19 91ApJ. . .380L. .17P 3 2 will spiraltogetherinlessthanaHubbletime.Theprescient, rate. should consequently beincreasedby true phase,j(df/dt)dt.Thecharacteristic amplitudeofthewaves,eq.(46b) but crudeestimateofthemergerratefromthisoneobject by system, PSR1913+16(Taylor&Weisberg1989),whosestars of wavesfrommergingneutronstarbinariesliesintheevent coincidence noise,theonlyuncertaintyaboutdetectability give aneventrate10times lower thangivenbyClarketal. the methodsoutlinedbelowon thedataavailablethenwould tion volumebetweenPSR1913 +16andsinglepulsars(using by neglectofthedifferencesinlifetime,luminosity,anddetec- single pulsarsandasupernovarate.Thiswasseriouslyflawed Clark etal.(1979)wasbasedonamodel-dependentscaling to by Lincoln&Will(1990).Thus,fordetectorswithspecified The waveformshavebeencalculatedtopost-Newtonianorder from thelatestagesofinspiraiareeasilycalculated.The considerable importancetothedesignandfundingofgravita- adequate, NewtonianwaveformsisgivenbyThorne(1987). become significant.Apedagogicalsummaryofthesimple,but before hydrodynamiceffectsoftidesonthe~10kmstarshave waves atfrequencies(~10-300Hz)towhichaLIGOismost The mergerrateperunitvolumeintheuniverseisthusof event ratecanbedeterminedfromelectromagneticobserva- sensitive areemittedwhentheorbitalseparationofstarsis tional waveobservatories(e.g.,LIGO). tions (incontrasttomergingstellar-massblack-holebinaries). confidence (incontrasttosupernovaeandpulsars),whose tude atthefrequenciesofinterestcanbepredictedwith tional radiationsofaridentifiedwhosewaveformandampli- ~ 100km,whenpost-Newtoniantheoryisstillapplicable,and The AstrophysicalJournal,380:L17-L21,1991October10 © 1991.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. 2 1 Thornenotesthatinhiseqs.(42a) and (42b),ftshouldbereplacedbythe Until recently,therewasknownjustonebinaryneutronstar AlfredP.SloanFellowandPresidential YoungInvestigator. The propertiesofthe“chirp”gravitationalwaveemission Merging binaryneutronstarsaretheonesourceofgravita- © American Astronomical Society •Provided bythe NASAAstrophysics Data System Subject headings:blackholes—gravitationpulsarsstars:binariesneutron ble tothegivenrateofneutron-starbinarymergers. limit ofthreemergersperyearwithin23/hMpcissetbytherateTypelbsupernovae.Theratesblack in thatitconsidersonlysystemslikethosealreadyobserved,givesthreeperyearwithin200Mpc.Anupper hole binarymergersandblackhole-neutronstararemodel-dependent,butcouldbecompara- ultraconservative lowerlimittotherategivesthreeperyearwithin1Gpc.Ourbestestimate,stillconservative galaxies toscalewiththestarformationrate,wecomputemergerrateexpectedinlocaluniverse.An which willmergeinlessthanaHubbletimehavealreadybeenobservedasbinarypulsars:twothediskof a lowerlimittothemergerrateinourGalaxyandglobularclustersystem.Takingother our Galaxy,andoneinaglobularcluster.Fromthelifetimespositionsofthese,weinferwithconfidence the mostpredictable.Theirwaveformsatobservablefrequenciesareeasytocalculate.Andthreesystems Theoretical Astrophysics,130-33,Caltech,Pasadena,CA91125;andInstituteforPhysics,UniversityofCalifornia,SantaBarbara