DRAFTVERSIONJANUARY9,2014 PreprinttypesetusingLATEXstyleemulateapjv.2/16/10 THESPINOFTHEBLACKHOLEGS1124-683:OBSERVATIONOFARETROGRADEACCRETIONDISK? WARRENRMORNINGSTAR,1JONM.MILLER,1RUBENSC.REIS,1KENEBISAWA2 DraftversionJanuary9,2014 ABSTRACT Were-examinearchivalGingadatafortheblackholebinarysystemGS1124-683,obtainedwhenthesystem wasundergoingits 1991outburst. Ouranalysisestimatesthedimensionlessspin parametera∗ =cJ/GM2 by 4 fittingtheX-raycontinuumspectraobtainedwhilethesystemwasinthe“ThermalDominant”state. Forlikely 1 valuesofmassanddistance,wefindthespintobea∗=- 0.25-+00..6045(90%confidence),implyingthatthediskis 0 retrograde(i.e.rotatingantiparalleltothespinaxisoftheblackhole).Wenotethatthismeasurementwouldbe 2 betterconstrainedifthedistancetothebinaryandthemassoftheblackholeweremoreaccuratelydetermined. Thisresultis unaffectedbythe modelusedto fitthe hardcomponentofthe spectrum. Inorderto be ableto n a recoveraprogradespin,themassoftheblackholewouldneedtobeatleast15.25M⊙,orthedistancewould J needtobelessthan4.5kpc,bothofwhichdisagreewithpreviousdeterminationsoftheblackholemassand distance. Ifweallow f tobefree,weobtainnousefulspinconstraint. Wediscussourresultsinthecontext 8 col ofrecentspinmeasurementsandimplicationsforjetproduction. ] Subjectheadings:accretion,accretiondisks,blackholephysics,spin E H . 1. INTRODUCTION al1995,Milleretal. 2002,Milleretal. 2004). h A common XSPEC model to describe the thin accretion Spinningblackholes(BHs)areoffundamentalimportance p disk is kerrbb (Arnaud 1996; Li et al. 2005). This model toastrophysics,becausetheyrepresentlaboratoriesfortheex- - standsoutsinceittakesthespinasaparameterusedtodefine o plorationofGeneralRelativity.Spinisconstrainedbyindirect the modelspectrum. It also includesrelativistic effectssuch r measuresinvolvingtheaccretiondisk. Alow-massX-raybi- t aslimb-darkeningorselfirradiationofthedisk. Inorderfor s nary (LMXB) is an example of a binary in which the black a hole(orneutronstar)isorbitedbyasmallstar,usuallywitha this method to be used to estimate spin, the mass, distance, [ andinclinationangleofthediskmustbeknown(Zhang,Cui, masslessthanthatoftheSun.ThestarusuallyfillsitsRoche lobeanditsoutermostlayersofgasarestrippedoffitssurface &Chen1997). Additionally,thespinmeasurementisdepen- 1 dent on the color correction factor (f =T /T ). Again, v by the immense gravity of the compact object, and form an col col eff kerrbb is useful, since it accepts all of these as input model 4 accretiondisk. parameters. Other new models, such as simpl (Steiner et al. 9 Inperiodsofincreasedaccretionactivity,X-rayNovaecan 2009a)offeranimproveddescriptionofthehardcomponent 7 occur. X-rayNovaearegenerallytransientphenomena,wait- relativetoapowerlaw. Thepairingofkerrbbandsimplhave 1 ing on average 10-50 years between outbursts (Tanaka & beenusedseveraltimestomeasurespin(seeforexampleGou . Shibazaki 1996). Attempts to create a unified model of the 1 etal. 2009,Steineretal. 2010,etc). diskevolutionintheseoutbursts(Esinetal. 