The galaxy luminosity function of the Abell 496 cluster and its spatial variations

12 Pages·2008·1.68 MB·English

A&A479,335–346(2008) Astronomy
DOI:10.1051/0004-6361:20077723 &
(cid:1)c ESO2008 Astrophysics
The galaxy luminosity function of the Abell 496 cluster
(cid:1)
and its spatial variations
G.Boué1,C.Adami2,F.Durret1,3,G.A.Mamon1,4,andV.Cayatte5
1 Institutd’AstrophysiquedeParis(UMR7095:CNRS&UniversitéPierreetMarieCurie),98bisBdArago,75014Paris,France
e-mail:[email protected]
2 LAM,TraverseduSiphon,13012Marseille,France
3 ObservatoiredeParis,LERMA,61Av.del’Observatoire,75014Paris,France
4 ObservatoiredeParis,GEPI(UMR8111:CNRS&UniversitéDenisDiderot),61Av.del’Observatoire,75014Paris,France
5 ObservatoiredeParis,sectionMeudon,LUTH,CNRS-UMR8102,UniversitéParis7,5Pl.Janssen,92195Meudon,France
Received26April2007/Accepted27November2007
ABSTRACT
Context.Thefaintendslopesofgalaxyluminosityfunctions(LFs)inclustersofgalaxieshavebeenobservedinsomecasestovary
withclustercentricdistanceandshouldbeinfluencedbythephysicalprocesses(mergers,tides)affectingclustergalaxies.However,
thereisawidedisagreementonthevaluesofthefaintendLFslopes,rangingfrom−1to−2.3inthemagnituderange−18<M <−14.
r
Aims.WeinvestigatetheLFintheveryrelaxedclusterAbell496.
Methods.Our analysisisbasedon deepimages obtained atCFHTwithMegaPrime/MegaCam infour bands (u∗g(cid:3)r(cid:3)i(cid:3)) covering a
1×1deg2region,whichiscentredontheclusterAbell496andextendstonearitsvirialradius.TheLFsareestimatedbystatistically
subtractingareferencefieldtakenasthemeanofthe4DeepfieldsoftheCFHTLSsurvey.Backgroundcontaminationisminimised
bycuttingoutgalaxiesredderthantheobservedRedSequenceintheg(cid:3)−i(cid:3)versusi(cid:3)colour-magnitudediagram.
Results.InAbell 496, theglobal LFsshow afaint endslopeof−1.55±0.06andvarylittlewithobserving band. Withoutcolour
cuts, the LFs are much noisier but not significantly steeper. The faint end slopes show a statistically significant steepening from
α =−1.4±0.1inthecentralregion(extendingtohalfavirialradius)to−1.8±0.1intheSouthernenvelopeofthecluster.Cosmic
variance and uncertain star-galaxyseparation areour main limitingfactors in measuring thefaint end of the LFs.The large-scale
environmentofAbell496,probedwiththefairlycomplete6dFGScatalogue,showsastatisticallysignificant36Mpclongfilamentat
PA=137◦.
Conclusions.OurLFsdonotdisplaythelargenumberofdwarfgalaxies(α≈−2)inferredbyseveralauthors,whoseanalysesmay
sufferfromfieldcontaminationcausedbynon-existentorinadequatecolourcuts.Alternatively,differentclustersmayhavedifferent
faintendslopes,butthisishardtoreconcilewiththewiderangeofslopesfoundforgivenclustersandforwidesetsofclusters.
Keywords.galaxies:clusters:individual:Abell496–galaxies:luminosityfunctions,massfunction
1. Introduction The great majority of studies of the LF indicate faint end
slopesintherange−0.9to−1.5,butthesemostlydidnotreach
Clustersofgalaxiesrepresentanextremeenvironmentforgalaxy
veryfaintmagnitudes(seeTable1inDeProprisetal.2003,and
evolution, either in situ or through the accretion of galaxies
referencestherein).Recentdeepimaginghasshedmorelighton
withingroups,whicharesituatedinthefilamentarynetworkof
theLFatfaintluminosities.TableA.1showsdeep(fainterthan
ourhierarchicalUniverse. absolutemagnitudeM =−16)estimationsofthefaintendslope:
Theanalysisofthegalaxyluminosityfunction(LF)in sev- most studies conclude to fairly shallow slopes α (cid:6) −1.3 (with
eralwavebandsisagoodwaytosamplethehistoryofthefaint typical uncertainties of 0.1 to 0.2), while several point to faint
galaxypopulation(e.g.Adamietal.2007)includingstarforma- end slopes as steep as α ≈ −2.3, which divergesin luminosity
tion history, evolutionary processes and environmental effects. (unlesstheLFbecomesshalloweroriscutoffatsomeveryfaint
Inparticular,theslopeofthefaintendoftheLFisadirectindi- luminosity).
catoroftheimportanceofdwarfgalaxies,whichareexpectedto
Partofthewiderangeoffaintendslopesmaybecausedby
bemorefragileintheenvironmentofclusters.
cosmic variance of the background counts. The range of faint
endslopesoftheLFmayalsobeduetodifferentmassbuildup
(cid:2) BasedonobservationsobtainedwithMegaPrime/MegaCam,ajoint historiesofclusters,throughsphericalandfilamentaryinfalland
project of CFHT and CEA/DAPNIA, at the Canada-France-Hawaii
majorcluster-clustermergers.However,someofthisdispersion
Telescope(CFHT)whichisoperatedbytheNationalResearchCouncil
inslopescouldbecausedbysystematicuncertaintiessuchasin
(NRC)ofCanada,theInstitutNationaldesSciencesdel’Universofthe thestar/galaxyseparationorthroughdifferentsurfacebrightness
Centre National de la Recherche Scientifique (CNRS) of France, and
cuts.
theUniversityofHawaii.Thisworkisalsopartlybasedondataprod-
uctsproducedatTERAPIXandtheCanadianAstronomyDataCentre Spectroscopic-based LFs would alleviate this problem,
aspartoftheCanada-France-Hawaii TelescopeLegacySurvey,acol- but until recently, such spectroscopic-based LFs do not ex-
laborativeprojectofNRCandCNRS. tend fainter than M = −16. The exceptions are studies by
ArticlepublishedbyEDPSciences
336 G.Bouéetal.:GalaxyluminosityfunctionofAbell496
Table1.Observationcharacteristics.
Name Usefularea Exp.time PSF Obs.
(deg2) (s) (FWHMinarcsec) Date
u∗ g(cid:3) r(cid:3) i(cid:3) u∗ g(cid:3) r(cid:3) i(cid:3)
Abell496 0.82 13680 7820 3780 3570 1.13 1.06 0.88 0.94 11/2003
Deep1 0.77 38946 24893 60854 134863 1.06 0.96 0.92 0.91 <09/2006
Deep2 0.79 5281 16655 31988 72734 0.89 0.96 0.90 0.91 <09/2006
Deep3 0.83 19146 21392 59574 109049 1.15 0.96 0.94 0.89 <09/2006
Deep4 0.82 50867 24262 72736 140981 1.03 0.98 0.88 0.87 <09/2006
W1 —– 2215 2436 1179 4189 1.04±0.09 0.96±0.05 0.86±0.11 0.85±0.12 <09/2006
Note:TheW1valuesaremeansoverthe19WidesubfieldsoftheWidefield.
Rines & Geller (2007)and Mamonet al. (2008)who bothfind 2. Observationsanddatareduction
shallowslopesforVirgoclustergalaxiesdownto M = −14,as
r
2.1.MegaCamclusterdata
wellasPenny&Conselice(2007)forthePerseusclustercore.