Of themanysourceswhichgravitationalwaveobservatoriesmightsee,mergingneutronstarbinariesare THE RATEOFNEUTRONSTARBINARYMERGERSINUNIVERSE:MINIMAL 1. INTRODUCTION PREDICTIONS FORGRAVITYWAVEDETECTORS Received 1991July3;accepted25 1 E. S.Phinney ABSTRACT L17 each binary(fromresurrectiontomerger)canbeestimated as pulse periodPmuchlongerthanatrebirth,thetotallifetime of pulsar density. where ^a.isthevolumeofGalaxy.Ifpulsarsare not to bethecasein binarypulsarswithwhite-dwarf companions: good estimateofthetimesince thepulsarwasformed(known is calculatedfromtheobserved binaryperiodP,orbitaleccen- uniformly distributed,F(0and^Galaretobeweighted by are summarizedinTable1. The assumptionthatP/(2P)isa The timeruntilgravitational radiationmergesthetwostars be estimatedas volume F(0=XjVjthemergerrateinGalaxycan M byintegratingtheequations ofPeters(1964).Theresults tricity e,andthemassesof pulsaranditscompanion are detectedinsurveysjwhichcouldhavepulsaria makes itpossibletoconsideraseriouscalculationoflower and in§4extrapolatetotherestofuniverse. vable tracersoftherelevantpopulationsindistantgalaxies, parts ofourownGalaxy.In§3weidentifymoreeasilyobser- limit tothecosmologicalrateofmergers.In§2,weuse observed systemstoestimatetherateofmerginginvarious show thattheearlierdiscoverywasnotastatisticalfluke,and 2127 +11CintheglobularclusterM15(Princeetal.1991),and tainties inthissingle-objectestimate. PSR 1534+12nearbyintheGalaxy(Wolszczan1991).These b max mrg max 1979). Schutz(1989)summarizedmorerealisticallytheuncer- 2 If thepulsarhasconstanttorque,brakingindexn=3,and If dbinaryneutronstarsystemsi,eachoftotallifetimet(í), Since then,twomoresystemshavebeendiscovered:PSR 2. MERGERRATEINTHEGALAXY R =1 i =P/(2P)+T.(2.2) mrg V max(MÍ) i (2.1) 19 91ApJ. . .380L. .17P 3/2 -3 v1 -3 1 -1a 3 L18 caption toFigure1. been detecteddependsontheassumedGalacticdistributionof see Kulkarni1986)caneventuallybetestedasdescribedinthe pulsars. Forasimple,conservativeestimate,assumethatsuch mJy)~ =0.008—i.e.,Wolszczanwouldhavebeenverylucky kpc, andhalf-heightZ.ToestimateZ,wenotethatbothPSR systems areuniformlydistributedinacylinderofradius12 kpc abovetheGalacticplane.ItisimplausiblethatZ>1kpc, distant than0.5kpc,sinceitsDMsin6=9cmpc,anditis to finditsonearby(1534+12isunlikelybemuchmore since thenPSR1534+12wouldhaveF/F=(36mJy/1.5 z ~t/\/27®kms“,andreachmaximumheightsZ1.5 surrounded bythreepulsar-containingglobularclusters,Ml3, We adoptZ=1kpcasabestguess,butquoteresultsforother and z=5,6,18kpc—seeBhattacharya&Verbunt1991). binary pulsars.Intheabsenceofluminosityortorquedecay,oldbinaries values aswell. M5 andM53,withrespectivelyDMsinb=20,21,24cmpc 100 kmsj.Apopulationejectedisotropicallywouldhave 1957-1-20 (Fruchteretal.1990)havetransversevelocitiesv~ 1913-1-16 (Taylor&Weisberg1989)andtherecycledPSR edge wouldhaveshortorbitalperiods andbehardtodetect.Pulsarswould should beuniformlydistributedon the line.Binariesclosetoright-hand which thesediskpulsarscouldhavebeendiscovered,wecon- Narayan (1988),plustheonedescribedinWolszczan(1991), distribution