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Testing the Randomness in the Sky-Distribution of Gamma-Ray Bursts

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Xiv:0806.3932v1 [astro-ph] 24 Jun 2008Mon.Not.R.Astron.Soc.000,1–17(2007)Printed24June2008(MNLATEXstylefilev2.2)

TestingtheRandomnessintheSky-Distributionof

Gamma-RayBursts

R.Vavrek,1⋆L.G.Bal´azs,2A.M´esz´aros,3I.Horv´ath4andZ.Bagoly5

1ESA/ESACP.O.Box50727VillafrancadelCastillo,28080Madrid,Spain2KonkolyObservatory,P.O.Box67,H-1525Budapest,Hungary3AstronomicalInstituteoftheCharlesUniversity,VHoleˇsoviˇck´ach2,18000Prague8,CzechRepublic4DepartmentofPhysics,BolyaiMilitaryUniversity,P.O.Box15,H-1581Budapest,Hungary5LaboratoryforInformationTechnology,E¨otv¨osUniversity,P´azm´anyP´eters´et´any1/A,H-1518Budapest,Hungary

AcceptedXXXX...XX.ReceivedXXXX...XX;inoriginalformXXXX...XX

ABSTRACTWestudiedthecompleterandomnessoftheangulardistributionofgamma-raybursts(GRBs)detectedbyBATSE.SinceGRBsseemtobeamixtureofobjectsofdifferentphysicalnaturewedividedtheBATSEsampleinto5subsamples(short1,short2,intermediate,long1,long2)basedontheirdura-tionsandpeakfluxesandstudiedtheangulardistributionsseparately.Weusedthreemethods,Voronoitesselation,minimalspanningtreeandmulti-fractalspectratosearchfornon-randomnessinthesubsamples.Toinvestigatetheeventualnon-randomnessinthesubsampleswedefined13test-variables(9fromtheVoronoitesselation,3fromtheminimalspanningtreeandonefromthemultifractalspectrum).AssumingthatthepointpatternsobtainedfromtheBATSEsubsamplesarefullyrandomwemadeMonteCarlosim-ulationstakingintoaccounttheBATSE’ssky-exposurefunction.TheMCsimulationsenabledustotestthenullhypothesisi.e.thattheangulardis-tributionsarefullyrandom.WetestedtherandomnessbybinomialtestandintroducingsquaredEuclideandistancesintheparameterspaceofthetest-variables.Weconcludedthattheshort1,short2groupsdeviatesignificantly(99.90%,99.98%)fromthefullyrandomnessinthedistributionofthesquaredEuclideandistancesbutitisnotthecaseatthelongsamples.Attheinter-mediategroupthesquaredEuclideandistancesalsogivesignificantdeviation(98.51%).2R.Vavreketal.

1INTRODUCTIONRecently,thereisnodoubtaboutthecosmologicaloriginofthegamma-raybursts(hereafter

GRBs)(Zhang&M´esz´aros2004;Foxetal.2005;M´esz´aros2006).Then,assumingalargescaleisotropyfortheUniverse,oneexpectsthesamepropertyfortheGRBsaswell.Another

property,whichisalsoexpectedtooccurthatGRBsshouldappearfullyrandomly,i.e.

ifaburstisobserveditdoesnotgiveanyinformationabouttheplaceofthenextone.

Ifbothpropertiesarefulfilled,thenthedistributioniscalledcompletelyrandom(forthe

astronomicalcontextofspatialpointprocessesseeP´asztor&T´oth(1995)).Thereareseveral

testsforcheckingthecompleterandomnessofpointpatterns,however,theseproceduresdo

notalwaysgiveinformationforbothpropertiessimultaneously.

ThereareincreasingevidencethatalltheGRBsdonotrepresentaphysicallyhomoge-

neousgroup(Kouveliotouetal.1993;Horv´ath1998;Mukherjeeetal.1998;Hakkilaetal.

2000;Horv´ath2002;Bal´azsetal.2003;Hakkilaetal.2003;Horv´athetal.2006).Hence,itis

worthinvestigatingthatthephysicallydifferentsubgroupsarealsodifferentintheirangular

distributions.Inthelastyearstheauthorsprovided(Bal´azsetal.1998,1999;M´esz´arosetal.

2000a,b)severaldifferenttestsprobingtheintrinsicisotropyintheangularsky-distribution

ofGRBscollectedinBATSECatalog(Meeganetal.2000).Shortlysummarizingthere-

sultsofthesestudiesonemayconclude:A.Thelongsubgroup(T90>10s)seemstobe

distributedisotropically;B.Theintermediatesubgroup(2s<=T90<=10s)isdistributed

anisotropicallyonthe≃(96−97)%significancelevel;C.Fortheshortsubgroup(2s>T90)

theassumptionofisotropyisrejectedonlyonthe92%significancelevel;D.Thelongand

theshortsubclasses,respectively,aredistributeddifferentlyonthe99.3%significancelevel.

(AboutthedefinitionofsubclassesseeHorv´ath(1998);T90isthedurationofaGRB,during

whichtimethe90%oftheradiatedenergyisreceived(Meeganetal.2000).)

Independentlyandbydifferenttests,Litvinetal.(2001)confirmedtheresultsA.,B.and

C.withoneessentialdifference:fortheintermediatesubclassamuchhigher-namely99.89%

-significancelevelofanisotropyisclaimed.Again,theshortsubgroupisfoundtobe”sus-

picious”,butonlythe≃(85−95)%significancelevelisreached.Thelongsubclassseemsto

bedistributedisotropically(butseeM´esz´aros&ˇStoˇcek(2003)).Magliocchettietal.(2003)

foundsignificantangularcorrelationonthe2◦−5◦scaleforGRBswithT90<2sdurations.

Tanviretal.(2005)reportedacorrelationbetweenthelocationsofpreviouslyobservedshortSky-distributionofGamma-RayBursts3

burstsandthepositionsofgalaxiesinthelocalUniverse,indicatingthatbetween10and25

percentofshortGRBsoriginateatlowredshifts(z<0.025).

Itisareasonablerequirementtocontinuethesetestsusingmoresophisticatedprocedures

inordertoseewhethertheangulardistributionofGRBsiscompletelyrandomorhassome

sortofregularity.Thisisthesubjectofthisarticle.Newtestswillbepresentedhere.Mainly

theclarificationoftheshortsubgroup’sbehaviourisexpectedfromthesetests.Inthis

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