Unfortunately, galaxy formation simulations do not yet Abell 496 is centred at J2000 equatorial coordinates
probethegalaxyLFdowntosufficientlyfaintluminosities:the 04h33m37.1s,−13◦14(cid:3)46(cid:3)(cid:3). It has an angular virial radius
deepeststudy,byLanzonietal.(2005),probedtheLFwiththe of 0.77◦ (virial radius of 1.9 Mpc), obtained by extrapolating
GALICSsemi-analyticalgalaxyformationmodelonlydownto theradiusofoverdensity500(Markevitchetal.1999,measured
M < −16.5 (they found α (cid:6) −1.3 in the B band and (cid:6)−1.4 relative to the critical density of the Universe) to the radius of
B
in the K band within the virial radii of clusters, and α (cid:6) −1.0 overdensity100.
between1andtypically3virialradii). The MegaCam field covers an area correspondingto 2.3×
2.3 Mpc2 at the cluster redshift. We centred our images of
Thepresentpaperaimsatclarifyingthe debateonthe faint
Abell 496 on the cluster centre (i.e. on the cD galaxy). This
endoftheLFandonunderstandingthedifferenteffectsofspher-
means that we can cover the whole Abell 496 area and its im-
ical and filamentary infall on the LF. Indeed, the influence of
mediateinfallinglayerswithinthevirialradius.
infallonthegalaxypopulation,inparticularontheLFisnotal-
Abell 496 was observed at CFHT with the large field
ways wellunderstood,exceptfora few clusters, such as Coma MegaPrime/MegaCam camera in November 2003 on program
(e.g.Adamietal.2007).Toachievethisaim,wechosetoanal-
03BF12,P.I.Cayatte(seeTable1).Imageswerereducedbythe
ysetheveryrelaxedcluster,Abell496,knowntobeveryregular
TERAPIX pipeline using the standard reduction tool configu-
bothatX-rayandopticalwavelengths,andalsofromadynam- ration. We refer the reader to http://terapix.iap.fr/for
ical point of view (Durret et al. 2000). Our data cover a field
reductiondetails.
of view that is wide enough to reach the virial radius and thus
Object extraction was made using the SExtractor pack-
probea varietyof environments.TheLFs are computedafter a
age (Bertin & Arnouts 1996) in the double-image mode. The
better filtering of artefacts througha minimumgalaxywidth, a CFHTLSpipelineattheTERAPIXdatacentrecreatesaχ2 im-
better filtering of backgroundgalaxies through the rejection of agebaseduponthequadraticsumoftheimagesinthedifferent
galaxies redder than the Red Sequence of early-type galaxies,
wavebands.Objectsarethendetectedonthisimage.Incontrast
andmakeuseofathoroughanalysisoftheuncertaintiesdueto withtheCFHTLSimages,oursetofu∗g(cid:3)r(cid:3)i(cid:3) imagesforeachof
cosmic variance, photometric errors and imperfect star/galaxy thetwoclusterspresentsimportantdifferencesintheirPSFs(see
separation. Our general motivation is to obtain LFs in various Table 1). For this reason, we chose a different approach from
regionsofAbell496andcomparethemwithpreviousworks. thatoftheTERAPIXdatacentre:insteadofusingtheχ2 image
Thepaperisorganisedasfollows.WepresentourMegaCam as the reference image, we used the band with the best seeing
dataanddatareductioninSect.2.InSect.3,wedescribehowwe in ourdata:r(cid:3).Detectionswereperformedinthisbandandob-
compute LFs using large comparison fields from the CFHTLS ject characteristics were measured in all bands. The detections
tostatisticallysubtractthefore-andbackgroundgalaxypopula- andmeasuresweremadeusingtheCFHTLSparameters,among
tion. In Sect. 4, we present our results obtained for the LFs of which an absolute detection threshold of 0.4 ADU above the
Abell 496in variousregions.In Sect. 5, we brieflydiscuss our background(µ<27.34inallbands),aminimaldetectionareaof
resultsconcerningtheLFsintermsoflargescaleenvironmental 3pixelsanda7×7pixelGaussianconvolutionfilterof3pixels
effects onthe cluster galaxypopulations.Finally, in Sect. 6 we ofFWHM.Ineachoftheu∗,g(cid:3),r(cid:3) andi(cid:3) outputcatalogues,we
compare our LFs to other determinationsof the Abell 496 LF, only keptobjects with semi-minoraxeslarger than 1 pixeland
andwediscussthediscrepancybetweenourmoderatefaintend meansurfacebrightnesswithinthehalf-lightradiusgreaterthan
slope and the steep faint end slopes recently found by several µ=26.25inordertoremoveartefacts.
authorsinseveralclusters. We measured Kron magnitudes (MAG_AUTO in SExtractor),
with the default SExtractor settings. We used the photometric
With a mean heliocentric velocity of 9885kms−1 (Durret
calibrationgivenbytheTERAPIXdataprocessingcentre.Since
et al. 2000), Abell 496 has a (luminosity) distance modulus of thefluxesindifferentbandsaremeasuredwithinthesameKron
35.73,andthescaleis0.636kpcarcsec−1(includingcosmologi-
elliptical aperture, we derive colours by simply subtractingthe
calcorrections1).WegivemagnitudesintheABsystem. magnitudes.Therefore,ourcoloursarenotaffectedbyaperture
effects and are only slightly affected by the differences in the
PSFbetweenthetwobandsinvolved.
1 WeusedthecosmologicalcorrectionsintheCMBframeasprovided Usingsimulations,wealsoestimatethecompletenesslevels
intheNASA/IPACExtragalacticDatabase(NED). andreliabilitiesofourdetections(see e.g.Driveretal. 1998b).
G.Bouéetal.:GalaxyluminosityfunctionofAbell496 337
This is crucial, since we intend to compare our data with 10000
stars
CFHTLSdatathatwerenotobservedexactlyinthesamecondi-
galaxies
tions.Forthis,weusedtheSkyMakerpackage(Bertin&Fouqué
all
2007)tobuildimageswiththesamenoiseandpointspreadfunc-
tion as our MegaCam images on the one hand and CFHTLS 2 1000
g
Deepimagesontheotherhand.TheobjectsfedintoSkyMaker e
d
were either spherical to flattened Sérsic bulges2 or thin expo- /
x
nential disks. The Sérsic shape and effective radius are speci- e
d
fied functions of luminosity that Mamon & Łokas (2005) ob- 1 100
0
tainedfromtheluminousgalaxiesofAbell496andComadata
.
0
ofMárquezetal.(2000),whileforthedwarfsweconsideredthe /
s
relationsgivenbyBinggeli&Jerjen(1998).ThecentralB-band t
n
disksurfacemagnitudeswereextrapolatedfromaGaussiandis- u
o 10
tributionµB(0) = 21.5±1.Thefractionofellipticalsis60%in c
clustersandnullinthefield.Thegalaxyluminosityfunctionwas
takenfromPopessoetal.(2006)fortheclusterandfromBlanton
etal.(2003)forthefield.
