19 94MNRAS.2 7IL. .IOS 2 12 2 1 Mon. Not.R.Astron.Soc.271,L10-L14(1994) J. Casares The massoftheblackholeinV404Cygni T. Shahbaz,F.A.Ringwald,*J.C.Bunn,Naylor,RCharlesand Accepted 1994August22.Received10;inoriginalformJuly8 DepartmentofAstrophysics,NuclearPhysicsLaboratory,KebleRoad,Oxford0X13RH DepartmentófPhysics,KeeleUniversity,Keele,StaffordshireST55BG where alate-typestarislosingmaterialviaanaccretiondisc The low-massX-raybinary(LMXB)transientsaresystems for months,witharecurrencetimeoftheorderdecades. to ablackholeorneutronstar.Themassaccretiononthe These systemsarediscoveredbytheirX-rayemissionduring compact objectisepisodic,leadingtooutburstswhichlast follow-up opticalspectroscopyshowingtheperiodtobe outburst, but,whentheyreturntoquiescence,detailed has beentypicalofthispattern,beingdiscoveredbythe observations canbemadeofthesecondarystar.V404Cyg function ofq.Justsuchinformationisprovidedbythe yield themassratio,q,ofbinary(Casares&Charles the hypothesisthatitisablackholecandidate.Itcanalso object (inthiscase6.08M)andthusprovidesupportfor Wagner etal.(1992).Wehavecarriedoutsuchobservations requires afurthermeasurementoftheinclination(/)as a 6.5 d(Casares,Charles&Naylor1992).Opticalspectro- distorted star,whichhasbeenobservedintheopticalby caused byobservingthechangingaspectofagravitationally ellipsoidal variationofthesecondarystar,i.e. scopy canprovidealowerlimittothemassofcompact 1 INTRODUCTION more ofthecontinuumflux close toHacomingfromthe disc. AgainV404Cygseems typical,with84percentor appears tobelittleornocontribution fromtheaccretion and limb-darkeningparameters becomenegligible,andthere in theinfraredKband,sincehereuncertaintiesgravity- Ginga AllSkyMonitor(Makinoetal.1989),andwith 1994); toobtainthemassofcompactobject,however, 0 Optical Astronomy Observatories. * Visitingastronomer,KittPeak NationalObservatory, © Royal Astronomical Society • Provided by the NASA Astrophysics Data System ABSTRACT We haveobtainedaX-bandinfraredlightcurveofthelow-massX-raybinary transient V404Cygni.Wemodelitastheellipsoidalvariationofasecondarystar the binary.Combiningthiswithpreviouslypublishedspectroscopicdata,we distorted inthegravitationalfieldofablackhole,andthusdeduceinclination Key words:accretion,accretiondiscs-blackholephysicsbinaries:close determine themassofblackholetobeapproximately12M©. spectroscopic -stars:individual:V404CygX-rays:stars. - images,andthensubtractthe darkcurrent.Next,askyimage 2 ber usinginfraredarraycamerasonthe3.8-mUnited We observedV404Cygin1992Augustand1993Septem- binary V616Mon(=A0620-00),wherethederivedmass with thecanonicalneutronstarmass(Shahbaz,Naylor& henceforth CNP).Wehaveappliedthistechniquetothe December ontheKittPeakNationalObservatory(KPNO) Kingdom InfraredTelescope(UKIRT),andin1993 neutron starsystemCenX-4,wheretheresultwasconsistent length whiletheveilingratiofalls(seeCasaresetal.1993, Charles 1993,henceforthSNC93);andtotheblackhole HgCdTe array,whichgives1.96arcsecperpixelonthe device, usedat0.62arcsecperpixel.TheKPNOimageris a 2 OBSERVATIONSANDREDUCTION mass ofasecondblackhole,thatinV404Cyg. lay intherange5to17M(Shahbaz,Naylor&Charles secondary star,afractionwhichriseswithincreasingwave- long-wavelength cut-offat2.4pm,whilsttheKPNOK'-filter taken ingroups,usingaslightlydifferenttelescopepointing cut-off isat2.3pm.Atbothtelescopestheimageswere position