ofweights wouldindicatethatP/(2P)wasa goodestimateofage. sidered 12pulsarsurveysj:theninedescribedinKulkarni& close totheirbirthperiods,soP/{2P) > t.IftheradioluminosityLdecreasesas bunched attherightifthereweretorque decay,orifmanystillhadperiods removed withoutmodelingbygiving eachpulsaraweight1/K.Auniform binaries arediscovered,theseluminosity andperiodselectioneffectscanbe the pulsarspinsdown[e.g.,L=(l +i/io)]>flux-limitedsamplewould 0.3 kpc,and^+16)=20. and thetwoCaltech-Arecibosurveys(Navarro&Kulkarni be bunchedattheleft[~T/ln(T/i ) fort<£t],asobserved.Asmore max 1991, privatecommunication).Wefind^I+max(1534+12)= t max 0 0 3 The volumewithinwhicheachpulsarinTable1couldhave Fig. 1.—Whereintheirtotallifetimestareeachofthethreeneutronstar Thus F=900(Z/1kpc)kpc.Tocomputethevolumesin Using equation(2.1)andtheFvaluesof§2.2,wefinda gal max ID co © American Astronomical Society •Provided bythe NASAAstrophysics Data System t/T =[P/(2P)]/[(P/(2P)+T] mrg CO 05 •'—I t-h C2 ^-t 02 M + e Distance ^mrg (GRdecay) P/(2P) q =M(psr)/M P Flux (400MHz) Reference i2 12 b 0.5 Parameter 9 8 9 0.5 kpc 0.27367 Wolszczan etal.1991 0.97 +0.03 2.73 x10yr 2.5 x10yr 2.679 M 36 mJy 3.0 x10yr 10.098 hr short P 0 h PSR 1534+12 Galactic BinaryNeutronStarSystems PHINNEY Vol.380 TABLE 1 8 8 8 Taylor &Weisberg1989 0.61713 4.1 x10yr 7.3 kpc 2.82837 M 7.7519 hr 5 mJy 3.01 x10yr 1.04 1.1 x10yr q -1 8 10 8 -3 Galactic diskmergerrate consider theCaltechsurveys).Sincepulsarluminosityfunc- distribution concentratedtotheGalacticcenter,anddonot tion issteep[AT(>L)ocL],itnotsurprisingthatluminous Shemi 1991,whouseanoptimisticdistancescale,apulsar recycled pulsarsknown.Thereareundoubtedlymanymore times lessluminousthan1913+16,andoneofthefaintest systems notdetectedbecause:(1)theyarestillfainterthan PSR 1913+16shouldbethetipofaniceberg:1534+12is30 neutron starshavemagneticfieldssolowthattheydonot less thanthelifetimetogravitationalradiation(Figure1sug- have magneticfieldssohighthattheirradiolifetimeismuch space density,e.g.,becausetheyarebornwithT10yr,or shine intheradio,or(4)havealargermergerratebutlow 1913 +16(aslightlyhigherrateisfoundbyNarayan,Piran,& (for 1534+12and1913+16,respectively),reducingtheir gests thatthismaybetruefortheobservedsystems). inferred mergerratesby4and6,respectively.(2)AsZvaries to thepulsarswereunderestimatedbyafactorof2(very factor of2. from 0.5kpcto3kpc,VJVincreasesandthemergerrate unlikely), Fwould(forZ=2kpc)beincreasedby4and6 decreases: for1534+12byafactorof3and1913+16 1534+ 12,(2)thepulsarbeamdoesnotcrossEarth,(3)both formation ofmassivestars.Thisismadereasonablebythe fact tion ofsuchsystemsoughttobeproportionaltherate of the resultofevolutionmassivestars,rateforma- that thereisnoevidenceforastrongdependence(i.e.,more mrg initial mass-function(Scalo1987;Phinney1991). than afactorof3)onmetallicitybinaryfraction(Latham et al. 1988;Duquennoy&Mayor1990;Pryoret1989) or (van derKruit1987). 