1
Completeness (ratio of real detections to real sources) and
reliability (ratio of real to total detections) were then mea- 1 10
suredbycross-correlationbetweentheSkyMakerinputandthe r (pixels)
SExtractor output catalogue. We found that up to i(cid:3) = 23, for 50
both kindsof images,SExtractorfinds80%ofthe objects, and Fig.1. Distributionof half-lightradiiinthemagnitude bin22 < r(cid:3) <
amongthedetectedobjects,only10%areartefacts. 22.5. Theverticallineshowsthestar/galaxyseparationdeduced from
We then performed a star-galaxy separation. Instead of theBesançonmodel.
using the neural-network star-galaxy classification method of
SExtractor, we placed the detections in a diagram of size (i.e. Mr’
thehalflightradius)versusmagnitudeinthebandwiththebest
−18 −17 −16 −15 −14 −13
seeing. Thevariationof thePSF overtheimageshasbeencor-
rectedforusingatechniquesimilar tothatofMcCrackenetal. Besançon model star count
(2003).Starsarethesmallestobjectsandarelocatedinawellde- stars in Abell 496 field
finedstripuptor(cid:3) ≈21,thusallowingtheseparation.Atfainter
1000
magnitudes,starsandgalaxiesoverlapandindividualclassifica-
2
tion is no longer possible. For the magnitude range where the g
e
htiaclafllsigtahrt/graaldaixuyssdeisptarribatuitoino,naisssubmiminogdaGl,awusesipaenrfdoirsmtreibduatiosntastios-f ag/d
m
lTohgisr5i0sfiolrlubsotrtahtesdtarins aFnidg.g1alafoxrietsh,einfadiirfflyerfeaninttmmagangintuitduedebibnisn. 0.5 500
21<r(cid:3) <21.5. nts/
u
Figure 2 compares our star counts with those from the o
c
Besançonmodel(Robinetal.2003).WerantheBesançonmodel
six times in order to get the error on these counts. We did the
samewithouralgorithm.Atbrightmagnitudes(r(cid:3) <21),thetwo
distributionscoincide. However,at faint magnitudes(r(cid:3) > 21),
ourstarcountsdecrease,whiletheBesançonmodelcountskeep
17 18 19 20 21 22 23
increasing.Thiscouldbeduetoasteeperfallofthestellarden-
sity distribution in the direction of Abell 496, in comparison r’
with what is in the Besançon model. Alternatively, we may be
Fig.2. Comparison of star counts obtained with the Besançon model
wronglyclassifyingstarsasgalaxiesatr(cid:3) > 21,andatr(cid:3) = 22 (Robinetal.2003)(orangeshadedregion)andfromtheAbell496im-
we may be overestimating the galaxy counts in the Abell 496 age(blacksolidhistogram)usingourstar-galaxyseparation.
field.Ifweadoptthestar countsfromtheBesançonmodel,we
wouldendupwith114,156and343fewergalaxiesatr(cid:3) =21.5,
22.0and22.5,respectively.However,iftherewereasmanystars all saturated stars, spikes and CCD edges. Galaxies and stars
as predicted by the Besançon model, then, for 22 < r(cid:3) < 22.5 brighter than r(cid:3) = 18 occupy less than 2% of the pixels of our
(seeFig.1),thedistributionofstellarhalflightradiiwouldrise image.
to a maximum(nearr = 2.3pixels),falltoa minimum(near The final catalogue will be electronically available at the
50
2.6pixels),thenriseagain(tothelimitof2.8pixels).Itisdiffi- following address: http://cencosw.oamp.fr/and in a few
culttounderstandwhatwouldcausethisfinalrise.Therefore,in monthstheimageswillbeavailableatthesameaddress.
whatfollows,weadoptourownestimationofthestarcounts.
We also corrected the magnitudes for Galactic extinc-
2.2.CFHTLScomparisonfielddata
tion based on the Schlegel et al. (1998) maps. We finally
computed the useful covered area (cf. Table 1), by masking We used the CFHTLS Deep (D1, D2, D3 and D4, i.e.
4 MegaCamfields) and Wide (W1, W2 andW3, 59 MegaCam
2 WemodifiedSkyMakertohandleSérsicprofilesratherthanjustthe fields)ascomparisonfielddata.BecausetheLFsarecomputed
deVaucouleursprofile. by subtraction of the average of the 4 Deep fields (DFs) from
338 G.Bouéetal.:GalaxyluminosityfunctionofAbell496
Abell 496 analytical approximation
0.14
deep 1 u*
0.6
g’
0.12 r’
i’
0.4
0.1
’-i’) 0.2 mag) 0.08
r
r’)-( 0 σ ( 0.06
-
’
g
(
0.04
-0.2
0.02
-0.4
0
15 16 17 18 19 20 21 22 23
-0.6 mag
0 0.5 1 1.5 2
r’-i’ Fig.4.Magnitudeuncertaintiesestimatedfromoverlappingareasinthe
19CFHTLSW1fields(dottedanddashedcurves)withtheiranalytical
Fig.3.Colour-colourdiagramfor17<r(cid:3) <20starsintheA496(open approximation(Eq.(1),solidcurves).
redcircles)andD1(blackcrosses)fields,correctedforextinction,and
withashiftoftheD1i(cid:3)photometryby+0.02mag.
on average. Therefore, the W1 magnitude uncertainties should
beupperlimitsfortheAbell496magnitudeuncertainties.
Theseuncertaintiescanbeapproximatedby
the Abell 496 field, objects were re-extracted from the 4 DFs (cid:1) (cid:2)
m−m
in exactlythesamemannerasintheclusterfield:i.e.,withthe σ =0.02+αexp 1 , (1)
same detection waveband (r(cid:3) rather than χ2 images) the same m δm
SExtractorparameters(includingthe same 0.4ADU threshold, where (α,m ,δ ) = (1.2,29.5,3.0),(2.5,29.0,1.5),(1.0,25.0,
whichgiventhesamezeropointcorrespondstothesameabso- 1.0)and(1.01,2m5.0,1.0)foru∗g(cid:3)r(cid:3)i(cid:3) respectively.These expres-
lutethreshold),andthe1pixelminimumsemi-minoraxis.Since
sions are used to compute the uncertainties on galaxy counts.
the DeepimagesaredeeperthantheAbell496images,we ap-
Note that although the W1 pointings had comparable PSFs to
plythesamecutofmeansurfacemagnitudewithinthehalf-light
theAbell496PSFs,theintegrationtimesweresmaller,exceptin
radiusofµ<26.25forall4wavebands. thei(cid:3) band(seeTable1).Hence,thephotometricerrorsderived
We chose the DFs as reference fields (rather than the fromtheW1fieldareupperlimitsintheu∗,g(cid:3)andr(cid:3)bands.
CFHTLS Wide fields) because their greater depth ensures
WealsorecomputedtheareacoveragefortheDeepandWide
smallerphotometricerrorsinourrangeofmagnitudesthanthose
fieldsfromtheCFHTLSmaskfiles(seeTable1).
of the Wide fields. Moreover,the DFs were selected to be free
of rich nearby structures, which is not the case for the Wide
CFHTLS fields, which are shallower (except in i(cid:3)) than the 3. Descriptionofthemethods
Abell496field.
