan2.

ThesimplestassumptionisthatthecharacteristicfrequenciesinthepowerspectraofthesourcesscaleasM−1(Shakura&Sunyaev1976).Thisscalinglawisvalidfore.g.thekeplerianfrequencyinthevicinityofthemarginallystableorbit,thethermalandsecularinstabilitiesoftheaccretiondiskintheregionofmainenergyrelease,andtheBalbus-Hawleyinstability.However,thisassumptiondoesnotaccountfortheobserveddifferenceinthehighfrequencyvariabilitybetweenneutronstarsandblackholes.

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