1534+12 havelifetimesmuchlessthanaHubbletime,and are from 1-3Mstarsinthedisks ofspiralgalaxies,formedinthe the disk,andonly~5%isfrom theoldspheroidpopulation our GalaxyisL=2x10 L,ofwhich~95%isfrom Ellis, &Peterson1988;seealsoPhillipsShanks1987) maGal max past 5Gyr.The extrapolationrequiredisthus thattheaverage j£?(obs) =1.9x\0hLgMpc . TheB-bandluminosityof q Gal B Q B ßq PSR 1913+16 The firsttermcomesfrom1534+12,thesecond There areuncertaintiesinequation(2.3).(1)Ifthedistances Since thebinarypulsarslikePSR1913+16and The B-bandluminositydensityoftheuniverseis(Efstathiou, The cosmologicalB-bandluminosity densityarisesmainly 3. EXTRAPOLATIONTOTHEUNIVERSE -6_17 R =10yr+1(Tyr".(2.3) 8 8 8 0.6 mJy 0.68141 Prince etal.1991 2.71 Mq 8.047 hr 2.20 x10yr 3.2 x10yr 10.6 kpc(inMl5) 1.0 ±0.2 1.0 x10yr PSR 2127+11C 19 91ApJ. . .380L. .17P 83 -1 1-3 No. 1,1991 which evolveintoclosebinaryneutronstarsisonaveragethe further assumethatthefractionofmassivestarsinbinaries rate offormation1-3Mstarsisproportionaltothatthe same asinourGalaxy. stars whichmakeneutronstars,perhaps8-25M.Onemust (Soifer etal.1987)J^=1.2x10^LMpc^.The the starlightemittedinÆ-bandemergesthere:someis red. Thefar-infraredluminositydensityoftheuniverseis absorbed bydust.Theenergyemergesintheinfra- models. Gyr andnoextinction,L/L~0.5L,forbothSalpe- spectral-synthesis programofBruzual(1983,but1988version massive starsrecently,andthusshouldnotbecountedinthe contributed byEandSOgalaxies,whichhavenotformed ter andScaloIMFs.Theeffective¿?“hidden”bydustisthus of codeused)gives,forastar-formationrateconstantover15 extrapolation ofthebirthrateyoungneutronstarbinaries. absorption, ands^0.4forconventionalselectiveextinction recent starformationis 0 more heavilyweightedtowardmassivestars,assomehave The ratedensitywouldbehigherifsomegalaxieshadIMFs 0 young, anddifferentinstellarcontent(Elsonetal.1989)from clusters aroundirregulargalaxies,sincemanyappearto be created inglobularclusters(Phinney&Sigurdsson1991),we proposed (e.g.,Larson1986). all galacticdisks)toamergerratedensityof hence extrapolates,withtheassumptionslistedabove(similar A mergerrateByrinthestar-formingdiskofGalaxy FIR0 the Galaxy’sclusters.Weuseclusterspecificincidence S are similartothosearoundtheGalaxy.Weneglectglobular assume thattheglobularclustersaroundearly-typegalaxies IMF from2-10M,similarbinaryfractionandevolutionin BQ bolo B ~6 xiOh/sLMpc,wheres<1;=forblackorgray 0 Q B Two smallcorrectionsshouldbeconsidered.First,notall Thus, thenetB-bandluminositydensityattributableto Second, about20%ofthecosmologicalB-bandstarlightis To estimatethecontributionfromneutron-starbinaries = © American Astronomical Society •Provided bythe NASAAstrophysics Data System 87 ^f b/Lg*\,b S g> =[(1-0.2)x1.910+6l0/s]h B 231 8-3 = (0.75+0.3/s)x10~hRMpc"yr".(3.2) = 2.1x10hLMpc.(3.1) q B 3.1. RateinGlobularClusters 10 2 3 2 3 2 3 2 3- column, convertingiftousing thecolorinfourthcolumn,andclusterincidence galaxy type:2.4forSa,Sb;1.7Sc,Sd; 1.3forIm.Lastcolumncomputedusingeq.(3.1)andfifth and Virgofractions—seealsoDavis & Huchra1982.TypelbSupernovaratesarepercentury, third column(seetext). 