3.1.Luminosityfunctioncalculations
We checked that the cluster and referencefields have com-
patible photometric calibration. For this we made a colour- The basic method to evaluate the LF is to statistically esti-
colourdiagram,showninFig.3,inwhichwecorrectedthemag- matethefore-andbackgroundcontributionstotheclusterlines
nitudes for galactic extinction using the Schlegel et al. (1998) of sight using comparison fields free of rich nearby structures
model, and shifted the D1 i(cid:3) magnitudes by +0.02 to force a (Oemler1974).
match. We compute the LF in the standard fashion: we subtract
The W1 region (19 MegaCam fields) of the CFHTLS was the reference field counts (the mean of the 4 DFs) from the
considered to estimate the magnitude uncertainties as a func- cluster field counts. The uncertainty is estimated as follows.
tion of magnitude in an external way. For this, we considered In a first step, we compute the uncertainties coming from er-
the overlapping areas of the 19 W1 fields. In these areas, we rors on magnitude measurements: starting from a catalogue of
compiledtheobjectsobservedtwice,andthisallowedustoes- magnitudes{mi},wecreatemockcatalogues{m(cid:3)i},wherem(cid:3)i are
timate the magnitude difference as a function of magnitude in Gaussian distributed random variables of mean mi and stan-
theu∗,g(cid:3),r(cid:3)andi(cid:3)bands.Weonlyselectedobjectslocatedmore darddeviationσ(mi)estimatedfromoverlappingareasinthe19
than 400 pixelsaway fromthe field edgesin orderto avoid ar- CFHTLS W1 fields (cf. Fig. 4). The uncertainty on the galaxy
tificially increasing the magnitude uncertainties due to border countsarisingfromphotometricerrorsinthenσm = σ{N(m(cid:3))}.
effects.TheseuncertaintiesareshowninFig.4. Inasecondstep,wecomputetheuncertaintiesduetothecosmic
WeusedtheTERAPIXobjectcataloguesfortheW1fields, varianceusingthe59CFHTLSWidefields:
forwhichdetectionsweredoneontheχ2images.Ineachwave- σ2 (m)=σ2{N (m)}−(cid:7)σ2(m)(cid:8) , (2)
band,theW1fieldshavethesamemeasurementthresholdasthe CV Wide m Wide
Abell496image.However,themeasurementisophoteisnoisier where(cid:7)(cid:8) meansthemedianoverthe59Widefields.Itshould
Wide
in the W1 fields(exceptin thei(cid:3) band).butwith the same area bestressedthatσ (m)definedinthiswayimplicitlytakesinto
CV
G.Bouéetal.:GalaxyluminosityfunctionofAbell496 339
M M
r’ i’
-20 -18 -16 -14
-20 -18 -16 -14
net galaxy counts (Abell 496) 3
1000
Poisson uncertainties on gross counts
) Abell 496
2g cosmic variance (Abell 496)
e 2.5
d magnitude error (Abell 496)
ag/ cosmic variance (Deep fields)
m
magnitude error (Deep fields) 2
5
0. 100 star-galaxy separation
s/
ount g’-i’ 1.5
c
(
s
e 1
nti 10
ai
rt
e 0.5
c
n
u
0
1 14 16 18 20 22
14 16 18 20 22
r’ i’
Fig.5.UncertaintiesontheglobalLFofAbell496inther(cid:3)bandforall Fig.6.i(cid:3)/g(cid:3)−i(cid:3)colour-magnitudediagramforAbell496.Theredcurve
galaxies,i.e.withoutselectionfromthecolour-magnitudediagram.For showstheupperlimitofgalaxyselectiontocomputetheLFs.
comparison,weshowthePoissonerrorcalculatedonthegrosscounts
ofAbell496.Notethatwedefinedcosmicvariance(Eq.(2))withthe
Poissoncontribution. consistentwithwhathasbeenknownsinceBoweretal.(1992).
WeassumethatthisRedSequenceisrealandcorrespondstothe
accountthestatisticaluncertaintiesonthestar-galaxyseparation reddestgalaxiesofthecluster.Wethereforeselectonlygalaxies
(cf.Fig.2).Finally,weaddquadraticallyalluncertainties: slightly(0.15mag)aboveourRedSequence.Becauseourpho-
tometricerrorsincreasewithmagnitude,thestrictapplicationof
σ2{NCl(m)} = σ2{NCl(m)}+σ2 (m)
m los CV thiscolourcutwouldleadtoanincompletenessatthefaintend.
(cid:3) (cid:4)
+1 σ2{NDF(m)}+σ2 (m) , (3) Thereforeweusethecut
4 m CV (cid:5) (cid:6)
where NCl, NCl and NDF are the counts from the cluster, the g(cid:3)−i(cid:3) ≤ (g(cid:3)−i(cid:3))RS+Max 0.15,1.5σg(cid:3)−i(cid:3)
clusterfieldanlodsthemeanofthe4DFs,respectively.Thefactor = 1.75−(cid:7)0.05i(cid:3) (cid:8) (cid:9)
of4correspondstothe4DFs.Alltheseuncertaintiesareplotted
inFig.5forAbell496inther(cid:3)band. +Max 0.15,1.5 σ2g(0.95i+1.75)+σ2i(i) , (5)
TheuncertaintyinthegalaxycountsgiveninEq.(3)aswell
asthecontributionofstar/galaxyseparationtotheuncertaintyin where we wrote σ2g(cid:3)−i(cid:3) = σ2g(cid:3) + σ2i(cid:3), used the Red Sequence
thecountsshowninFig.5arepurelystatistical.Oneshouldalso (Eq. (4)) to translate g(cid:3) to i(cid:3), and took σ (g(cid:3)) and σ(i(cid:3)) from
g i
consider systematic contributions to this uncertainty, in partic- Eq.(1).Thefactor1.5inthefirstequalityofEq.(5)ensuresthat
ularthosefromstar/galaxyseparation.Indeed,thedifferencein we are 93% complete (assuming a Gaussian probability distri-
galaxycountsafter subtractionof the stars either fromour star butionfunction,hereafterpdf).
countsorfromtheBesançonmodelisalmostaslargeasthecos- ThecolourcutofEq.(5)isrepresentedinFig.6bythered
micvarianceofthegalaxycountsoftheAbell496clusterfield. curve.Whileourcolourcutmayleadtoalossofatypicallyred
However,ouranalysisofSect.2.1suggeststhatthissystematic cluster galaxies(e.g.dusty objects),we are confidentthat such
uncertaintyissmallerthanthedifferencebetweenourestimated a population,if it exists, is small, and will onlymarginallyde-
starcountsandthoseobtainedwiththeBesançonmodel. creaseourcompleteness.Ontheotherhand,thecolourcutwill
drastically improve our reliability in the net cluster counts (in-
deed,ourtestshaveshownthatwithoutthecolourcuts, theLF
3.2.Improvementusingcolourmagnituderelations
is much noisier). Hereafter,all LFs as well as the cosmic vari-
LFs computed directly from the method described above show ancearecomputedusingthisselection.
verybigerrorbarsmainlyduetothecosmicvariance(cf.Fig.5).
This problem has already been highlighted (e.g. Oemler 1974;
Durretetal.2002).Weimproveouranalysisbyremovingthose 4. Results
objectswhosecolourimplythattheyarebackgroundobjects.We
consideredg(cid:3) −i(cid:3) because it correspondsto the highestquality We computed LFs both for the whole field of view and for
16 subfields. The subfields define a regular square grid of
magnitudewavebands.
15 × 15 arcmin2 each and allow a good compromise between
Figure6showsthecolour-magnituderelationsofAbell496,
spatialresolutionanduncertaintiesinindividualmagnitudebins.
wherenobackgroundsubtractionhasbeenmade.Weseeawell
definedRedSequencethatdecreaseslinearlywithi(cid:3),downtoat We used 1 mag bins to limit the uncertainties. Several subre-
gions are then defined including a certain number of subfields
leastM =−14.5,as
i with common properties; they were chosen without assuming
(g(cid:3)−i(cid:3)) (cid:6)1.75−0.05i(cid:3), (4) circularsymmetryforthecluster.
RS
340 G.Bouéetal.:GalaxyluminosityfunctionofAbell496
Table2.faintendslopesofAbell496.