foreachimage.Weobservedthesourceof groups. order ofonehourpernight, madeupofaseriessuch frame wasthen flat-fieldedusingtheappropriate skyimage. image fromalltheotherframes withinthegroup.Eachdata was createdforeachdataframe, bymakingamedian-filtered 1994, henceforthSNC94).Inthispaperwemeasurethe 1.3-m telescope.TheK-bandfilterusedatUKIRThad a 1.3-m telescope.TheUKIRTarray(IRCAM)isanInSb 0 The firststepofthedatareduction wastolinearizethe 19 94MNRAS.2 7IL. .IOS 2 because ofanearby(1.4arcsecnorth)star.FortheUKIRT This contributionwasmeasuredbyusingprofilefitting which encompassedbothstars,andthensubtractedthe data wethereforeusedarelativelylargeaperture(2.4arcsec) contribution ofthecompanionfromallourmeasurements. check thatvariationsintheseeingwouldnotadverselyaffect (Stetson 1987)onframeswithrelativelygoodseeing.To CNP) whichshowthatsuchaneffectwouldnotconstitute such aprocedure,wehavecarriedoutsimulations(see large pixelsizemeantthatthestar5.6arcsecsouthofV404 an errorofmorethan0.7percent.FortheKittPeakdata, Cyg wouldalsocontaminateanaperturecontainingV404 Cyg, sowereducedthesedatausingtheprofile-fittingcode. Table 1.KmeasurementsofV404Cyg. Heliocentric JulianDatePhaseTelescope which observingrunthedataare taken: stars-UKIRT1993;triangles1992;crossesKitt Peak.Wheretheerrorislargerthan Figure 1.TheÄ-bandlightcurve ofV404Cyg,foldedontheorbitalphasewithacomparisonstar shownabove.Thesymbolsindicatefrom to thecomparison star. symbol, anerrorbarisplottedas a thinline.Thedashedcurveisthebest-fittingmodellightcurve,and thedashedstraightlineaconstantfitted Aperture photometryofV404Cygisproblematical 2448856.859 2449233.787 2448858.001 2449234.796 2449236.775 2449235.943 2449235.811 2449238.841 2449237.745 2449327.654 2449325.611 2449324.631 2449326.605 © Royal Astronomical Society • Provided by the NASA Astrophysics Data System -d -4-> 0) OS a 12.2 12.1 12.0 12.3 12.4 12.5 12.6 0.6376-0.6431 0.8832 0.8919 0.8185-0.8195 0.1899-0.2109 0.0405-0.0475 0.4971-0.5035 0.3442-0.3546 0.2110 0.2306 0.0747-0.0785 0.9231-0.9277 0.6657-0.6717 0.3921-0.3949 0.2278-0.2326 0.0 0.20.4 0.6 0.81.01.21.4 _ / +/ / + %*- / i 1r UKIRT 1992 UKIRT 1993 UKIRT 1993 UKIRT 1992 UKIRT 1993 UKIRT 1993 UKIRT 1993 UKIRT 1993 UKIRT 1993 ** \ Kitt Peak Kitt Peak Kitt Peak Kitt Peak I \ \ J L \ 12.361 ± 12.300 ± 12.476 ± 12.413 ± 12.325 ± 12.518 ± 12.388 ± 12.317 ± 12.471 ± 12.380 ± 12.240 ± 12.430 ± 12.359 ± \ / K magnitude N / 0.051 0.004 0.003 0.017 0.002 0.002 0.004 0.002 0.004 0.021 0.006 0.004 0.014 Orbital phase \ ! \ / \ To transformthislightcurveintoapparentmagnitude,we ‘local standards’ineachframe.Examinationoffieldstars divided thecountsobtainedfromV404Cygbythoseoftwo metric systemsissignificant,andsoweappliedacolour be extrapolated.Thismayleadtoacolour-dependenterror correction bothtothecomparisonstar,andV404Cyg.It showed thatthecolourcorrectionbetweentwophoto- fitting ahistogramofthedatavaluestoGaussiandistribu- ellipsoidal modulationofperiod6.5dissmall(abouthalfa further systematicuncertaintyof0.004magtoallthe (see Section3).Finally,wetiedthemagnitudesoflocal star intheUKIRTfieldofview,andsocorrectionhadto should benoted,however,thatV404Cygwasthereddest per cent).Thuswebinnedthedatapoints(748fromUKIRT the expectedvariationduringnightresultingfroman light curvegiveninTable1.Eachdatapointwasderivedby photometry. standards tothoseofUKIRTstandardstars,whichaddsa