1991, multipliedbythemeanextinction correctionappliedbySandage&Tammann1981tothat 10 Lofobservedgalaxyluminosity. RatesarefromTable8ofvandenBergh&Tammann BK 0 B Sc 1.3/i0.2h 0.6 adopt30%,plusallFIR(0.1+QA/s)hMpc“ Sb 0.6/z0.7/i0.7adopt20% 0.3h Mpc“ Sa O.l/i7h0.9adopt20% 4.0h Mpc~ E, SO09h1.0adopt20% 5.6/i Mpc Type R(Ib+le)SB—VContributiontoif Space Density B Notes.—Fractions ofB-bandlightfrom Fig.1ofBinggelietal.1988,adoptingmeanthefield Specific SupernovaRateRandGlobularClusterIncidenceS RATE OFNEUTRONSTARMERGERS TABLE 2 7 _1 -1 -1 (number ofglobularclustersperM=—15or8.5x10Lk mated fromthefar-infraredluminositydensity.Thevalues luminosity densityincludingtheabsorbedcomponentesti- values areforgalaxymagnitudescorrectedinternalabsorp- of F-bandgalaxyluminosity)vandenBergh(1984).His density of column ofTable2,wegetaglobularclustermeanspace adopted aregiveninTable2.Addingtheentrieslast tion, soforspiralgalaxies,theyshouldbeappliedtotheoptical be derivedasfollows.(1)Supposethatinonly10%ofall lapsed clusterscontainbinaryneutronstarslike2127+11Cin own inthat20%haveevolvedtocorecollapse(Chernoff& assume thatglobularsinearly-typegalaxiesaresimilartoour Only 3%oftheclustersareingalaxieslikeourown(Sb).We entire globularclustersystem.(5)TakeH=50kms luminous, orofshortradiolifetime.(4)AssumethatPSR no correctionforpulsarsbeamedawayfromEarth,notradio Galaxy. (2)Makenoextrapolationtofainterpulsars.(3) realizations ofthepulsardistributionarepulsarslikePSRs Djorgovski 1989).Wefurtherassumethathalfofthesecol- collapsed clusters.(5)TakeH=15kmsMpc and (2.3) by2,appropriateifthepulsarformationrateisascen- factor of3correctionforpulsarsbeamedawayfromEarthor derived asfollows.(1)SupposethatPSR1534+12and ultraconservative limittotheratedensity: and (3.4)byafactorof10,usingequation(3.2)findthe 2127 +11CistheonlyneutronstarbinaryinGalaxy’s by (4)and(5)adopttherate(3.4).Thus“bestguess” rate s =0.4.Thenby(2)and(3),weincreasetherate(2.3)6, and not radioluminous.(3)Increasethe“uniformgalaxy”rate h =0.5Rq.(4)AssumethatPSR2127+11Cistypicalofcore- trally concentratedasanexponentialdiskwithscalelength Mpc and5=1.Thenby(1)(4),wereducetherates(2.3) Ml5, withlifetimetfromTable1,giving v0> 1534+12 and1913+16asclosetoEarththeyareinthe 1913 +16areatdistancestypicaloftheirdensity.(2)Makea o 0 An ultraconservativelowerlimittotheeventratecannow A “bestguess”ratefromtheknownbinarypulsarscanbe -103 $ >6x10Mpcyr:3at1Gpc.(4.1) 93-_1 ^gc =3x\0~hMpcyr.(3.4) 3- Globular Cluster 0 =10hMpc.(3.3) gc 4. DISCUSSION L19 19 91ApJ. . .380L. .17P 4 1 -5 -1 2 8 12 8 -1 -1 cussed byNarayan etal.1991)couldbehigh: fewerstarsleave could thenremainbound. could havemuchlessmass-loss andrecoilvelocitythanthat mergers suggeststhatonly~2%ofsuchsystemssurvive or ablackholeandneutron star(bh-ns;scenariosaredis- nova explosion(Bailes1989). Collapse ofastartoblackhole rate iscomparabletothebirthR(Bc-X)^¿5x10“y r~ rate ofneutronstar(ns)binaries(seeabove)isÆ=10y r, associated withneutronstar formation.Mostsuchsystems spiral-in andthemasslossrecoilkicksofsecondsuper- supernova explosion.ThemuchsmallerrateRofns-ns of massiveX-raybinaries(predominantlyBe-nssystems; see