1997)haveledto 0 the description of the outbursts as the combination of a thin 4 accretion disk and an AdvectionDominated AccretionFlow 2. SOURCEANDDATASELECTION 1 : (ADAF).Observationally,these two migratethroughseveral GS1124-683(alsocalledNovaMuscae1991)isaLMXB v spectralstates (see e.g. Reynolds& Miller 2013). The state thatunderwentanoutburstin1991. ItwasdiscoveredinJan- Xi importanttothisanalysisistheThermalDominantState(TD uary1991bytheAllSkymonitorsonboththeGingasatelite, state, formerlyreferred to as High State or High/Soft state), andtheGranatsatelite (Makinoetal. 1991;Lund&Brandt r a in which the disk extends all the way to the innermost sta- 1991; Kitamoto et al. 1992; Brandt et al. 1992). It flared blecircularorbit(ISCO),anddominatestheemission(Esinet upto amaximumfluxof8Crab(1.92×10- 7 ergscm- 2 s- 1) al. 1997). Since the ISCO is entirely dependanton the spin onJanuary15,andsubsequentlydecayedexponentiallywith (rISCO =6rg for a schwarzschild BH, rISCO =rg for a maxi- atimescaleτ =30days(Ebisawaetal. 1994). Itwasstudied mally prograde BH, rISCO =9rg for a maximally retrograde usingGinga(Ebisawaetal. 1994)overthecourseofseveral BH),measurementsoftheradiusoftheISCOcanbeusedto months,duringwhichitmigratedthroughall5ofthetypical determinethespinoftheBH.Thisistheideabehindthecon- spectralstates. tinuumfittingmethod,inwhichonefitsamodelofathinac- The BH mass, distance, and inclination have been refined cretiondisktoThermalDominantStatespectraofaBHtoes- several times. Shahbaz et al. (1997) modeled the infrared timatetheISCO,andthusinferthespin(Zhang,Cui,&Chen lightcurvetodeducetheBHmass,themassofthesecondary 1997,Schafeeetal. 2006,McClintocketal. 2006,etc.). Spin star, the binary separation, and the binary inclination. They canalsobemeasuredbymodelingthebroadenedIronK-shell alsoinferredfromthesethedistancetotheBHusingBailey’s emissionlinethatoriginatesintheinnerdisk(e.g. Tanakaet relation (Bailey 1981). In fact the distance to GS 1124-683 hasbeenrevisedbyseveralauthors(Della Valleetal. 1991; 1DepartmentofAstronomy,UniversityofMichigan,500ChurchStreet, Oroszetal. 1996;Shahbazetal. 1997;Gelinoetal. 2001), AnnArbor,MI48109-1042,[email protected],[email protected] 2InstituteofSpaceandAstronauticalScience(ISAS),JapanAerospace themostrecentofwhichbeingGelino(2004,HereafterG04), Exploration Agency (JAXA), 3-1-1 Yoshino-dai, Chuo-ku, Sagamihara, whorefinedthemethodfromGelinoetal. (2001;therefined Kanagawa252-5210,Japan methodisdescribedinGelino,Harrison,&Orosz2001)and 2 Morningstaretal. 1 0.1 normalized counts s keV−1−1 01111.00000−−−−16543 ons cm s keV)−2−1−1 110 ot h 1.4 P V (2 1.2 ke ratio 1 0.1 0.8 0.6 2 5 10 20 1 10 Energy (keV) Energy (keV) FIG.1.—(Left)AllspectraofGS1124-683usedinouranalysis,andthedatatomodelratios. Thelargeerrorsabove20keVareasaresultofdiminishing sensitivityathigherenergy. (Right)Bestfitmodeltoourdata. Inallcasesthediskdominatestheemission,andinseveralofthespectra,thehardcomponent becomesveryfaint foundthe distance to be 5.89±0.26kpc, which falls within spectrum.WealsoignoredtheApril19observationaltogether the range allowed by Orosz et al. (1996), but is better con- becauseitrequiredanexcessivelylowcolorcorrectionfactor strained. The inclination angle measurement is much better in orderforthe spin to be consistentwith the otherobserva- agreedupon,withthevaluefromG04of54◦±1◦.5agreeing tions(1.36),andbecauseithadaχ2 valuethatwastoohigh ν