Region 20≤u∗≤23 18≤g(cid:3)≤22 17≤r(cid:3)≤22 17≤i(cid:3)≤22
−15.73≤ Mu∗ ≤−12.73 −17.73≤Mg(cid:3) ≤−13.73 −18.73≤Mr(cid:3) ≤−13.73 −18.73≤Mi(cid:3) ≤−13.73
All −1.68±0.35 −1.53±0.08 −1.62±0.05 −1.52±0.05
All(nocolourcuts) −1.78±0.51 −1.61±0.17 −1.73±0.18 −1.58±0.24
Centre −1.60±0.27 −1.43±0.07 −1.39±0.08 −1.41±0.05
South −1.87±0.34 −1.89±0.14 −1.79±0.11 −1.80±0.10
east-north-west −1.88±0.69 −1.48±0.22 −1.40±0.25 −1.58±0.12
Note:themagnitudeintervalscorrespondtothecentresof0.5magbins(All)and1.0magbins(Centre,South,east-north-west).
M M
u* g’
-22 -20 -18 -16 -14 -22 -20 -18 -16 -14 1000
1000
Abell 496 2 Abell 496 2 100
= - = -
α α 10
2
g
e
d 100
g/
a
m 1000
5
unts/0. 10 2eg 11000
o d
c g/
a
m
1 nts/ 1000
u
14 16 18 20 22 14 16 18 20 22 o
c 100
u* g’
10
M M
r’ i’
-22 -20 -18 -16 -14 -22 -20 -18 -16 -14
1000
1000
Abell 496 2 Abell 496 2
α = - α = - 100
2
g
e 10
d 100
g/
a
m 18 20 22 18 20 22 18 20 22 18 20 22
5
ounts/0. 10 Fig.8. Local luminosity functions for Ar’bell 496 in the r(cid:3) band. Each
c subfieldis15×15arcmin2.X-rayintensitycontourswithlogarithmic
stepsfromROSAT/PSPCdataaresuperimposed.Threemainareasare
1
14 16 18 20 22 14 16 18 20 22 defined in blue, red and green, which correspond respectively to the
r’ i’ centre, thewell populated Southern rectangle and thesparse northern
ring.
Fig.7.GloballuminosityfunctionsforAbell496inthefourbandswith
thebestfits(inred).
Had we adopted instead the star countsfrom the Besançon
model (see Fig. 2), the slope of the LF in the i(cid:3) band for the
TheLFsofAbell496inthefourbandsaredisplayedinFig.7 globalfieldwouldhavebeen−1.27±0.04.
(thecorrespondingdataaregiveninTableA.2oftheappendix), WealsocomputedtheLFsforgalaxiesintheRedSequence
showingthattheshapesoftheglobalLFsoftheAbell496field (where the redder limit is taken from Eq. (5), while the bluer
aresimilarinthefourbands,withthefaintendsincreasinglin- limitisthesymmetricalcut,withrespectivetotheaverageRed
early.AstheseLFsdonotlooklikeSchechterfunctions,wede- Sequence given in Eq. (4)). The slopes for the Red Sequence
cidedtofitonlythefaintendsbyapower-law.Theexpressionin galaxiesmatchedthoseoftheglobalLFsinallbands.TheLFs
termsofmagnitudeisgivenby: for galaxies bluer than the Red Sequence are not significantly
differentbutwithlargererrorbars(α≈−1.65±0.15).
Φ(M)=10−0.4(α+1)(M−M0). The local r(cid:3) LFs in the 16 subfields of Abell 496 are dis-
playedin Fig. 8.Thisfigureshowsthatthe LFsare notsimilar
ThebestfitslopesαoftheoverallLFsaregiveninTable2.We overthewholeclusterfield:subfieldsinthenorth,eastandwest
used the Levenberg-Marquardtmethod (e.g. Press et al. 1992) extremities of the cluster are sometimes poorly populated and
tofitthedata.Errorbarswerecomputedfrom1000parametric exhibit large error bars, while subfields in the Southern region
bootstraps,wherethepdfofthenetcountsisassumedGaussian showrisingLFs.Wecanthusdividetheclusterintothreemain
withawidthobtainedfromthepdfofthegrossgalaxycountsof regions: a central region 30 × 30 arcmin2 (1.15× 1.15 Mpc2,
the59Widefields.Thefaintendslopesvaryfrombandtoband, in blue inFig. 8),an east-north-westregionaroundthiscentral
butaretypicallyα=−1.55±0.05. zone(ingreeninFig.8)andaSouthernregion(inredinFig.8).
WerecomputedtheLFinther(cid:3)bandusingamuchmorecon- Thecentralregionextendstoroughlyonehalfofthevirialradius
servativecutinsurfacebrightness:µ <24.25(insteadof26.25). andcorrespondstothedensestregionofthecluster.
r
The faint end slope becomes α = −1.60 ± 0.05 (instead of Figure9showstheLFscomputedinthesethreesubregions,
−1.62±0.05).Hence,thefaintendslopesappearrobusttodif- inthefourphotometricbands(thecorrespondingdataaregiven
ferentcutsinsurfacebrightness. in Table A.2 of the appendix). The LFs have faint end slopes
G.Bouéetal.:GalaxyluminosityfunctionofAbell496 341
M M
u* g’
-19 -18 -17 -16 -15 -14 -13 -19 -18 -17 -16 -15 -14 -13
10000
Abell 496 Abell 496
2
g
de 1000
g/
a
m
1
unts/ 100
o
c
10
17 18 19 20 21 22 23 17 18 19 20 21 22 23
u* g’
M M
r’ i’
-19 -18 -17 -16 -15 -14 -13 -19 -18 -17 -16 -15 -14 -13
10000
Abell 496 Abell 496
2
g
de 1000
g/
a
m
1
unts/ 100
o
c
Fig.10.LargescalestructuresurroundingAbell496,inaregionof17×
10 17 18 19 20 21 22 23 17 18 19 20 21 22 23 17 deg2 (41×41 Mpc2), in a redshift slice within ±0.005 of that of
r’ i’ thecluster.Thegalaxiesaretaken from6dFGS-DR3(points),limited
to the completeness limit of K < 12.65, which corresponds to L∗/4
Fig.9.LuminosityfunctionsforAbell496inthefourbandsandinthe s
(usingtheK fieldLFofJonesetal.2006).Wealsoshowgroups(blue
threemainareasdefinedFig.8.Thebluecolourcorrespondstothecen- s
triangles) and clusters(large blue circles) found inNED in thesame
tralregion,redisfortheSouthandgreenfortheuppereast-north-west
redshiftinterval(withtheirredshiftshighlighted).Thesurroundedred
zone.
circleshowsthepositionoftheclustercentre.
(see Table 2) that are significantly shallower in the centre than
in the Southernperipheryin all bandsexceptu∗. The Southern massivecluster(1000kms−1),orexpressedintermsofphysical
region has a surface density of faintgalaxies (Mr(cid:3) > −14) that distancetoasliceof45MpcattheredshiftofAbell496.Onthe
ishigherthanorcomparabletothatofthecentralregion.Ifthis planeofthesky,welimitedoursearchtoaboxof17×17deg2
is not caused by field contamination (see Sect. 6.3), then one
(40Mpcattheclusterredshift).Thissizeistypicalofthelargest
wouldconcludethatthefaint(Mr(cid:3) > −14)galaxiesdonottrace cosmicbubbles(Hoyle&Vogeley2004).
thecluster,whichpresentsnosurfacedensityenhancement.
Figure 10shows thatthe 6dFGSgalaxiesin the neighbour-
Although they are both contained within the virial radius
hood of Abell 496 are more concentrated along a strip in the
of the cluster, the two external regions present LFs differing southeast/northwestdirection.Thisisconfirmedbythedistribu-
from one another. The Southern region (red) is still quite pop-
tionofgroupsandclustersthatwefoundinNED(whichismuch
ulated comparedto the greenregion,which is sometimesquite
lesshomogeneous)usingthesamesearchcriteria.Notethatthe
poor with LFs often not significantly positive. Since there are 6dFGS-DR3iscompletetoK ≤12.65(Jonesetal.2008)down
noclustersorgroupsknownnearby(assearchedwithNED,see togalacticlatitude|b|>10◦,asndinourzone,wehaveb<−24◦.
