Structural Properties of Central Galaxies in Groups and Clusters

2.3 MB·English

by  Yicheng Guo

Mon.Not.R.Astron.Soc.000,1–22(2008) Printed23January2009 (MNLATEXstylefilev2.2)
Structural Properties of Central Galaxies in Groups and Clusters
Yicheng Guo1⋆, Daniel H. McIntosh1†, H. J. Mo1, Neal Katz1, Frank C. van den Bosch2,
Martin Weinberg1, Simone M. Weinmann3, Anna Pasquali2, Xiaohu Yang4,5
9
0 1AstronomyDepartment,UniversityofMassachusetts,710N.PleasantSt.,Amherst,MA01003,USA
0 2Max-Planck-Institutfu¨rAstronomie,Ko¨nigstuhl17,D-69117Heidelberg,Germany
2 3Max-Planck-Institutfu¨rAstrophysik,KarlSchwarzschildStr.1,Postfach1317,85741Garching,Germany
4ShanghaiAstronomicalObservatory,thePartnerGroupofMPA,NandanRoad80,Shanghai200030,China
n
5JointInstituteforGalaxyandCosmologyofShanghaiAstronomicalObservatoryandUniversityofScienceandTechnologyofChina
a
J

1
1 DRAFT: 23January2009

]
O
ABSTRACT
C Using a statistically representative sample of 911 central galaxies (CENs) from the SDSS
DR4GroupCatalogue,westudyhowthestructure(shapeandsize)ofthefirstrank(bystellar
.
h mass)groupandclustermembersdependson(1)galaxystellar mass(Mstar),(2)theglobal
p environmentdefinedbythedarkmatterhalomass(Mhalo)ofthehostgroup,and(3)thelo-
-
o calenvironmentdefinedbytheirspecialhalo-centricposition.WeestablishaGALFIT-based
r pipelinefor2DSe´rsicfittingofSDSSdatatomeasuretheSe´rsicindex,n,andhalf-lightra-
st dius,r50,fromr-bandgalaxyimages.Throughtestswithsimulatedandrealimagedata,we
a demonstratethatourpipelinecanrecovergalaxypropertieswithoutsignificantbias.Wealso
[ findthatuncertaintiesinthebackgroundskyleveltranslateintoastrongcovariancebetween

thetotalmagnitude,thehalf-lightradius,andtheSe´rsicindex,especiallyforbright/massive
2
v galaxies.WeapplyourpipelinetotheCENsampleandfindthattheSe´rsicindexnofCENs
0 dependsstronglyonMstar,butonlyweaklyornotatallonMhalo.Then-Mstarrelationholds
5 forCENsoverthefullrangeofhalomassesthatweconsider.LessmassiveCENstendtobe
1 disk-like and high-masssystems are typically spheroids, with a considerable scatter in n at
1 allgalaxymasses. Similarly,CEN sizesdependongalaxystellar massandluminosity,with
1. earlyandlate-typegalaxiesexhibitingdifferentslopesforthesize-luminosity(r50-L)andthe
0 size-stellarmass(r50-Mstar)scalingrelations.Moreover,totesttheimpactoflocalenviron-
9 mentonCENs,wecomparethestructureofCENswiththatofcomparablesatellitegalaxies
0 (SAT).Wefindthatlowmass(<1010.75h−2M )SATshavesomewhatlargermedianSe´rsic
⊙
: indices compared with CENs of a similar stellar mass. Also, low mass, late-type SATs are
v
moderatelysmaller in size than late-type CENs of the same stellar mass. However,we find
i
X nosizedifferencesbetweenearly-typeCENsandSATsandnostructuraldifferencesbetween
r CENsandSATswhentheyarematchedinbothopticalcolourandstellarmass.Thesimilarity
a
in the structureofmassive SATsand CENs demonstratesthatthis distinctionhasnosignif-
icantimpactonthe structureof spheroids.We concludethatMstar is the mostfundamental
propertydeterminingthebasicstructuralshapeandsizeofagalaxy.Incontrast,thelackofa
significantn-Mhalorelationrulesoutacleardistinctgroupmassforproducingspheroids,and
themorphologicaltransformationprocessesthatproducespheroidsmustoccuratthecentres
ofgroupsspanningawiderangeofmasses.
Keywords: galaxies:clusters:general—galaxies:evolution—galaxies:formation—galax-
ies:fundamentalparameters—galaxies:structure.
