The Direct Test of Cosmological Model for Cosmic G

arXiv:astro-ph/9707128v111Jul1997TheDirectTestofCosmologicalModelforCosmicGamma-RayBurstsBasedonthePeakAlignmentAveragingIgorG.Mitrofanov,MaximL.LitvakandDmitrijA.UshakovSpaceResearchInstitute,Profsojuznayastr.84/32,117810Moscow,RussiaReceived;accepted–2–ABSTRACTThecosmologicaloriginofcosmicgamma-rayburstsistestedusingthemethodofpeakalignmentfortheaveragingoftimeprofiles.Thetestisappliedtothebasiccosmologicalmodelwithstandardsources,whichpostulatesthatdifferencebetweenbrightanddimburstsresultsfromdifferentcosmologicalred-shiftsoftheirsources.Theaverageemissivitycurve(ACEbright)ofthegroupofbrightBATSEburstsisapproximatedbyasimpleanalyticalfunction,whichtakesintoaccounttheeffectofsqueezingofthetimepulseswithincreasingenergyofphotons.ThisfunctionisusedtobuildthemodellightcurveforACEdimofdimBATSEbursts,whichtakesintoaccountboththecosmologicaltime-stretchingofburstslightcurvesandthered-shiftingofphotonsenergies.DirectcomparisonbetweenthemodellightcurveandtheACEdimofdimburstsisperformed,whichisbasedontheestimatedprobabilitiesofdifferencesbetweenACEsofrandomlyselectedgroupsofbursts.Itshowsnoevidenceforthepredictedcosmologicaleffects.The3σupperlimitoftheaveragered-shiftzdimofemittersofdimburstsisestimatedtobeassmall,as∼0.1−0.5,whichisnotconsistentwithvalues∼1predictedbytheknowncosmologicalmodelsofgamma-raybursts.Subjectheadings:cosmology:theory-gammarays:bursts–3–1.IntroductionThecosmologicalmodelofcosmicgamma-rayburstsiscommonlyaccepted,asoneofthemostpromisingconceptoftheoriginofgamma-raybursts(GRBs).However,ithasnotbeenfinallyapprovedyetbytheobservationaldata.Twocriticaltestsweresuggestedtoverifythebasicmodelwithstandardcosmologicalsources:dimburstshavetobetime-stretchedandred-shiftedincomparisonwithbrightevents.Gamma-rayburstsareknowntohaveverydifferenttimehistories,andonehardlycouldcheckthecosmologicaleffectsbydirectcomparisonbetweenparticularevents.Thesetestsshouldbebasedonsomeaveragedtime-basedandspectrum-basedsignatures,whichrepresentthebasicpropertiesofGRBs.SeveralstatisticaltestshavealreadybeenimplementedtocomparedifferentgroupsofGRBsandtoresolvethepredictedcosmologicaleffects.Inthecaseoftime-dilation,twoscientificgroupshavecheckedtheaverageemissivitycurves(ACEs)derivedfromthepeakalignmentaveragingofbrightanddimbursts,andcametooppositeconclusions:time-dilationofdimburstswasseenbyonegroup(Norrisetal.1994a,1994b,1996;Bonneletal.1996)anditwasnotseenbyanotherone(Mitrofanovetal.,1992a,b,1994,1996).Possiblereasonsfordisagreementwerediscussed(Band1994,Mitrofanovetal.1996),andthetentativeconclusionhasbeendrawnthattheclaimeddilationofdimburstswaspossiblyresultedfromsomesystematicinseparationofbrightanddimgroupsofevents.Ontheotherhand,inthecaseofspectralred-shift,allgroupsinvolvedhaveaconsensusthatbrightGRBshavelargeraveragedspectralhardnessthandimevents.Itwasnamed,astheeffectofhardness/intensitycorrelation(Mitrofanovetal.1992b,c,1994,1996;Paciesasetal.1993,Norrisetal.1994a,b).Whilethiseffectwasoriginallyseenfortheaveragehardnessratio(definedastheratioofcountsathighandlowenergychannels),recentlyitwasfoundalsofortheaveragepeakenergyEpofνFνenergyspectra(Mallozziet–4–al.1995).TheaveragepeakenergiesEpoftheintegralspectraofphotonswerefoundtocorrelatewiththephotonspeakfluxesF(256)maxatthe256mstimescale.Theeffectofhardness/intensitycorrelationmaybeinterpreted,asaresultofcosmologicalred-shiftofdimgamma-rayburstsinrespecttobrightevents.Thecorrespondingcosmologicalred-shiftfactorabout1.6-2.2(Mallozzietal.1995)isconsistentwithoriginalcosmologicalmodelsbasedontheinterpretationsoflogN-logFdistribution(e.g.seeEmslieandHorrack1994).Therefore,thereisadiscrepancybetweendifferentgroupsabouttime-dilationofdimGRBsinrespecttobrightbursts,but,ontheotherhand,thereisancommonlyacceptedagreementbetweenthemforthehardness/intensitycorrelation.SeparatepulsesofGRBsareknowntosqueezewithincreasingenergyofphotons(Norrisetal.1986,Fenimoreetal.1995),and,therefore,theaveragecurveofemissivitybecomesnarrowerathigherenergies(Mitrofanovetal.1996).Accordingtothecosmologicalmodel,whenbrightanddimburstsaredetectedatthesameenergybandintheobserverframeofreference,theirtimeprofileswereactuallyemittedatlesshardandmorehardenergyrangesatcomovingframesofreference,respectively.Therefore,makingacomparisonofbrightanddimburstsfromsourceswithsmallandlargered-shifts,oneshouldsupposethattheintrinsicsqueezingofthelightcurvesofdimburstsduetotheincreaseofenergyoftheemittedphotonscouldpartiallycompensatetheirstretchingduetothecosmologicaltime-dilation.ThispaperprovidesatestofthebasiccosmologicalmodelsofGRBsassumingthemtobestandardsources.Itusestheaverageemissivitycurvesforgroupsofbrightanddimburstsandtakesintoaccounttheeffectsofcosmologicaltime-stretchingintheobserverframetogetherwiththeinternalenergydependentsqueezingofburstslightcurvesinthecomovingframes.–5–2.AnalyticApproximationoftheAverageCurveofEmissivityforGroupofBrightGRBsTheaveragecurveofemissivity(ACE)ofGRBswasintroduced(Mitrofanovetal.1994,1996),asageneralsignatureofburststimevariability.TobuildanACE,alltimehistoriesofaveragingbur