3.4.Di useGalaxyClusterEmission
Weusedwavdetecttosearchforlarge-scalestructuresinthefull32.3ksXRTdataset.Thepixelscalessearchedwere(20,28.28,40,56.57,80).Thecenterofthedi useemissionpresumablyassociatedwiththegalaxyclusterhadawavdetect-determinedpositionof12h36m18s26,+28 59′06′′.7.Figure5showsanadaptivelysmoothedimage(usingtheCIAOtoolcsmooth)oftheXRTdatawiththeclustercenterandGRBindicated.Thecolorsrepresentthe0.3–10keVcountdensity.Contoursaredrawnat0.00449,0.00646,0.00934,0.0136,0.0197,and0.0273countarcsec 2.Astheimageshows,thewavdetect-determinedpositionofthedi useemissionisabout14′′tothewestand4′′southofthepeakofthedi useemission,whichisat12h36m19s33,+28 59′10′′.8(J2000).[Notethattheopticalclustercenteris12h36m10+28 59′00.9′′(J2000)asde nedbythecenterofthegalaxyoverdensity;thisisabout125′′eastand10′′southofthepeakofthedi useX-rayemission.]Wethus ndthattheXRTafterglowpositionis75′′west,6′′northoftheclustercenter,asde nedbythepeakofthedi useX-rayemission,about270kpcinprojection.
Weextractaspectrumfromaregionof110′′inradiuscenteredonthewavdetectposition.Weuseasimilar-sizedregioninasource-freeareatoextractaspectrumforbackgroundsubtraction.Werequiretheclusterspectrumtocontainatleast20countsperbin,andweconsidertherange0.3–10keV.We tthebackground-subtractedclusterspectruminXspecv12.2(Arnaud1996)withaMEKAL(warmplasma)modelabsorbedbyaGalacticcolumndensityof1.52×1020cm 2(Dickey&Lockman1990).WesettheMEKALredshiftatz=0.2248andthemetallicityat[Fe/H]=0.26(Mushotzky&Loewenstein1997)and
.36allowthetemperatureandnormalizationtovary.Thebest ttemperatureiskT=5.25+3 1.68keV,which
givesχ2/dof=22.4/20.
4.AssociatingGRB050509bwithG1
WearenowinapositiontoexplorethepossibleassociationofGRB050509bwiththeclusterandwiththenearbyellipticalgalaxyG1.FocusingontheBATlocalizationalone,we rstconsidertheprobabilitythatarandompositionintheskywouldbeinarichclusterofgalaxies(hereweneglectthee ectsoflensing,