withthatfromShahbazetal. (1997). Themassisalsofairly (∼3)when f wasrequiredtobewithinourallowedrange col well agreedupon, with the measurementof 7.24±0.70M⊙ (1.5-1.9,seeShimura&Takahara1995). Forallotherobser- from G04 correspondingto those made previouslyby Shah- vations,weexaminedovertheentirereliableenergyrangefor bazetal. (1997),andthosemadebyOroszetal. (1996). We dataobtainedwithGinga;1.2-37.0keV(Ebisawa1991). usedthebestfitvaluesfromG04formass, distance, andin- 3. ANALYSIS clinationbecausetheyare newerand better-constrainedthan other determinations, and since they were found using in- AllanalysiswasperformedinXSPECversion12.8.0(Ar- fraredphotometry,fromwhichthe disk andhotspotproduce naud1996). The modelcentralto ouranalysis is kerrbb (Li lesscontaminationinthelightcurve. Itshouldalsobenoted et al. 2005), which models a thin accretion disk around a thatweassumetheinclinationangleoftheinnerdisktobethe kerrblackhole.Kerrbbisconvolvedwithsimpl(Steineretal. same as that of the binary, which is not necessarily the case 2009a),anempiricalmodelforComptonization. Thismodel (e.g.Maccarone2002). providesa more physicaldescriptionof the hard component TheX-raydataweconsiderarethosepresentedinEbisawa (as opposed to powerlaw), and yields fits of equal statisti- et al. (1994). For the continuumfitting method, we wantto cal quality. It also has the virtue of simplicity compared to usespectraobtainedwhenthesourcewasintheTDstate. As morerigorousmodelsofComptonization(suchascompTTor per McClintock et al (2006), we selected disk luminosities compBB). less than 30% of the Eddingtonlimit, and restricted our ob- Inaddition,weincludedtheeffectsofabsorptionbythein- servationsto those in which the soft flux contributesat least terstellarmedium,tbabs(Wilms,Allen,&McCray2000).We 90% of the total flux (F /F ≥0.9) based on the results fixedthehydrogencolumndensityto1.5×1021cm- 2, which soft tot reported in Ebisawa et al. (1994). Assuming a distance of isthebest-fitvaluefoundforNH inEbisawaetal. (1994).We 5.89kpc(G04),wefindthatthepeakluminosityreachedwas alsofounditnecessarytoaddaGaussianlinewithenergy6.5 7.97×1038 ergs s- 1, which, assuming a black hole mass of keV,andwithitswidthallowedtovarybetween0and1keV. 7.24 M⊙ (G04), is about 0.87 Ledd. Assuming an exponen- Relativisticlinesdidnotimprovethefitbyastatisticallysig- tialdecaywithatimescaleof30days(Ebisawaetal. 1994), nificantmargin.Altogether,thismodelisshowninFigure1. wefindthatobservationsfallingintoourluminositycriterion We fixed the mass, distance, and inclination to the mea- begin32daysafterJanuary15(Feburuary16). Observations surementsgiven by G04, and fixed the norm of kerrbb to 1, fallingintoourhardnesscriteriabeganonFebruary16aswell, as should be done when mass, distance, and inclination are and ended on May 18, when the source transitioned to the fixed(Shafeeetal. 2006,McClintocketal. 