the Galaxy(vandenBergh&Tammann1991).Sincelatter about 10“therateofType(lb+Ic)supernovaexplosions in stars arereplacedbyablackhole?The“bestguess”merger (4.3), butmostarepresumablysinglestars,orinbinariestoo formation ofeachbinaryneutronstarsystemrequirestwo Pols etal.1991),mostsuchsystemsseemtosurvivethe first wide formasstransfertooccur. it assumesthatall(lb+Ic)supernovaeoccurinbinaries Type lborIcsupernovae).Thisisagenerousupperlimit,since novae (halfbecauseweassumethatbothneutronstarprogeni- Type IIsupernovarateisabout4timeshigherthanequation whose othermemberis,orwillbecomeaneutronstar,andit tors losetheirhydrogenenvelopesinmasstransfer,so sensitive tosourcesatcosmologicaldistances. rate ofstarformationingalaxiesappearstoincreaserapidlyas populations, andsystemsbornwithT10yr,couldhave With theratesgivenbyvandenBergh&Tammann(1991), enough thatthestarswillmergeinaHubbletime.UsingTable the starformationmayunderestimateratesforLIGOs one looksbackeventoredshift0.3.Thusourlocalestimateof a largebirthrate,withoutappearinginpulsarsamples.(3)The to be assumes thatallthebinariesremainbound,withorbitstight lifetimes muchlessthantheorbitaldecaytimescale.Both shine asradiosources;thosewithB>10Gwillhave in ourownGalacticnucleus.(2)Neutronstarswithdipole much largernumbersofstars.Theymightcontainalarge surface fieldsB<10Gwillneitherhavepaircascades,nor population ofexchangebinarieslikethoseintheglobulars. those inthecoresofpost-corecollapseclusters,butinvolve from 3yrnoisecoincidences.Themorereasonable“best still further:(1)Conditionsingalacticnucleiaresimilarto neutron stars100timeshigher.Severaleffectsmightraisethis guess” givesaneventratefromknowntypesofmerging gives arateof3yrwithindistancewheretheproposed 1, wefindtherateofType(lb+Ic)supernovaeinuniverse Pulse smearingintheISMmakesitimpossibletodetectthese 9.4 ofThorne1987),wouldbeabletodistinguishrealmergers In bothequations(4.1)and(4.2),diskbinariesdominate0t. density is LIGOs, withadvanceddetectors(seeeqs.[124]-[126]andFig. mrg L20 PHINNEYVol.380 Thus thebirthrateofbinaries withtwoblackholes(bh-bh), What ofanalogousbinariesinwhichoneorbothneutron An upperlimittoRishalftherateofType(lb+Ic)super- Even theultraconservativelowerlimittoratedensity 831 ^ =8x10“Mpc“yr“:3yr"at200Mpc.(4.2) 531 ^(Ib +Ic)/2=6x1(T/iMpc"yr": © American Astronomical Society •Provided bythe NASAAstrophysics Data System -1 3 yrat23/hMpc.(4.3) 2 3 NAGW-2394 and theAlfredP.SloanFoundation forsupport. (NSF grantPHY89-04035), for hospitality,andNASAgrant and distances.IthanktheInstitute forTheoreticalPhysics and J.Navarroforelucidating thesubtletiesofpulsardetection of notes,E.vandenHeuvel for discussions,andJ.H.Taylor aged. IthankR.Narayanand T.Piranforafriendlyexchange accepted abet,andKipThorne hadnotnaggedandencour- life. matter. Gravitywaveobservatoriesshouldhaveanexciting coalescence intothehigh-frequencyphaseoftidaldisruption, massive stars,independentoftheselectioneffectswhichplague giving furtherinsightintotheequationofstatenuclear galaxy surveys.Speciallytuneddetectorscouldfollow