points withalargedeviationfromthemean,whichare tion, andtakingtheresultingmeanvalue.Thisremoves and 151fromKPNO)intolongertime-spans,toyieldthe target orthelocalstandardstarphotometricaperture.The caused bypoorlycorrected‘bad’pixelslyingwithineitherthe to lessthanabout1percentdataframe,however,the robust estimateoftheerrors.Whenexpectederrorfalls aperture photometryroutinethatweused(SNC94)givesa observed scatterintheobservationsremainsatabout -N i The durationofeachnight’sobservationissoshortthat I * \ V T V404 Cyg Comparison star The blackholeinV404CygLI1 / \ ** \ I * \ \ 19 94MNRAS.2 7IL. .IOS 2 L12 T.Shahbazetal. (SNC93). ThustheerrorsgiveninTable1arestandard These dataweredominatedbyamodulationof0.2-mag V404Xyg from1990,aboutayearafteroutburst(CNP). given byCasares&Charles(1994),toproduceanorbital time-bin. Finally,thedatawerefoldedonephemeris light curve(Fig.1). errors calculatedusingthestandarddeviationwithineach was stillpresentintheIR,weobtainedabout6hofcontinu- it weakeningintheyearsafteroutburst.Toseewhetherthis modulation isstillunknown,butthedataareconsistentwith optical photometryandspectroscopy.Thecauseofthis amplitude ataperiodof5.9h,whichwasalsopresentin ous coverage;theresultsareshowninFig.2,alongwith set. Thedatadonotshowanysignificanttrendsorflaring behaviour, anydeviationfromtheexpectedlightcurvebeing overall ellipsoidallightcurvefromthefittoentiredata We fittedtheorbitallightcurvewithanellipsoidalmodel was avariablecontaminatingcomponentin1991. behaviour. Weconclude,therefore,thatthe6-hperiodicity less than0.03mag,andshort-lived(lessaboutanhour). temperature ofeachelementthesecondarystarsurface, PARAMETERS than itwasin1991(K=12.1to12.4),thissuggeststhatthere reduced inamplitude.SinceV404Cygisnowslightlyfainter observed inearlieryearsisnoweitherabsentormuch Our shorterrunsonothernightsareconsistentwiththesame SNC94). Theonlydifferenceisthat,aftercalculatingthe 1 percentlevel,probablybecauseofgapsbetweenpixels similar tothatusedforCenX-4andA0620-00(SNC93; 3 MODELFITTINGANDDERIVED Figure 2.K-bandlightcurvesof V404Cygandacomparisonstar,lastingforabout6h.Theslow increaseinfluxisconsistentwiththe caused bythetarget orlocalstandardstarsfallingon apoorlycorrected‘bad’pixel. ellipsoidal modulation,whosebest-fitting lightcurvetotheentiredatasetisshownasadashedline. Thefewpointswithlargedeviationsare We havealreadypresentedlimitedIRphotometryof © Royal Astronomical Society • Provided by the NASA Astrophysics Data System •d 5 o ñ 11.8 12.0- 0.18 0.190.20 0.210.22 Orbital phase 2 2 2 1 ó 1 The bestfitgives^=15.2at<7=5,i62°.Fittingofacon- model atmospherewithsurfacegravitylogg=4.0(Kurucz the fluxiscalculatedbyassumingaKuruczsolar-abundance dary beingtakenas4360K,closetothatderivedbyCNP, parameters wereqand/,phasezerobeingfixedbythe therefore derivedtheerrorsforourfitbyrescalingerror bars suchthatthebest-fittingxlwas1,andthenchoosing colour correctionbetweentheUKIRTandKPNOdata.We is notaboutunitysuggeststhatthereaproblemwiththe and consistentwiththetemperaturederivedinSection4. spectroscopic ephemeris,andthetemperatureofsecon- fashion toV404Cyggives%J=4.5.Thatthisvalueof stant magnitudetoacomparisonstarreducedinanidentical Margon &Bowyer1976).Fig.3showsdieresultingallowed tribution fromabrightspot,andtoshiftphasezerowith 90 percentconfidenceregiontobe%+6.25(Lampton, iments significandyaffectedthefittodata,andnone