1 INTRODUCTION
Understandingtherolethatenvironmentplaysinshapingthemor-
phologyofgalaxiesremainsanimportantchallengeinthestudyof
⋆ E-mail:[email protected] galaxyformationandevolution.Inthestandard galaxyformation
† Currentaddress:DepartmentofPhysics,UniversityofMissouri-Kansas andevolution paradigm, allgalaxies startedasstar-formingdisks
City,KansasCity,Missouri64110,USA atthecentresofsmalldarkmatter(DM)haloes.Subsequenthierar-
(cid:13)c 2008RAS
2 Guo etal.
chicalevolutionhastransformedgalaxiesintospheroidstoproduce amoreearly-typemorphologybyheatingand’puffingup’thedisk
the bimodality observed in the present-day populations. Tied to component. Tidal stripping, the effect of the tidal force suffered
thestrongcolourbimodalityaredifferencesinmorphologyandre- byasatellitealongitsorbit,maytransformasatellitegalaxyintoa
latedgalacticstructure.Bluestar-forminggalaxiestendtobedisk- spheroidbyremovingitsdisk,anditmaybeeffectiveinhaloesover
dominatedwithexponentialradiallightprofiles(late-types),while alargemassrange.Sincetheabovetwoprocesseschangethestellar
red non-star-forming systems have spheroidal mass distributions massofagalaxybyatmostafactoroftwo,iftheyareresponsible
withsteeperlightprofiles(early-types).Manyobservationssuggest forthemorphologicaltransformationonewouldexpecttoseesatel-
that there may be an environmental component to differences in liteswithstatisticallysignificantdifferencesintheirmorphological
galaxyproperties;e.g.,dependence ofmorphology (e.g.,Dressler andstructuralpropertiescomparedwithcentralsofasimilarstellar
1980;Gotoetal.2003;McIntoshetal.2004;Blantonetal.2005) mass. However, vandenBoschetal. (2008) and Weinmannetal.
andstarformationrelatedproperties(e.g.,Hashimotoetal.1998; (2008)findthatsatellitegalaxiesareonlymarginallymoreconcen-
Baloghetal. 2004; Kauffmannetal. 2004) to local galaxy den- tratedthancentralgalaxieswithsamestellarmass,whichsuggests
sity.Presumably,thephysicalprocessesthathavebuiltlargerDM that satellite galaxies only undergo a minor change in their mor-
haloeshousinggroupsandclustersofgalaxiesmustberesponsible phologyaftertheyfallintoamassivecluster,andthattheabovetwo
atsomelevelfortheobservedevolutionofthetwoprimarygalaxy processesmaynotbesufficienttoexplainingtheirmajormorpho-
populations. logicaltransformation.Itisimportanttonotethattheseprocesses
The latest theoretical models of galaxy evolution invoke the basicallyproduceearlytypesbydiminishingthediskstructureof
transformation of blue disks into red spheroids within a hierar- later-typespirals;i.e.,thesemechanismsmayproduceS0/Saearly
chical framework to explain the factor of two growth observed types,buttheydonotcreatemassivespheroidsorellipticalgalax-
in the early-type galaxy (ETG) population since z = 1 (e.g., ies.
Belletal.2004;Blanton2006;Borchetal.2006;Faberetal.2007; Besidestheaforementioned cluster-specificmechanismsthat
Brownetal. 2007). It is usually assumed that to successfully re- appear to have only minor impact on the morphologies of satel-
producethegalaxybimodalityrequiresphysicalmechanismsthat litegalaxies,numericalsimulationsdemonstratethatthemergerof
bothtransformstarformationandmorphology.Avarietyofgalaxy twodiskgalaxieswithsimilarmassesproducesaspheroidgalaxy
transformation scenarios can be found in the literature, many of (e.g., Toomre 1977; Barnes&Hernquist 1996; Naab&Burkert
which are predicted to be important only in particular environ- 2003; Coxetal. 2006) and, hence, are likely an important mech-
ments.Yet,recentadvances inunderstanding bimodalityhavefo- anismfortheformationofspheroids andellipticals.Majormerg-
cused on environmental processes that mostly impact star forma- ersarebelievedtobeefficientingroup-sizehaloesandtobesup-
tion.Forexample,vandenBoschetal.(2008)successfullydemon- pressed in more massive haloes because of the increasing differ-
strate that quenching is important for producing redder galaxies ences in the relative velocities between member galaxies com-
overarangeofdifferentenvironments,butaclearpictureofwhat pared to their own internal velocity dispersions. It has long been
governsmorphologicalbimodalityisstilllackingandcontroversial. assumed that the smaller velocity dispersions found in galaxy
Toshedlightonwhetheraspecialenvironmentexistsforthetrans- groupsallowmoregalaxyinteractions(Cavaliereetal.1992);also
formationofgalaxymorphology,westudytheshapesandsizesof the orbital decay timescale is shorter in lower-mass haloes (e.g.