the certain ns-nsmergerswillalsoallowthemassdistribution of (Schutz 1986),thedistributionofmassesmergingbodieswill nation oftheHubbleconstant,andcosmography of systems canbedetermined(Schutz1986),allowingadetermi- neutron starstobedetermined.Thedistancesthemerging hole mass(determinedbypost-collapseinfall).Themuchmore masses ofthemergingbodiestobedeterminedaccurately which determinethefinalperioddistribution.Sincegravi- merge dependsonthemiasmaofmasstransferandspiral-in shed lightonthisphysics,aswelltheminimumblack- is notrequired. tational waveformsofanymergingsystemswillallowthe the ns-nsmergerrateinequation(4.2),butfractionwhich black holeremnantsdonotexpandmuch,soasecondspiral-in massive than3M(asneededforPSR1913+16and (L/Mc). Ifspiral-indoesoccur,however,thesubsequentevol- Hubble time.ThemoremassiveHecoreswhichcouldleave second spiral-intomakeans-nsbinarywhichwouldmergein ically duringcorecarbonburning(Habets1986),requiringa lower massobjectlikeaneutronstar.Ifthecompanionhas ution canbesimplerthaninthens-nscase.Heliumstarsless envelope ejectionmightbelessefficientthanthatbyaneutron strong stellarwind,spiral-inmightneverbegin;ifitdoes, ing itscompanion’sheliumcoremass.Hencespiral-inneednot star, sinceblackholeaccretioncouldhaveaverylowefficiency occur, asitmustexceptinverynonconservativetransfertoa To mergeinaHubbletime,spiral-inmustthusreducethe lar orbit,takes orbital periodto<1day.Ablackholecanhaveamassexceed- bh-bh andbh-nsbinariesdependsontheorbitalperiodsafter spiral-in, andhenceontheill-understooddetailsofprocess. of closens-nsbinaries. panions havelifetimes~10timeslessthanthoseoftheBe holes orblackholecandidates.Theholes’massivecom- X-ray binariesintheGalaxy(Polsetal.1991)containblack For gravitationalradiationtomergeabinaryoftotalmass stars. Thusthe(X-rayluminous)blackholebinarybirthrateis binary birthratefollowsfromthefactthat>3of~10 disrupted intheirformation.Alowerlimittotheblackhole black holeremnants,butthebinaryismuchlesslikelytobe 1534+12 ifthereisnorecoil)expandtheirenvelopesdramat- 0 10M, massratioq,andperiodPdaysinanearlycircu- > 0.03thatofBe-nsbinaries,comparabletothemergerrateR qd This wouldnothavebeenwrittenupifJohnBahcallhad Thus bh-bhandbh-nsbinariesformatratescomparableto Unfortunately, therateofgravitationalmergersamong 98/35 T =1.0x10PMr(l+q)(l1/q)yr.(4.4) mrg 19 91ApJ. . .380L. .17P No. 1,1991RATEOFNEUTRONSTARMERGERSL21 Phinney, E.S.1991,MNRAS,inpress Phillips, S.,&Shanks,T.1987,MNRAS,227,115 Narayan, R.,Piran,T.,&Shemi,A.1991,ApJ,inpress Lincoln, C.W.,&Will,M.1990,Phys.Rev.,D,42,1123 Latham, D.W.,Mazeh,T.,Carney,B.McCrosky,R.E.,Stefanik,P.,& Peters, P.C.1964,Phys.Rev.,B136,1224 Larson, R.B.1986,MNRAS,218,409 Kulkarni, S.R.,&Narayan,R.1988,ApJ,335,755 Kulkarni, S.R.1986,ApJ,306,L85 Habets, G.M.H.J.1986,A&A,167,61 Frachter, A.S.,etal.1990,ApJ,351,642 Elson, R.A.W.,Fall,S.M.,&Freeman,K.C.1989,ApJ,336,734 Efstathiou, G.,Ellis,R.S.,&Peterson,B.A.1988,MNRAS,232,431 Duquennoy, A.,&Mayor,M.1990,inNewWindowstotheUniverse,ed.F. 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