Closing in on a Short-Hard Burst Progenitor Constraints from Early-Time Optical Imaging and(20)

The localization of the short-duration, hard-spectrum GRB 050509b was a watershed event. Thanks to the nearly immediate relay of the GRB position by Swift, we began imaging the GRB field 8 minutes after the burst and continued for the following 8 days. No

bluewardof5200 A.Nevertheless,thespectralslopeiswellconstrainedanditsuggeststhatthesegalaxiesareformingstars(i.e.,thecontinuumisrelativelyblue).Thelackofcorrespondingemissionlines(Hα,Hβ,

[OIII]λ5007,[OII]λλ3727)fallinginourspectralwindowthereforesuggeststhatS1andS2havez>～1.3.Additionalspectroscopywillberequiredtocon rmourhypothesisthatS1andS2arefaintbluegalaxymembersofasmallgroupatmoderateredshift.

6.TheoreticalInterpretation

The uenceofthepromptgamma-rayemissionmeasuredbytheSwiftBATisf=(2.3±0.9)×10ergcm 2(Barthelmyetal.2005b),whichattheredshiftofthetentativehostimpliesanisotropicequivalentenergyoutputofEγ,iso=(2.7±1)×1048erg.SinceνFνisstillrisingroughlyasν0.5inthe15–150keVSwiftrange,thetotal uencecouldbe 3timeslargerifthepeakenergyEp 1–2MeV.Figure9showstheisotropicequivalentluminosityofGRBX-rayafterglowsscaledtot=10hraftertheburst(inthecosmologicalrestframeofthesource),LX(10hr),asafunctionoftheirisotropicgamma-rayenergyrelease,Eγ,iso,forGRB050509btogetherwithasampleoflongGRBs.LX(10hr)forGRB050509bisestimatedbyextrapolatingthe uxmeasuredbytheSwiftXRTusingthebest- tpower-lawdecayindexofα=1.3,whichisalsoconsistentwiththeChandraupperlimit. 8

Alinearrelation,LX(10hr)∝Eγ,iso,seemstobebroadlyconsistentwiththedata,probablysuggestingaroughlyuniversale ciencyforconvertingkineticenergyintogammaraysinthepromptemissionforbothshortandlongGRBs.This“universal”e ciencyisalsolikelytobehigh(i.e.,theremainingkineticenergyiscomparableto,orevensmallerthan,thatwhichwasdissipatedandradiatedinthepromptemission).Ifthisisthecase,thewell-knowne ciencyproblemforlongGRBsalsopersistsforshortGRBs.

TheX-rayluminosityat10hrisusedasanapproximateestimatorfortheenergyintheafterglowshock,since(a)at10hrtheX-raybandistypicallyabovebothνmandνcsothatthe uxhasaveryweakdependenceon B[tothepowerof(p 2)/4]andnodependenceontheexternaldensity,bothofwhichhaverelativelylargeuncertainties(Freedman&Waxman2001;Piranetal.2001;Bergeretal.2003);and(b)at10hrtheLorentzfactoroftheafterglowshockissu cientlysmall(Γ≈10)sothatalargefractionofthejetisvisible(outtoanangleof～Γ 1≈0.1radaroundthelineofsight)andlocalinhomogeneitiesonsmallangularscalesareaveragedout.Furthermore,thefactthattheratioofLX(10hr)andEγ,isoisfairlyconstantformostGRBssuggeststhatbothcanserveasreasonablemeasuresoftheisotropicequivalentenergycontentoftheejectedout ow.ApossiblecaveattotheabovestatementarisesiftheobserverisinfactnotwithintheapertureoftheGRBjet(asissuggestedtobethecaseinbothX-ray ashesandX-rayrichGRBs;Granotetal.2005).InthiscaseEγ,isocanbesigni cantlysmallerthantheisotropicequivalentkineticenergyintheafterglowshock,whichisbetterre ectedbyLX(10hr).ThisislikelytobethereasonwhyGRB031203isabovethecorrelationshowninFigure9(Ramirez-Ruizetal.2005).Ano -axisinterpretationforGRB050509b,ontheotherhand,isunlikelysinceitsX-rayafterglowlightcurvewasobservedtodecayfromaveryearlyepoch(att≈102s).ThisisalsoconsistentwiththefactthatGRB050509bfallsclosetothecorrelation.