2006,etc.). We Low/Hardstate. didnotincludetheeffectsoflimb-darkening.Weallowedthe Some spectra required additional consideration due to spin(a∗),effectivemassaccretionrate(M˙),photonindex(Γ), anomalousbehaviorstheyexhibited. AsnotedinEbisawaet andfractionoftheseedphotonsscattered(fsc)tovaryfreely al. (1994),observationsoccuringinlateMarchandthrough- andunconstrained,andthecolorcorrectionfactor fcoltovary outApril had a hard componentthat was too faintto be ob- between1.5and1.9(ShimuraandTakahara1995).Weadded seervedbytheGingadetectors. Forthosespectra(March28, a 2 percent systematic error to all energy bins to ensure ac- 29,30,andApril2),wewererequiredtoignoreoutsideofthe ceptablefits,typicalforanalysesofGingadata. energyrange1.2-10keV.ForthefirstoftheMay17spectra, We fitted spectra individually at first. For those fits that thehardcomponentbecametoofainttobeobservedatener- ignoredlargeportionsofthehardcomponent,thespinswere giesexceeding 25keV,so we ignoredthoseenergiesin that notverywellconstrained.Inordertoplacetighterconstraints on the spin, we found it better to jointly fit all spectra. For 3 retrograde. The lower boundhere is very relaxed, since our analysisallowsuncertaintytopropagatefromuncertaintiesin the mass and distance withouttaking accountof the statisti- calpreferencesinside of our allowed range. Figure 2 shows 6.15 1.0 the result of the grid search, which expresses the extent at whichdifferentpairingsofmassanddistanceaffectourmea- surement of the spin. For all parameters, the uncertainties 0.8 expressed in Table 1 reflect the upper and lower limits esti- d5.89 mated fromour grid search. The χ2ν valuesfor this analysis 0.6 favorasmallermagnitudeofthespin,smallermagnitudesof the distance, and larger masses for the BH than the best-fit 0.4 valuesfromG04. Toplaceatighterconstraintona whiletakingaccountof ∗ 5.63 0.2 ouruncertaintiesinthemassanddistance,weallowedMand d to vary within our grid range but kept them jointly deter- mined. Wedidfitssteppingthrough20evenlyspacedvalues 6.54 7.24 7.94 M ofa between-0.97and0.03usingsteppar. Figure3shows ∗ the result. Here the bestfit value for the spin lies between - FIG.2.— Results ofa Gridsearch through the mass/distance parameter space. Thesizeofthecircles isproportional tothemagnitude ofthespin 0.5and-0.2with90%confidence,whichisbetter-constrained |a∗|.Circlesfilledbluehavelowerχ2thanthefitusingthebest-fitmassand than the value estimated from the grid search since it takes distanceinG04(439.0≤χ2≤441.5), andtheredcircles havehigherχ2 account of the behavior of χ2 with respect to mass and dis- (443.0≤χ2≤447.0).Allabovefitshaveν=344. tanceratherthanthegridsearch,whichtreatseachpairingas equallylikely. The spin hereisgreaterthan -1.0at justover 3σ, is less than -0.15 at the 6σ level, and is less than 0 at 10 >>8σ (the p-value for a∗ =0 is ∼10- 102). We choose to usetheconfidencerangeestimatedfromourgridsearchhow- ever, since it was calculated with M and d fixed, which is a 8 necessityforfindingspinbyfittingthecontinuum. Asacheckonourresults,wedecidedtoexaminethebehav- 99% iorofa aswechangedcertainotherparameters,namelythe ∗ 6 colorcorrectionfactor f . Thisisa usefulcheck, sinceour col 2∆χ valueof fcolisclosetotheminimumoftheallowedrange.We fixeditsvalueto1.7andfitallotherparameters. Wefindthat 4 raisingthevalueof f eventhishighresultsinthespinim- col 90% mediatelybeingpeggedata∗=- 1,thetheoreticallimit. This furthersolidifiesourdeterminationofa asbeingretrograde. 