Deprojection of luminosity functions of galaxies in the Coma cluster

DeprojectionofluminosityfunctionsofgalaxiesintheComa

cluster

arXiv:astro-ph/0205483v1 28 May 2002M.Beijersbergen,W.E.SchaapandJ.M.vanderHulst

KapteynAstronomicalInstitute,P.O.Box800,9700AVGroningen,TheNetherlandsReceiveddate;accepteddate

Abstract.Weuseasimpleanalyticmodeltodeproject2-dluminosityfunctions(LF)ofgalaxiesintheComaclustermeasuredbyBeijersbergenetal.2002.WedemonstratethattheshapesoftheLFschangeafterdeprojection.Itisthereforeessentialto

∗

correctLFsforprojectioneffects.ThedeprojectedLFsofthecentralareahavebest-fittingSchechterparametersofMU=

+0.20+0.016+0.14+0.018+0.08∗∗

−18.31−0.08andαU=−1.27−0.018,MB=−19.79−0.15andαB=−1.44−0.016andMr=−21.77−0.28andαr=

.012

−1.27+0−0.012.Thecorrectionsarenotsignificantenoughtochangethepreviouslyobservedtrendofincreasingfaintendslopeswithincreasingdistancetotheclustercenter.TheweightedU,B,andrbandslopesofthedeprojectedLFsshowaslightlyweakersteepeningwithincreasingprojectedclusterradius.

Keywords.Galaxies:clusters:individual:Coma(A1656)–Galaxies:luminosityfunction–Galaxies:evolution–Galaxies:formation.

1.Introduction

InthepastlargefieldstudiesofthephotometricpropertiesofgalaxiesintheComaclusterhavebeenbasedonphoto-graphicplates(e.g.Godwinetal.1983;Lugger1989).MorerecentstudieshavebeenmadewithCCDdetectorswhichpro-videhigherphotometricaccuracy.However,alimitationoftheuseofCCDshasbeentherelativelysmallfieldofview.Consequently,thesestudieshavebeenlimitedtoverysmallar-eas,rangingfrom∼50arcmin2(e.g.Bernsteinetal.1995;Mobasher&Trentham1998)to1500arcmin2(e.g.Loboetal.1997),mainlyfocusedontheclustercenter.Thesesmallfieldscannotbeusedtostudythedependenceofthelumi-nosityfunction(LF)ontheprojecteddistancefromtheclustercenter.Furthermore,lackingthephotometricdataatlargerdis-tancesfromthecoreitisnotpossibletocorrectacentralLFforprojectioneffects.Accordingly,thepublishedLFsofgalaxiesintheComaclusterareallprojectedandare,therefore,lumi-nositydistributionsratherthanactualLFs.ItisimportanttotesthowwellthesecorrespondtotheactualdeprojectedLFs.

Recently,Valottoetal.(2001)usednumericalsimulationstoanalysesystematiceffectsinthedeterminationofthegalaxyluminosityfunctioninclusters.Theyfindthatprojectionef-fectsconspiretoproduceartificiallysteepfaintendslopes.Beijersbergenetal.(2002,hereafterBHDH)presentedstatis-ticalU,BandrbandprojectedLFsforgalaxiesintheComaclusterinfiveannuliouttoaprojectedradiusof1.4degreesfortheBandrbandsand0.74degreesfortheUband.Intotalanareaof5.2deg2inBandrand1.3deg2inUhasbeensur-

2M.Beijersbergen,W.E.SchaapandJ.M.vanderHulst:Deprojectionofluminosityfunctions

Fig.1.Outlineofthemodelusedtodeproject2-dluminosityfunctions.Thefigurecanbeseenasacutthroughasphereandasitsprojectionasseenbytheobserver.ThefivecirclesmakeuptheprojectedannuliasusedinBeijersbergenetal.2002.Radiiare:I:0-0.2,II:0.2-0.3,III:0.3-0.42,IV:0.42-0.74and

−1

V:0.74-1.4degrees(1◦=1.22h100MpcatComadistance).bysubtractingthecontributionsfromtheothershellsduetoprojection.InFig.1weshowanoutlineofthismodel.

Thenumberofprojectedgalaxiespermagnitudem,Ni,m,inannulusi,andthegalaxydensitypermagnitude,φm,arerelatedas:

5󰀃

Ni,m=φi,mF(Ri,Ri−1,Ri)+󰀁

φj,m

󰀂

(1)

j=i+1

[F(Rj,Ri−1,Ri)−F(Rj−1,Ri−1,Ri)]

whereRiaretheradiioftheannuliandthefunctionFis

definedby:F(α,β,γ)≡

4

M.Beijersbergen,W.E.SchaapandJ.M.vanderHulst:Deprojectionofluminosityfunctions3

Fig.2.TwoandthreedimensionalluminosityfunctionsofareaIcompared.Opensymbolsrepresent2-dluminosityfunctionsandsolidsymbolsrepresent3-dluminosityfunctions.Thesolidlinesrepresentbest-fittingSchechterfunctionstothe3-ddata.Forclaritytheerrorbarsofthe2-dluminosityfunctionsarenotshown.

Fig.3.TwoandthreedimensionalluminosityfunctionsofareasIItoVcompared.Opensymbolsrepresent2-dluminosityfunctionsandsolidsymbolsrepresent3-dluminosityfunctions.Forclaritytheerrorbarsofthe2-dluminosityfunctionsarenotshown.

bythiseffect.BelowwestudyhowtheshapesoftheluminositydistributionsgiveninBHDHareaffectedbyprojectioneffects.

Intheoutermostannulustheprojectedareaisconvertedtovolumethroughafactordependingontheadoptedgeometry(radii),i.e.forthisannulustheshapesofthe2-dand3-dLFs

4M.Beijersbergen,W.E.SchaapandJ.M.vanderHulst:Deprojectionofluminosityfunctions

Table1.Comparisonofbest-fittingSchechterparametersfor2-dand3-dLFs.M∗isnotcorrectedforextinction.

Filter

α

2-d

M

∗

3-dα

M∗