Fig.10),thissuggeststheremaybematterintheSouthernregion
ThegalaxiesdisplayedinFig.10areclearlydistributedalonga
infalling from the surroundingcosmologicalweb, as discussed
large-scalefilament,whichappearstobeatleast30Mpclong.
inthenextsection.
We tested the prominence of this filament in the following
manner.Wesearchedfortherectangleoflength15◦ (36Mpcat
5. LargescalefilamentintheAbell496 thedistanceofAbell496)andwidth2◦encompassingthelargest
amountofgalaxies,imposingthatAbell496liesalongthelong
neighbourhood
axisoftherectangle,within4◦ fromtheclosestedgealongthat
Abell496has beenshownto be a noticeablyquiescentand re- axis.Wefoundthatthefurthestedgealongthelongaxisisatpo-
laxed cluster (e.g. Durret et al. 2000). The only sign of sub- sitionangle(PA)137◦ anti-clockwisefromnorth.Wethenbuilt
structurefoundwasanenhancedconcentrationofemissionline 1000randomsamplesofasmany(487)galaxiesintheframeof
galaxiesinthenorthwest.FromFig.8,wealsoseethatthesouth- Fig. 10 as observed, and checked for the most populated rect-
ernpartofthesurroundingareaaroundtheclustershowsasig- angle,definedasabove,covering360PAsinstepsof1◦.While
nificantgalaxypopulation,withanLFthatresemblesthatofthe thefilamentintheobserveddatasethas221galaxieswithinthe
centralcluster. rectangle,noneofthe1000randomdatasetseverreachedmore
We searched the Six degree Field Galaxy Survey than81galaxies.Therefore,thefilamentatpositionangle137◦
(6dFGS-DR3) database (Jones et al. 2004, 2005, 2008) for ishighlysignificant.Thisfilamentshouldconstituteapreferen-
nearbygalaxiesin thelarge-scaleneighbourhoodofAbell496, tialavenueforinfallingmaterialintoAbell496,aswellasback-
ina±0.005redshiftslicearoundthemeanvalueof0.033.This splashingmaterialfromthecluster.However,thisfilamentdoes
slice corresponds to ±1.5 times the velocity dispersion of a notfullyexplaintheexcessofgalaxiesinthesouthernregionof
342 G.Bouéetal.:GalaxyluminosityfunctionofAbell496
Abell496sinceitisinclinedrelativelytothenorth-southdirec- (e.g.,Pracyetal.2005).Finally,tidaleffectsfromtheclusterpo-
tion. tential are the same,to firstorder,ongiantanddwarfgalaxies.
Given the trend that low luminosity ellipticals are less concen-
tratedthanmoreluminousones(Grahametal.2001),thelatter
6. Discussionandconclusions
willsurvivebetterthestrongtidesneartheclustercentre,which
shouldmaketheLFshallower,notsteeper.Theonlypossibleex-
6.1.ComparisonwithpreviousanalysesofAbell496
planationforasteeperfaint-endslopeinclusterswouldbethat
TheLFofAbell496waspreviouslymeasuredbyMolinarietal. galaxiesofmoderatelylowluminosityaretidallyfragmentedby
(1998), who analysed the cluster in 4 small fields, one includ- theclusterpotentialorbycloseencounters.
ingtheclustercentre,andbyDurretetal.(2002),whomeasured Now,ifthefieldcountsintheclusterfieldareunderestimated
thLFina42(cid:3)×28(cid:3) fieldinthe I band.Thefaint-endslopesof (because the reference fields are slightly underdense), the re-
−1.69±0.04inrand−1.49±0.04inifoundbyMolinarietal. sultant net cluster counts will be highly contaminated by field
areconsistentwithourslopesof−1.62±0.05and−1.52±0.05 counts. Writing the field counts as dN/dm = dex[β(m− m )]
0
in thesebands.Moreover,theirfaint-endslopeof−1.34±0.04 andtheclusterfaint-endluminosityfunctionasΦ(L) ∝ Lα,itis
ingisprobablyconsistentwithourslope(−1.53±0.08),given easy to show that if the field dominates the net cluster counts,
thattheirestimatederrorneglectscosmicvariance,which,aswe one will end up measuring α = (−β/0.4)−1. For example, if
showinFig.5,ismanytimesgreaterthanthePoissonvariance. β = 3/5 (Euclidean counts), one would measure α = −5/2,
Durret et al. (2002)find a slope of −1.79±0.01 in I, whereas while if β (cid:6) 0.36(asin the DFsin the magnituderangewhere
wefindhereaslopeof−1.52±0.05.Givenouranalysisofcos- wearemeasuringthefaint-endslopeoftheLF),oneshouldfind
micvariance,weestimatetheerrorfromcosmicvarianceonthe α=−1.9.
slopeofDurretetal.(2002)toberoughly0.08.Ifthiserrores- Weareconfidentthatwesufferlittlefromabackgroundcon-
timate is correct, then the difference in faint-end slopes would taminationofourLFs.Indeed,thefaint-endslopesthatwehave
bestatisticallysignificant.Thisdifferencemaybecausedbythe computedfortheglobalLF(Table2)andforthecentralregion
differentregionsprobedinthetwostudiesandthedifferentref- ofAbell496(Table2)areallconsiderablyandsignificantlyshal-
erencefieldsused. lower than α = −1.9(exceptin the less sensitive u∗ band).We
alsotookgreatcarenottounderestimatethecountsinourfield
count process by the use of very homogeneousfield data cov-
6.2.Comparisonofradialtrendswithotherclusters
eringalargeenoughfieldofviewinordertotreatproperlythe
Our g(cid:3), r(cid:3) and i(cid:3) LFs exhibit slopes that increase significantly cosmic variance (as described above). Finally the selection in
from the centre outwards (Table 2). This agrees with the trend colourthatwehaveappliedeliminates(bothintheclusterfields
for flatter LFs aroundcluster cDs foundby Lobo et al. (1997), andinthefieldsusedforstatisticalsubtraction)veryredobjects
with the steeper slope in the outer envelope of Coma found that are veryunlikely to belong to the cluster, so the field sub-
by Beijersbergen et al. (2002), and with the greater dwarf-to- tractionisquiteconservativeandthereforesecure.
giant ratio found by Driver et al. (1998a). Note, however, that The MegaCam colour redshift diagrams derived by Ilbert
all three trends are either qualitative or of marginal statistical et al. (2006)from the VIMOS VLT Deep Survey (VVDS) fol-
significance.Althoughourradialtrendisoppositetothatfound lowupoftheCFHTLSDFshowthatgalaxyspectraareshiftedto
by DeProprisetal.(2003)in 2dFGRS clusters, their shallower theredtosuchanextentthat,intheredshiftrange0.4<z<0.6,
slopeintheclusterenvelopesisnotstatisticallysignificant. thebulkoffield(intrinsicallybluespiral)galaxiesbecomered-
dering(cid:3)−r(cid:3)thannearbyellipticals,andthesamehappensinthe
range0.5<z<1.2forr(cid:3)−i(cid:3)colours.Wearethereforeprobably
6.3.Aubiquitousdwarfpopulation?
contaminatedbyintrinsicallyblue(spiral)backgroundgalaxies
Whereas our faint-end slope for the core of Abell 496 is fairly withcoloursalmostasredasourRedSequenceatz<0.4or0.5.