experimented byallowingthefittingproceduretoaddacon- values fortherotationalbroadeningofvsini=39.1kms" 1991), ratherthanbyassumingablackbody.Thefree with thevalueformassfunctionallowsustoobtaina with thisvalueof<7,wefindi=56,whichwhencombined the (/,q)relationshipobtainedfromellipsoidalstudy (Casares &Charles1994),weobtain<7=16.7.Constraining and theradialvelocitysemi-amplitudeofK=208.5kms“ in asimilarmannertothatdescribedbySNC94.Usingthe scopic studytoobtainthemassesofsystem’scomponents changed thederivedinclinationofsystembymorethan respect tothespectroscopicephemeris.Noneoftheseexper- 0.4 percent. complete solutionforbothmasses,theorbitalseparationand parameter spaceforV404Cyginthei-qplane.Wealso 2 We cannowcombinetheellipsoidalstudywithaspectro- 0.23 0.24 19 94MNRAS.2 7IL. .IOS (1971) formularespectively.WepresenttheseinTable2, mass oftheblackholeasafunctionsecondarystarmass. technique discussedbySNC94.Fig.4showstheallowed the radiusofsecondarystar.Thelattertwoparameters along withtheirerrors,derivedusingtheMonteCarlo are obtainedusingKepler’sThirdLawandPaczyñski’s The massesdeducedfortheblackholesinbothV404Cyg that wecanimmediatelyruleoutscenarioswheretheblack tively large.TheerrorsforV404Cygaresufficientlysmall (10-15 M)andV616Mon(5-17:SNC94)arerela- 4 DISCUSSION Figure 3.The68percent(dashedline)and90(solid 0 ratio planeresultingfromourfittotheellipsoidallightcurve. confidence regionsallowedforV404Cygintheinclination-mass © Royal Astronomical Society • Provided by the NASA Astrophysics Data System Table 2.SystemparametersforV404Cyg(with90percentconfidenceregionsderived using aMonteCarloerrorpropagationtechnique). Parameter Inclination i(degrees) Secondary effectivetemperatureatpole (K) Secondary luminosityL2(L©) Secondary coremassM(M©) Secondary radiusR2(R©) Secondary massM2(M©) Parameters derivedfromellipsoidalstudyandspectroscopicdata: Secondary predictedcolour(V—K) (mags) Mean secondaryabsolutemagnitude Mk(mags) Assuming strippedgiantmodel: Orbital separationa(R©) Primary massMi(M©) Visual extinction A (mags) System distanceD(kpc) Mean secondaryabsolutemagnitude My(mags) Matching strippedgiantluminosityto ellipsoidalmodelluminosity: c v hole isformedbythemergerofneutronstars,providedonly Friedman &Ipser1987). maximum massforamaximallyrotatingneutronstar-see that theyhadmassesoflessthanabout4M(thetheoretical binary. Ifcollapsetoablackholeoccurswiththesame binary isalow-mass(approximately1M)starinwide classical scenariosofLMXBformation,wheretheinitial velocity kick(e.g.Bailes1989),whichislikelytounbindthe unbind theLMXBprogenitor.Secondly,observations degree ofasymmetry,itslargermassisevenmorelikelyto orbit aroundtheblackholeprogenitor.Itisthoughtthat supernova collapseintoaneutronstarproduceslarge suggest thatbinarieswithextrememassratiosmaybevery 0 0 Figure 4.The68percent(dashedline)and90(solid the spectroscopicmassfunctionandratio. resulting fromcombiningourfittotheellipsoidallightcurvewith confidence regionsallowedforV404Cygintheplane High blackholemassespresenttwoproblemsforthe 0.5 0.60.70.80.91.0 Lower 0.213 limit 10.18 4170 0.5 5.5 0.1 3.3 2.2 3.2 2.2 52 32 10 The blackholeinV404CygL13 MASS OFSECONDARY(M) 0 Most likely value 0.216 10.20 4355 0.7 6.0 0.0 3.4 3.4 56 34 12 Upper 0.221 10:23 limit 4490 -0.1 6.7 3.6 1.0 3.6 3.7 3.3 60 37 15 19 94MNRAS.2 7IL. .IOS 38-1 2 wachs 