2 ∗ 68% 5. DISCUSSION A retrograde spin is atypical in a black hole LMXB. 0 −1.0 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 a Nonethelessourmeasurementisconsistentwithpreviousat- ∗ temptstomeasurethespinforGS1124-683.Suleimanovetal FIG.3.—SpinContoursforGS1124-683obtainedwhileholdingmassand (2008)constrainedittobe≤0.4,andZhang,Cui, andChen distance withinthe parameter space usedforthegridsearch, butallowing (1997)estimatedittobenearlySchwarzschild,yetretrograde themtobevariable, jointly-determined parameters. Horizontaldottedlines aredrawnatthe68%,90%,and99%confidencelevels. (-0.04). Although our method is descendant from Zhang et al. (1997), ours yields a different measurement of the spin jointfits,werequiredthespin,andspectralhardeningfactorto sinceittakesadvantageofnewermodelsdeveloped(kerrbb& bejointlydetermined,andallowedtheresttovaryasbefore. simpl),whichprovideamorephysicaldescriptionofthespec- To examine the full allowable parameter space (since we trum,andallowforrelativisticeffects. Recentworks(Reiset do not have entirely precise measurements of mass and dis- al. 2013, Gou et al. 2010)have measured spins for SWIFT tance),wedida3×3gridsearchofmassanddistance,fitting J1910.2-0546 and A06200-00 that are either retrograde, or the spectra for each pairing, finding the best fit parameters, consistentwithbeingretrograde,implyingthatsuchspinsare andestimatingtheiruncertainties.Thepointsonourgridcor- lessrarethanpreviouslythought. respond to the best fits of mass and distance from G04, and Furthermore, as shown in Figure 3, our upper limit to the theirupperandlowerlimits. Theuncertaintyfoundhereprop- spinisstillretrograde. Ifthespinisactuallyprogradeoneof agatesinto the uncertaintyin our spin measurement,since it twothingsmustbetrue.Eitherthedistancemustbeconsider- isentirelyallowedthattheBHcouldhaveanycouplingofpa- ablysmallerthanthatgivenbyG04,ortheBHmassmustbe rameterswithinthatgrid.Togloballycoverthisspace,andto larger.Tofindouthowmuchcloser,ormoremassiveitneeds findthebest-fitvaluesofallparameters,we fittedwithmass to be, we fixed eithermass or distanceto their best determi- anddistancerequiredtobejointlydetermined,butallowedto nationfromG04,andslowlyraisedorloweredtheotheruntil varywithinthisgridrange. theirbestfitvalueofa wasgreaterthan0. Whenwevaried ∗ the mass, and held the distance constant, we found that GS 4. RESULTS 1124-683must have MBH ≥15.25 M⊙. This is in disagree- Table 1 shows the results of spectral fitting. The best-fit mentnotonlywithG04,butalsowithShahbazetal. (1997), valueofthe spinis a∗=- 0.25+- 00..0654, implyingthatthe spin is whoconstrainedtheBHmasstobelessthan10.5M⊙ atthe 4 Morningstaretal. TABLE1 SPECTRALFITTINGRESULTS Time Γ fsc a∗ M˙ fcol σ norm (UT;1991) (10- 3) (cJ/GM2) (1018gs- 1) (keV) (10- 3photonscm- 2s- 1) 2/20 23:31-23:36 2.08+- 00..0043 13.9+- 10..07 - 0.25+- 00..0654 8.0+- 40..12 1.51+- 00..1001 1.0+- 00.07 22±3 2/21 0:23-0:29 2.12+- 00..0043 14.8+- 10..18 - 0.25+- 00..0654 8.0+- 40..12 1.51+- 00..1001 1.00+- 00.04 26+- 43 3/8 18:04-18:21 1.68+- 00..1019 0.9+- 00..21 - 0.25+- 00..0654 5.5+- 20..81 1.51+- 00..1001 1.0+- 00..003 4.1+- 10..07 3/10 16:56-17;16 1.8±0.3 0.8+- 00..53 - 0.25+- 00..0654 5.0+- 20..61 1.51+- 00..1001 1.0+- 01.0 0.7+- 10..17 3/20 12:56-13:56 2.8+- 00..32 2.5+- 10..47 - 0.25+- 00..0654 5.0+- 