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Orbital inspiral into a massive black hole in a galactic center

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arXiv:astro-ph/0305062v1 5 May 2003AcceptedtoApJLett.PreprinttypesetusingLATEXstyleemulateapjv.19/02/01

ORBITALINSPIRALINTOAMASSIVEBLACKHOLEINAGALACTICCENTER

TalAlexanderandClovisHopmanFacultyofPhysics,TheWeizmannInstituteofScience,POB26,Rehovot76100,IsraelAcceptedtoApJLett.

ABSTRACT

Amassiveblackhole(MBH)inagalacticcenterdrivesaflowofstarsintonearlyradialorbitsto

replacethoseitdestroyed.StarswhoseorbitscrosstheeventhorizonrSorthetidaldisruptionradiusrtarepromptlydestroyedinanorbitalperiodP.Starswithorbitalperiapserpslightlylargerthan

thesinkradiusq≡max(rS,rt)mayslowlyspiralinduetodissipativeinteractionswiththeMBH,e.g.

gravitationalwaveemission,tidalheatingoraccretiondiskdrag,withobservableconsequencesandimplicationsfortheMBHgrowthrate.Unlikepromptdestruction,theinspiraltimeistypically≫P.

Thistimeislimitedbythesamescatteringprocessthatinitiallydeflectedthestarintoitseccentric

orbit,sinceitcandeflectitagaintoawiderorbitwheredissipationisinefficient.Theratiobetweenslowandprompteventratesisthereforemuchsmallerthanthatimpliedbytheratioofcross-sections,

∼rp/q,andsoonlypromptdisruptioncontributessignificantlytothemassoftheMBH.Conversely,

moststarsthatscatterofftheMBHsurvivetheextremetidalinteraction(“tidalscattering”).Wederivegeneralexpressionsfortheinspiraleventrateandthemeannumberofinspiralingstars,andshowthat

thesurvivalprobabilityoftidallyscatteredstarsis∼1,andthatthenumberoftidallyheatedstars

(“squeezars”)andgravitywaveemittingstarsintheGalacticCenteris∼0.1–1.

Subjectheadings:blackholephysics—Galaxy:center—stellardynamics—gravitationalwaves

1.introduction

Evidenceforthepresenceofmassiveblackholesinthe

centersofmostgalaxies(e.g.Gebhardtetal.2003),to-getherwithrecentandanticipatedadvancesinobserving

capabilities,havefocusedinterestontheobservationalim-

plicationsofstar-MBHinteractionssuchastidaldisrup-tion(Frank&Rees1976;Frank1978;Lightman&Shapiro

1977;Syer&Ulmer1999;Magorrian&Tremaine1999),

tidalscattering(Alexander&Livio2001),gravitationalwave(GW)emission(e.g.Hils&Bender1995;Sigurdsson

&Rees1997;Freitag2001,2003),interactionwithamas-

siveaccretiondisksurroundingtheMBH(Ostriker1983;Syer,Clarke&Rees1991;Vilkoviskij&Czerny2002),

andtidalcaptureandtidalheating(Novikov,Petchik&

Polnarev1992;Alexander&Morris2003,AM03).Muchefforthasbeendevotedtothestudyoftidaldisruption,

whichplaysanimportantroleinthegrowthoflow-mass

MBHs(Murphy,Cohn&Durisen1991;Freitag&Benz2002)andcanprovideasignaturefortheexistenceofMBH

ingalacticnucleibytheemissionoftidalflares.

Dynamicalanalysesindicatethatmostofthestarsscat-teredintoradialorbitsoriginateattheMBHradiusofin-

fluence,rh,wheretheenclosedstellarmassroughlyequals

theMBHmassmandthescatteringisroughlyisotropic.Eventhorizoncrossingortidaldisruptionisprompt;the

starsplungetowardtheMBHwithacross-sectionthat

scalesas∼rp(Hills1975)andreachitinlessthantheinitialorbitalperiod,P0,irrespectiveoforbitalperiapse,

aslongasrp

time,e.g.P0(rh)∼105yrintheGalacticCenter(GC).Incontrast,theotherprocesseslistedaboveproceed

graduallyoveraninspiraltimet0≫P0,asasmallfrac-

tionoftheorbitalenergyisdissipatedeveryperi-passage.Theinspiraltimetypicallyrisessteeplywiththeperiapse.

Inorderfortheextractedorbitalenergytoheatthedisk,tidallyheatthestarorpowerahighluminosityofgravitywaves,thestarhasfirsttodecayintoashortperiodorbit.

Novikovetal.(1992)estimatethattidalcapturebyaMBHoccursfororbitswithrp/rt

thatstarsarescatteredintotidalcaptureorbitsatarate

b0−1∼2timesfasterthanthatforprompttidaldisruptionorbits.Theorbitalenergythestarhastolosetocircular-

izefarexceedsitsownbindingenergy,soitislikelythat

itwillultimatelybedisrupted(Rees1988;AM03).Thishasledseveralauthors(Frank&Rees1976;Novikovet

al.1992;Magorrian&Tremaine1999)tosuggestthat

slowtidalinspiralmaybeatleastasimportantaspromptdisruptionforfeedingtheMBHandforproducingtidal

flares.Simulations(Murphyetal.1991;Freitag&Benz

2002)indicatethatprompttidaldisruptionssupplybe-tween∼0.15to0.65ofthetotalmassofalowmassMBH

(m󰀂107M⊙)inalow-densitygalacticnuclearcore.Ifthecontributionofinspiralingstarswereindeedashighas

impliedbytheratioofthecross-sections,thiswouldhave

far-reachingimplications:starscouldsupplymostorevenalloftheMBHmass,therebyestablishingadirectlink

betweenmandstellardynamicsonascaleofrh.

However,asmallinitialperiapsedoesnotinitselfguar-anteeultimatedisruption.Thestarmustalsohaveenough

timetocompleteitsorbitaldecay.InthisLetterwerevisit

thequestions:whatisthetimeavailablefororbitaldecay,andwhatistheinspiraleventrate?

2.calculations

2.1.Scatteringintoinspiralingorbits

WefollowtheanalysisofMiralda-Escud´e&Gould

(2000,MG00)oftheinfallofasinglemasspopulation

ofstellarBHsintoaMBHbydiffusionintotheloss-conedueto2-bodyencountersinaKeplerianpotential.

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The universe is an infinite expanse of space, filled

with mysteries and unknowns. In the universe, there are

countless galaxies, planets, stars, and black holes, among

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中文回答：

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