arepresentativesampleofcentralgalaxiesfromgalaxygroupsand Cooray&Milosavljevic´ 2005). However, McIntoshetal. (2008)
clustersintheSloanDigitalSkySurvey(SDSS,Yorketal.2000). findthatmajormergersamongmassivegalaxiesoccursatthecen-
Quantifyingthestructuralpropertiesofgalaxies,suchasthesteep- tres of clusters, as well as large groups, yet this merely makes
ness of the light profile shape, provides a direct means to assess biggerspheroidsfromsmallerspheroids.Moreover,Hopkinsetal.
morphologicaltransformation. (2008) also show, using theoretical arguments, that the massive
Ifallgalaxiesstartedassmalldisks,thenthesimpleexistence centralgalaxiesofclustersstillhavealargechancetomergewith
of spheroidal systems makes it clear that morphological transfor- theirsatellites.Thesefindingshighlightonceagaintheopenques-
mationoccurs.Thetransformationfromlatetoearly-typegalaxies tionof whichenvironment or halomass isideal for transforming
mayoccurinonetraumaticeventorbetheresultofmultiplepro- disks into spheroids. It appears that major mergers preferentially
cesses over billions of years. There is no shortage of theoretical happen betweencentral andsatellitegalaxies; therefore,theexis-
predictions for the creation of ETGs, from violent galaxy-galaxy tenceofaspecialhalomassformajormorphological transforma-
mergerstotheslowfadingofdisks.Generallyspeaking,theearly tionssuchasmergersmightmanifestitselfasanoticeablechange
typepopulationincludesarangeofspheroid-dominatedmorpholo- inthemorphological distributionofcentral galaxiesatsomespe-
gieswithand without adisk component (e.g.,ellipticals,lenticu- cific halo mass. We already know that central galaxies living in
lars, and bulge-dominated spiral galaxies). Thus, it is likely that smallhaloeshavedisk-likeshapeswithlowconcentrationsandflat
more than one physical mechanism is responsible for the variety lightprofileswhilethoseinlargehaloeshavespheroid-likeshapes
amongETGs.Narrowingdowntheprocessesthataremostrespon- withhighconcentrationsandsteeplightprofiles.Acarefulstudyof
sibleforturningdisksintospheroidsremainsacriticalpieceofthe thedistributionofstructuralpropertiesinhaloesspanningarange
galaxy evolution puzzle. In this paper, we approach thisproblem inmasswillhelpshedlightonthisopenquestion.
bytestingwhether or not thereisaspecificenvironment wherea Ouranalysisisbasedontwoquantitativemeasuresofgalac-
strongmorphologicaltransitiontakesplacethatcanthenbetiedto tic structure, the Se´rsic index and the size, which are directly
aparticularprocess. related to galaxy morphology. The measurement of galaxy light
There are several morphologically-altering mechanisms that profile shapes and sizes has a long history (Shaw&Gilmore
are predicted to be effective mainly in the high-density environs 1989; Byun&Freeman 1995; deJong 1996; Simard 1998;
ofmassivegroupsandclusters.Harassment,thecumulativeeffect Khosroshahietal. 2000, and references therein) and the develop-
ofmanyhighspeedencounterswithsatellitegalaxies(Mooreetal. ment of automatic routines to handle the huge number of galax-
1996),ispredictedtooccurprimarilyingroupsandclustersafter ies from modern surveys is well-motivated. In this work, we de-
asatellitegalaxyisaccreted,andmaytransformadiskgalaxyinto velop a powerful pipeline for applying a well-tested and popular
(cid:13)c 2008RAS,MNRAS000,1–22
StructuralPropertiesofCentralGalaxies 3
software package for two-dimensional (2D) galaxy image fitting ThedetailsofthegroupfinderusedtoconstructtheDR4ver-
(GALFIT,Pengetal.2002)toSDSSr-banddata.WefitaSe´rsic sionofthegroupcataloguearegiveninYangetal.(2005,2007).