shallow (α (cid:6) −1.4), it is still steeper than most estimates of Note that two of the studies concluding to steep faint-end
the field LF: Blanton et al. (2003) find α = −1.05±0.01 for LFslopes(DeProprisetal.1995;Milneetal.2007)haveneg-
r
the SDSS galaxies, while Jones et al. (2006) find α between ativeLFsatsomemagnitudes,whichsuggestsinadequateback-
−1.10 ± 0.04 (J-band) and −1.21 ± 0.04 (r-band) for 6dFGS ground subtraction (Fig. 8 shows that 4 of our 12 non-central
galaxies. However, Blanton et al. (2005) estimate that a care- localLFsalsodisplaynegativeLFsatsomeintermediatemagni-
ful inclusion of SDSS low surface brightness galaxies yields tudes,whichmakestheseparticularLFssuspicious).Moreover,
α < −1.3 and perhaps as steep as −1.5. But several authors all steep faint-end slopes were found by authors who made no
r
found very steep slopes (α as steep as −2.2) for faint galaxy colour cuts, with the exceptionof Popesso et al. (2006).These
populationsinclusters(seeTableA.1),suggestinganimportant authorsestimatedtheLFsofclustersintheSDSS,usingthesta-
populationofdwarfgalaxiesinclusters,whichisnotseeninthe tistical subtraction method, and found α ≈ −2.2. The range of
fieldLFs. absolutemagnitudeswherePopessoetal.seetheriseinthefaint-
Itisdifficulttounderstandhowdwarfgalaxiescouldsurvive end LF, [−17.7,−13.7],correspondsto apparentmagnitudesin
betterinthehostileclusterenvironmentthaninthefield.Direct therange18.03<m<22.03,whichmatchesouranalysedrange
galaxymergersshouldhavelittleeffectondwarfs,whosecross- of apparent magnitudes. It is puzzling that we do not find in
sectionsaresmall.Mergersofdwarfsafterorbitaldecaybydy- our deeperimagesthe low surface brightnessdwarf population
namicalfrictionintothecentralcDcannotbeanexplanation:the foundbyPopessoetal.intheSDSSimages.
decay timesare expectedto be proportionalto galaxymass, so Figure 11 displays the u∗ − r(cid:3) vs. i(cid:3) colour-magnitude dia-
the giant galaxies can disappear into the central cD. However, gram of the Abell 496 field. The Red Sequence is clearly visi-
theorbitaldecaytimesforthelowmassgalaxiesshouldbelong ble at bright magnitudesand its red edge is still sharp at mag-
enoughthatthefaint-endmassfunctioninclusterswouldbethe nitudes18 < i(cid:3) < 22. The galaxiescalled red cluster members
sameasthefield,notsteeper.Moreover,thereisnoobservational byPopessoetal.andfainterthan M(cid:3) = −19arealmostallfield
i
evidenceforluminositysegregationoffaintgalaxiesinclusters galaxiesaccordingtoourcolour-magnitudediagram.Similarly,
G.Bouéetal.:GalaxyluminosityfunctionofAbell496 343
result is that X-ray selected clusters show shallower faint-end
slopes than do non X-ray clusters (Valotto et al. 2004), which
areexpectedtobemorepronetoprojectioneffects.
Apossiblecauseforthediscrepancybetweendifferentanal-
ysescouldbetheuncertaintiesfromstar/galaxyseparation.This
isaseriousissueforouranalysis,becauseAbell496liesatlower
absolutegalacticlatitude(b=−36◦)thanourreferenceDFfields
(b=−58◦,42◦,60◦and−53◦),sothatAbell496ismorecontam-
inatedbystars.Indeed,ouri(cid:3)-bandLFhasaconsiderablyshal-
lower faint-end slope of −1.27±0.04 instead of −1.52±0.05
(Table2).Moreover,ingeneral,theerrorsonstar/galaxysepara-
tioncouldgoeitherway,leadingtoeitheranunderestimationor
overestimationofthefaint-endLFslope.
Apossibleexplanationforthewiderangeoffaint-endslopes
(see Table A.1) is cosmic variance: some clusters may exhibit
steeperslopesthanothers.However,inspectingtheslopesfound
intheliterature(TableA.1),onenoticesawiderangeofslopes
for the same cluster analysed in similar wavebands,magnitude
ranges and fields of view (contrast the slopes in similar re-
gionsofComaof−1.7,−1.8ofLoboetal.1997;andTrentham
1998a; with the slopes shallower or equal to −1.4 of Andreon
&Cuillandre2002).Moreover,thetwostudiesthathaveenough
clustersto“beat”cosmicvariancehaveinconsistentslopes(−2.2
Popessoetal.2006and−1.4Trentham1998b)inthemagnitude
Fig.11.Ouru∗−r(cid:3)vs.i(cid:3)colour-magnitudediagramforAbell496.The range−18to−14.
dashed contours are for our selected cluster members using Eq. (5),
while the solid (red) contours (same levels, spaced by factors of 1.6)
arethegalaxiesidentifiedasfieldgalaxies,becausetheyareredderthan 6.4.Conclusions
ourRedSequenceofEq.(5).AlsoshownarethelimitsusedbyPopesso
etal.(2006)toseparatetheirredclustergalaxiesandfieldgalaxies(up- WehaveanalysedthegalaxyLFsintherelaxedclusterofgalax-
perhorizontalline)andtheirblueandredclustergalaxies(lowerhori- ies Abell 496. We have shown that the LFs are not only well-
zontalline),aftercorrectingbothfor(u∗−r(cid:3)) =(u−r) −0.35, definedinthecentralregion(withafaint-endslopeα = −1.4±
MegaCam SDSS
asfoundusingthematchesinafieldofAbell85forwhichwehadboth 0.1),butalsointhesouth.Aconcentrationofclustersisindeed
SDSScataloguesandreducedMegaCamimages.Theverticallinesde- observed towards the southeast and along a filament extending
limittheregionwherePopessoetal.clearlyfoundasteepfaint-endLF southeast to northwest (Fig. 10), suggesting the existence of a
slope.
cosmologicalfilamentlinkingAbell496withvariouspoorclus-
tersandgroups.However,suchafilamentcannotbeverydense
sincenoX-rayemissionisdetectedinthisdirection,contraryto
atMi(cid:3) =−16.5,ourRedSequence(oritsextrapolation)becomes whatisobservedinAbell85(Durretetal.2003).
bluerthantheblue-redgalaxycutofPopessoetal.Thissuggests
We discussthedisagreementofourfairlyshallowfaint-end
thatanincreasingfractionofbothPopessoetal.’sredandblue
slopeforAbell496withthatfoundbyotherauthorsinthisand
galaxiesareinfactfieldgalaxies.