1987).Boththeseeffectswilltendtomakeblackhole fact, theoppositeseemstobecase,relativeproximity rare comparedwiththoseofmoreequalmassratios(Halb- LMXBs rarecomparedwith,say,thebrightbulgesources.In problem isinsurmountable,astheremaybeproblemswith of theknownblackholeLMXBscomparedwithneutron Thorne-Zytkow object,assuggestedbyPodsiadlowski, It isinterestingtonote,though,thatevolutionviaa the velocitykickimpartedduringcollapseintoablackhole. (Halbwachs 1987),andfurtherinvestigationsareneededinto observational selectioninourstatisticsforbinarymassratios ous (butseethediscussionbyvandenHeuvel1992).Neither star LMXBssuggestingthattheformermaybemorenumer- upper limittothedistancecanbeobtainedbyassumingthat problems. Cannon &Rees(1994),wouldnotsufferfromsuch the observedpeakX-rayluminositywasEddington-limited. Using anobservedpeakX-rayluminosityof obtain liescomfortablybetweentheSchönberg-Chand- implies acoremassof0.216M.Thethatwe equation fortheradiusgivenbyKing(1993),our models ofWebbink,Rappaport&Savonije(1983),as used tomakefurtherpredictionsusingthestrippedgiant limit forMj,weobtaina90percentuppertothe L14 T.Shahbazetal the masstransferisdrivenbyexpansionofsecondary mass ofthesecondarystarabout0.7M.Thislends (above whichastrippedgiantcoremustlie)andthetotal rasekhar limitof0.17thetotalmasssecondarystar depends onlyonitscoremass.Usingtheapproximate distance ofZ)<3.7kpc. support totheevolutionaryscenarioforthesesystemswhere suggested byKing(1993).Theradiusofastrippedgiant Lpk= 1.4x10D£ergs(Tanaka1989)andourupper function ofcoremass.Wefind,usingtheapproximate (Mukai 1994);orthatofasubgiant,asmaybethecasefor SNC93; SNC94).Theexpansioncanbethatofamain- star, whichdrivesthesystemtolongerorbitalperiods(e.g. for astrippedgiant.Duetogravity-darkeningeffects,this L©. Wethereforeadjustedthetemperatureofpoleour equation forthemodelluminosity(King1993),L=10.20 of V404Cyg. Cen X-4(SNC93);orthatofastrippedgiant,asinthecase sequence star,whichmaywellbethecaseforA0620-00 model secondaryuntilitsluminositymatchedthatpredicted the secondarystar(seeTable1).Wecanderiveanupperlimit to predictabsoluteKandVmagnitudes,thecolourof temperature issignificantlydifferentfromthatpredictedfor to thereddeningbycomparingmodelandobserved a blackbodyofthesameradius.Themodelcanbeused colours. Wethusobtaina90percentconfidenceupperlimit upper limitsforthedistance andreddeningtoobtain A/=0.12 (Rieke&Lebofsky 1985).Wecanusethe of A<>33byassumingnoaccretiondisccontaminationin using theabsolutemagnitude (seeTable2)andthedistance corresponding lowerlimitsfor thereddeninganddistance 0 modulus formula. 0 kpc K, 0.1-magcontaminationinV(i.e.F=18.5:CNP)and eapc 2 Ky v Using thevalueformassofcompactobject,an Our solutionfortheradiusofsecondarystarcanbe The strippedgiantmodelalsopredictstheluminosityasa © Royal Astronomical Society • Provided by the NASA Astrophysics Data System We havepresentedanellipsoidalstudyofV404Cyg,which, when combinedwithspectroscopicdata,allowsustoobtain the blackholeisrelativelylarge(12M),whichpresents giant, theevolutionofwhichisdrivingmasstransferin of thesecondarystarisconsistentwithitbeingastripped a completesolutionforthebinaryparameters.Themassof 5 CONCLUSIONS ACKNOWLEDGMENTS some difficultiesforstandardevolutionarymodels.Themass We thankPATTforenablingustoobserveV404Cygat system. 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