20..61 1.51+- 00..1001 1.0+- 00..01 3.1+- 10..07 3/28 9:37-9:42 2.6(frozen) 2.0+- 00..43 - 0.25+- 00..0654 5.8+- 30..01 1.51+- 00..1001 0.4+- 00..64 0.7+- 10..57 3/29 5:54-6:05 2.6(frozen) 0.6±0.3 - 0.25+- 00..0654 5.7+- 20..91 1.51+- 00..1001 0.8+- 00..23 2+- 10..28 3/30 8:36-8:53 2.6(frozen) 1.1+- 00..42 - 0.25+- 00..0654 5.4+- 20..81 1.51+- 00..1001 0.8±0.1 5.4+- 10..17 4/2 5:04-5:29 2.6(frozen) 1.1+- 00..92 - 0.25+- 00..0654 5.4+- 20..81 1.51+- 00..1001 0.8±0.2 2.0+- 10..17 5/17 3:12-3:19 1.98+- 00..0087 9+- 21 - 0.25+- 00..0654 1.73+- 00..903 1.51+- 00..1001 1.00+- 00..007 4.8+- 00..56 5/17 4:34-4:56 1.88+- 00..0054 9.01-.01.7 - 0.25+- 00..0654 1.85+- 00..9053 1.51+- 00..1001 1.00+- 00..0005 7.0+- 00..45 5/17 7:49-8:09 2.05±0.04 15±1 - 0.25+- 00..0654 1.81+- 00..9033 1.51+- 00..1001 1.00+- 00..0002 7.4±0.5 NOTE.—Resultsofjointspectralfitstotheobservationsinoursample.Theχ2valueforthebestfitis439.57(342DOF). 90% confidence level using the maximum mass of the sec- ondary star (Inferred from the spectral type). This makes a 1000 massof 15.25M⊙ unlikely,so if the blackhole isprograde, it is more likely that the distance to the binary is lower. In fact, in orderforthespinto beprograde,thedistancewould 100 have to be d ≤4.5 kpc, still greater than the maximum al- lowed distance from Shahbaz et al. (1997). If we take their entirerangeof massand distanceinto accounthowever,and 10 performagridsearch,wefindthatthespinfoundusingtheir wer o bestdeterminationofthemassanddistanceisstillretrograde P (a∗=- 0.16forM=5.8M⊙ andd=4kpc),thereisnolower Jet 1 boundona∗,andtheupperboundisa∗<0.7. Other models, such as that from Ebisawa et al. (1994), whichassumea∗=0arealsoincompatiblewiththemassand 0.1 Γ=2 Γ=5 distance ofG04. These modelssuggestthat the masswould needtobeatleast16M orthedistancewouldneedtobeless ⊙ than 2.65 kpcin orderto measure an inner radiusconsistent 0.01 -1 0 0.5 0.9 -1 0 0.5 0.9 0.99 with a =0. An additionalway to retrieve a retrogradespin a ∗ ∗ wouldbetolower f to 1.0,whichissuggestedbyourmea- col sured value existing near the hard limit of 1.5. If we allow FIG.4.—Comparisonofourmeasuredspinandthecalculated jetpower (blue)withthebestfitempiricalmodelfromNarayan&McClintock(2012), fcol to be free, we find that its best fit is fcol =1.17-+00..2385, but andwithH1743-322(addedinSteiner,McClintock&Narayan2013),having the spin no longerhasany constraint. We choose to use our Γ=2(left)orΓ=5(right). range of f because these are the range of values expected col fortherangeofluminositiesinoursample(Shimura&Taka- was used by Steiner, McClintock & Narayan (2013) to pre- hara1995).TheEbisawaetal.(1994)modelcanalsobefixed dict the spins of 6 black holes including GS 1124-683. In byincreasingrin,implyinga∗<0. theiranalysis,theyonlyconsideredprogradespins,asnoret- Toexaminehowa isaffectedbythehardcomponentofthe rogradespinshadbeenobservedusingtheCFmethodatthat ∗ spectrum,wetriedusingpowerlawinsteadofsimpltomodel time. Tocalculatejetpower,weusedtheirprescription: the hard component. This represents a less physical model than simpl, but it producesa check on our result. For these P = ν Stνo,t0 D 2 M - 1 (1) fits Γ and the normalizationwere allowed to be free and in- jet (cid:18)5GHz(cid:19) (cid:18) Jy (cid:19) (cid:18)kpc(cid:19) (cid:18)M⊙(cid:19) dependantbetweenspectra. When thismodelis fitted to the data,wefindthespintobea∗=- 0.46+- 00..0223,consistentwiththe whereSνto,t0isthebeamingcorrectedflux. resultobtainedusingsimpl. Itisalsointerestingtoconsiderhowourresultfitsintothe Stνo,t0=Sν,obs×(Γ[1- βcosi])3- α (2) contextofjetproduction,sinceveryfewretrogradespinshave Γisthelorentzfactor,whichweassumedtobe2(tocom- been observed, making GS 1124-683 an interesting test of paretotheirderivedrelationshipforΓ=2.Itshouldbenoted currentempiricalmodels. Onesuchmodelwassuggestedby thatΓislikelynotthesameforalljetsources.),αistheradio Narayan&McClintock(2012),whichsuggeststhatthescaled spectralindex,whichis 0.5-0.6forGS1124-683(Balletal. jet power is proportionalto the black hole spin. This model 1995).βfollowsfromΓ,andiistheinclinationofthesystem, 5 forwhichwe used54◦ (G04),since we usedthe samevalue (1) For the most recentdeterminationsof mass and distance tomeasurethespin.Usingthemaximumradiofluxsuggested to GS 1124-683,the spin is most likely - 0.25+0.05. Thereis - 0.64 byBalletal. (1995)of≈0.2Jy,thescaledjetpoweristhen an upper limit to the spin of -0.15 (6σ level). This result is ≈0.92in naturalunits. Arbitrarilyassuming an error in the independantofthemodelusedtofitthehardcomponent. radiofluxofafactorof≈0.5(followingthemethodologyof (2)KeepingthedistanceheldwithintheconstraintsfromG04, Narayan & McClintock 2012), and using our determination the minimum mass for GS 1124-683where we can derive a ofspinfoundfromourstepparrun,wefindthatourspinmea- progradespinisM=15.25M⊙. surementisconsistentwiththeirbestfitmodel(seeFigure4) (3) Keeping the mass held within the constraints from G04, which predicts Pjet =1.08+- 00..6493 for a∗ =- 0.25, It is different themaximumdistancefromwhichwecanpotentiallyresolve fromthedeterminationofthespininSteiner,McClintock,& aprogradespinisd=4.5kpc. Narayan(2013)onlybecausetheyhadassumedthatthespin (4)Ifwerequirethecolorcorrectionfactor fcol tobefixedat would be prograde, and because they used values for mass 1.7forallspectra,thespinbecomespeggedatthehardlimit andinclinationdifferentfromthemeasuredmassandinclina- of-1. Theupperlimitnecessarytoavoidthisis fcol=1.67. tion.Wenotethatafullconsiderationofthecurrentdatadoes (5)GS1124-683agreeswiththeempiricallyderivedrelation- ˙ notfindstrongevidencethatspinpowersjets, withM or|B| shipbetweenblackholespinandjetpowerfromNarayan& potentiallyactingasathrottle(Kingetal. 2013). McClintock(2012)withΓ=2,thoughtherearemanycaveats andassumptions. 6. CONCLUSIONS REFERENCES Arnaud,K.A.,1996,inAstronomicalDataAnalysisSoftwareandSystems McClintock,J.E.,Shafee,R.,Narayan,R.Remillard,R.A.,Davis,S.W.,Li, V,ed.J.H.Jacoby&J.Barnes(SanFrancisco:ASP),17 l.,2006,ApJ,652,518 Baily,J.,1981,MNRAS,218,619 Miller, J. M., Fabian, A. C., Wijnands, R., Reynolds, C. S., Ehle, M., Ball,L.,Kesteven,M.J.,Campbell-Wilson,D.,Turtle,A.J.,&Hjellming,R. Freyberg,M.J.,VanDerKlis,M.,Lewin,W.H.G.,Sanchez-Fernandez, M.,1995,MNRAS,273,722 C.,andCastro-Tirado,A.J.,2002,ApJ,570,L69 Brandt,S.etal.,1992,A&A,254,L39 Miller, J. M., Fabian, A. C., Reynolds, C. S., Nowak, M. 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