From inspection of the u∗ − g(cid:3) and g(cid:3) − r(cid:3) colour-redshift otherclusters.Althoughitisclearthatacarefulestimateofthe
diagramsofIlbertetal.(2006),oneinfersthattheu∗−r(cid:3)colour referencefieldgalaxycountsandtheircosmicvariancearecru-
cial,theremayalsobeacosmicvarianceinthefaint-endslopes
cutusedbyPopessoetal. shouldvarynegligiblywithredshift.
ofclusterLFs.Wefindthatuncertaintiesinthestar/galaxysep-
Thisexplainswhythegalaxiesweassignto thefield(solidred
arationcanberesponsibleforsome(butprobablynotall)ofthe
contours in Fig. 11) – because they are redder than our sharp
g(cid:3) − i(cid:3) vs. i(cid:3) Red Sequence – pollute the u∗ −r(cid:3) vs. i(cid:3) colour- scatterinthefaint-endLFslopesgivenintheliterature.Wehigh-
magnitude diagram. Therefore, colour cuts based upon u∗ −r(cid:3) lighttheremovalofgalaxiesredderthantheRedSequenceasa
meanstoreducethenoiseintheLFs,butitisnotclearifthelack
arenotefficientinrejectingbackgroundgalaxies(withz<∼0.4).
ofadequatecolourcutscausesabiastowardssteeperslopes.The
Nevertheless, while LF analyses based upon the statistical
adventofverydeepspectroscopyinclusterfieldsshouldrapidly
subtraction method with inappropriate or non-existent colour
settletheissueofthefaint-endslopeoftheclusterLF.
cuts should lead to noisier LFs, it is notclear whythey should
bebiasedtosteeperslopes,unlessthenoiseissuchthatthefaint
endoftheLFfluctuatesfrompositivetonegative(whichisnot
the case for the globalLF of Popesso etal.). Althoughsimula- Acknowledgements. Theauthorsthanktherefereeforhisdetailedandconstruc-
tive comments. Theauthors would like tothank Elisabete DaCunha, Andrea
tionsbyValottoetal.(2001)showedthatclustersselectedin2D
Biviano,VincentLeBrunandDidierPelatforusefuldiscussions,PaolaPopesso
will have faint-end slopes much steeper than what they put in forusefulcommentsandAndreaBivianoforacriticalreadingofthemanuscript.
theirsimulations(−1.4insteadof−1inroughlythesameabso- TheauthorsarealsogratefultotheCFHTandTERAPIXteamsfortheirhelp,
lute magnituderangeas where Popesso et al. foundtheir slope inparticulartoEmmanuelBertinandHenryMcCrackenfordiscussions,andto
of −2.3), Valotto et al. have also shown that LFs measured in theFrenchPNG,CNRSforfinancialsupport.TheyalsothankMatthewColless
forpermissiontouse6dFGS-DR3,inadvanceofpublication.Thisresearchhas
clusters selected in 3D, such as all the clusters reportedin this madeuseoftheNASA/IPACExtragalacticDatabase(NED)whichisoperated
paper(includingtheX-rayselectedclustersstudiedbyPopesso bytheJetPropulsionLaboratory,CaliforniaInstituteofTechnology,undercon-
etal.),shownobiasinthefaint-endslope.Aconfirmationofthis tractwiththeNationalAeronauticsandSpaceAdministration.
344 G.Bouéetal.:GalaxyluminosityfunctionofAbell496
Appendix
TableA.1.Comparisonofdeepphotometrically-estimatedclustergalaxyluminosityfunctions.
Cluster(s) r /r abs.magrange α Reference
max 100
LocalGroup 3.6 M <−9 –1.1 Pritchet&vandenBergh(1999)
V
Virgo 1.1 M <−13.1 –1.25 Sandageetal.(1985)
B
Virgo 1.1 M <−11.1 –1.3 Sandageetal.(1985)
B
Virgo 0.24×0.24 −15.6<M <−11.1 –2.26 Phillippsetal.(1998)
R
Virgo 2×0.4×1.2 −18<M <−11 –1.35 Trentham&Hodgkin(2002)
B
Virgo 2×0.4×1.2 −17<M <−14 –1.7 Trentham&Hodgkin(2002)
B
Coma 0.08×0.08 M <−11.6 –1.42 Bernsteinetal.(1995)
R
Coma 0.08×0.08 −11.6<M <−9.4 –2.0 Bernsteinetal.(1995)
R
Coma 0.58×0.24 M <−15.5 –1.8 Loboetal.(1997)
V
Coma 0.3×0.3 −15.6<M <−10.6 –1.7 Trentham(1998a)
B
Coma 0.3×0.3 −17.6<M <−11.6 –1.7 Trentham(1998a)
R
Coma 0.8 M <−13.4 –1.32 Beijersbergenetal.(2002)
U
Coma 0.8 M <−13.4 –1.37 Beijersbergenetal.(2002)
B
Coma 0.8 M <−13.4 –1.16 Beijersbergenetal.(2002)
r
Coma 0.28×0.43 M <−12.8 –1.25 Andreon&Cuillandre(2002)
B,V,R
Coma 0.28×0.43 M <−11.3 –1.4 Andreon&Cuillandre(2002)
V
Coma 0.28×0.43 M <−11.8 –1.4 Andreon&Cuillandre(2002)
R
Coma 0.6×0.6 −19.1<M <−14.6 –1.55 Iglesias-Páramoetal.(2003)
R
Coma 0.01 M <−9.1 –2.29 Milneetal.(2007)
R
Coma 0.01 M <−11.3 –1.9 Adamietal.(2007)
R
Coma(north) 0.28×0.22 M <−10.5 –1.48 Adamietal.(2007)
B
Coma(north) 0.28×0.22 M <−11.3 –1.74 Adamietal.(2007)
R
Coma(south) 0.28×0.22 M <−10.5 –1.32 Adamietal.(2007)
B
Coma(south) 0.28×0.22 M <−11.3 –1.28 Adamietal.(2007)
R
Abell426 0.1×0.1 −19.4<M <−13.4 –1.56 DePropris&Pritchet(1998)
I
Abell496 4×0.19×0.19 M <−13.2 –1.34 Molinarietal.(1998)
g
Abell496 4×0.19×0.19 M <−13.2 –1.69 Molinarietal.(1998)
r
Abell496 4×0.19×0.19 M <−13.2 –1.49 Molinarietal.(1998)
i
Abell496 0.9×0.6 MAB<−13.7 –1.79 Durretetal.(2002)
I
Abell539 0.24×0.24 −18.5<M <−14.0 –1.42 DePropris&Pritchet(1998)
I
Abell1185 0.9 M <−12.4 –1.25 Andreonetal.(2006)
B
Abell1185 0.9 M <−13.2 –1.28 Andreonetal.(2006)
V
Abell1185 0.9 M <−13.7 –1.28 Andreonetal.(2006)
R
Abell1367 0.7×0.7 M <−14.3 –1.07 Iglesias-Páramoetal.(2003)
R
Abell2199 0.04×0.04 M <−10.5 –2.16 DeProprisetal.(1995)
B
3clusters 0.05×0.05 M <−13.0 –2.28 DeProprisetal.(1995)
I
9clusters 0.25×0.25 −19<M <−14 –1.4 Trentham(1998b)
B
9clusters 0.25×0.25 −14<M <−11 –1.8 Trentham(1998b)
B
UrsaMajor 6.8 −17<M <−11 –1.1 Trenthametal.(2001)
R
69RASS/SDSSclusters 0.7 M <−13.7 –1.98 Popessoetal.(2006)
g
69RASS/SDSSclusters 0.7 M <−13.7 –2.19 Popessoetal.(2006)
r
69RASS/SDSSclusters 0.7 M <−13.7 –2.26 Popessoetal.(2006)
i
69RASS/SDSSclusters 0.7 M <−13.7 –2.25 Popessoetal.(2006)
z
Notes:Themethodusedisfieldsubtraction,exceptfortheLocalGroupstudyofPritchet&vandenBergh(1999)andthefirstlineoftheVirgo
analysisbySandageetal.(1985),whicharebaseduponrawcounts,whilethesecondlineoftheVirgoanalysisofSandageetal.addsastatistical
backgroundcorrection.ThevirialradiiarefromMamonetal.(2004)(Virgo),Łokas&Mamon(2003)(Coma),thispaper(Abell496),Markevitch
etal.(1999)(Abell2199),andotherwiseadaptedfromthevelocitydispersionsmeasuredbyFaddaetal.(1996),whenavailable(onlyfor5outof
the9clustersofTrentham1998b;and3of4forDeProprisetal.1995).MagnituderangesareconvertedtoH =72kms−1Mpc−1.Typicalerrors
0
onαareintherange0.1to0.2.