model(Se´rsic1968)totheimagesofgalaxiesandusetheSe´rsicin- Briefly,thegroupfinder startswithafriends-of-friends(FOF)al-
dex,n,andhalf-lightradius,r ,ofthebestfitmodelstodescribe gorithmusingarestrictivelysmalllinkinglengthtodefinepoten-
50
the shapes and sizes of galaxies, respectively. A well-known, yet tial groups and their centres in agalaxy redshift survey. A rough
oftenoverlooked,issueinprofilefittingisthecriticalsensitivityto groupmassisestimatedfromthetotalgroupluminosity,assuming
theestimateofthebackground skylevel(MacArthuretal.2003). amass-to-lightratio1.Fromthegroupmass,thegroup-finderuses
Weexplorethisissueindetailanddiscussitsimpactonquantify- an adaptive filter to iterate on the virial search parameters (pro-
ingthestructureofgalaxies,inparticularthatofhigh-masscentral jectedradiusandvelocitydispersion),whichinturnareusedtose-
galaxies. lectgroupmembersinredshiftspace.Thismethodisiterateduntil
In this paper, we try to answer two questions about the en- thegroupmembersconverge.Thisalgorithmhasbeenthoroughly
vironment of morphological transformation: (1) isthereacritical testedwithmockgalaxyredshiftsurveysandisshowntobemore
DM halo mass where central galaxies are transformed from late- successful thanconventional FOFfinders. Theaveragecomplete-
typetoearly-type?(2)isthecentralpositioningroupsandclusters nessofindividualgroupsintermsofmembershipis∼90percent,
aspecialplacefordeterminingthestructureofgalaxies.Previous withonly∼ 20percentcontaminationfrominterlopers.Thehalo
workarguingwhethergalaxymorphology(e.g.,Dressler1980)or massofeachgroupisestimatedusingtwomethods:(1)theranking
starformation(e.g.,vanderWel2008)dependsmorecriticallyon ofitstotalcharacteristicluminosityand(2)therankingofitstotal
environment employ local galaxy density measurements that are characteristicstellarmass.AsshowninY07,bothmethodsagree
lessnaturalandlessphysicallymeaningfulthanthehalomassand verywellwitheachother,withascatterof0.1dex(0.05dex)atlow
the location within a host halo (Weinmannetal. 2006). Here we (high)halomasses.Inthispaper,weusethehalomassfromstellar
usetheSDSSDR4GroupCatalogueofYangetal.(2007),which massranking.Finally,owingtother<17.7(extinction-corrected)
providesstatisticalmeasuresofthehosthalomass(globalenviron- magnitudelimitoftheMainsample,theminimumM forwhich
halo
ment)andthehalo-centricposition(localenvironment) forSDSS the group selection is complete changes with redshift. Therefore,
galaxies.Westudythequantitativestructureofgalaxieslivingatthe welimitouranalysistogroupswithz ≤0.08,whicharedetected
presumed dynamical centresof DM haloes spanning nearly three with high completeness down to log(Mhalo/h−1M⊙) = 11.78,
ordersofmagnitudeinmass.Inhierarchicalmodelsofgalaxyfor- allowingustostudygalaxiesfromsmallgroupswithgoodimage
mation,allgalaxiesbeginasthecentralgalaxyinasmallerhaloand resolution.
thenbecomesatellitegalaxiesifthesmallhalomergeswithabig- Thespectroscopiccompletenessofthesampleusedtodeter-
gerone.Therefore,comparingthestructuralpropertiesofcentrals minegalaxygroupsplaysacrucialroleinidentifyingCENs.Owing
andsatellitescanshedlightontheevolutionofgalacticmorphol- tofibrecollisions,theMainsamplemissesabout8percentofSDSS
ogyanditsdependenceonenvironment,andhelpanswerwhether galaxiesmeetingthespectroscopictargetingcriteria(Blantonetal.
centralgalaxiesareadistinctpopulationwithuniqueformationhis- 2003).Thiseffectissevereinregionsofhighgalaxynumberden-
tories. sity(Hoggetal. 2004), such as in large groups and clusters. The
In§2wepresent our sampleselection.In§3wepresent and Y07 group catalogue contains three samples that address this in-
test our fitting pipeline and show the sensitivity of the fits to the completenessdifferently.Eachsamplespanstheredshiftrangeof
backgroundskylevel.Wepresenttheresultsofourfitstothecen- 0.01 ≤z ≤0.20.SampleIcontains362356Maingalaxies.Sam-
tralgalaxiesin§4,boththeirSe´rsicindicesandsizes,andcompare ple II includes 7091 additional galaxies with spectroscopic red-
themtosatellitegalaxies.Wesummariseourmainconclusionsin shiftsmeasuredfromothersurveys(e.g.,2dF,Collessetal.2001).
§5.Wealsoincludeanappendixwherewecompareourfitstothose Sample III adds 38672 galaxies missing redshifts due to fibre-
of theNYU-VAGC(Blantonetal.2005).Throughout weadopt a collisions, which are assigned a redshift based on their nearest
flat ΛCDM cosmology with Ω = 0.3, Ω = 0.7 and use the neighbour.Forthethreesamples,thegroupfinderdetects201621,
m Λ
Hubbleconstantintermsofh≡H /100kms−1Mpc−1. 204813and205846groups,respectively.
0
Note that the fibre-collision correction applied to sample III
maytransfersomeCENsinsampleIItosatellitegalaxiesinsam-
2 SAMPLESELECTION pleIIIandviceversa.Forourselection,wechooseonlygalaxies
identifiedasCENsinbothsampleIIandsampleIII.Thesegalaxies
2.1 CentralGalaxySamplefromSDSSGroupCatalog
areguaranteedtobeCENsregardlessofwhetherthefibre-collision
To study the structural properties of central galaxies (CENs) correction was applied or not. In addition, we use the Mhalo of
in groups and clusters, we use the SDSS galaxy group cata- theseCENsdrawnfromsampleII.Ouranalysis(discussedin§3)
logueofYangetal.(2007,hereafter Y07).Thiscatalogueiscon- isbasedonaCPU-intensivegalaxyimagefittingroutine,thus,to
structed using the New York University Value-Added Galaxy constructarepresentativesamplewerandomlyselectCENsfrom
Catalog (NYU-VAGC, Blantonetal. 2005) reprocessing of the halomassbinsspanningthefullrangeofgroupsinthez ≤ 0.08
spectroscopic ’Main’ selection (Straussetal. 2002) from the volume-limitedsample.Forlog(Mhalo/h−1M⊙)=[12.0 :14.0],
fourth data release of Sloan Digital Sky Survey (SDSS DR4, werandomlyselect100CENsfromeightbinsof0.25dexwidth.At
Adelman-McCarthyetal. 2006). The NYU-VAGC provides im- higherhalomassesthenumberofgroupsdecreasesrapidly,thusto
proved reductions and additional galaxy property measurements. maintaingoodstatisticsweselect100CENsfromthe[14.0:14.5]
Thegroupcatalogue providestwophysicallymotivatedmeasures bin, and useall 11 CENsingroups withlog(Mhalo/h−1M⊙) >
ofenvironmentforeachgalaxy:(i)thedarkmatterhalomassofits
hostgroup(M ),and(ii)itsdistancetothecentral(i.e,highest
halo
stellarmass)groupmemberofthegroup.Herewebrieflydescribe
thegroupcatalogueandwediscussitsredshiftcompletenessasit 1 Theresultinggroupcatalogueisinsensitivetotheinitialassumptionre-
relatestoourfinalselectionofarepresentativesampleofCENs. gardingtheM/Lratios.
(cid:13)c 2008RAS,MNRAS000,1–22
4 Guo etal.
11.5
1
]
)
⊙
M
2 11
r) 0.8 -h
-
g (
/
( r
1 a
0. st 10.5
160 M 160
0.6 80 g[ 80
o
40 40
l
20 10 20
10 10
0.4
10 10.5 11 11.5 12 13 14 15
-2 -1
log[M /(h M )] log[M /(h M )]
star ⊙ halo ⊙
Figure1.Thecolour-MstarandMstar-MhalodistributionsofourselectedCENsample(blackcircles).Contoursshowthedistributionofallz≤0.08CENs
fromtheSDSSDR4groupcatalogue.Contourswithdifferentcoloursconnectbinswithsamenumberofgalaxiesaslabelled.Eachbinhasawidthof0.03in
colourand0.05dexinMstarintheleftpanel,andawidthof0.05dexinMstarand0.06dexinMhalointherightpanel.
14.5. The total number of CENs in our representative sample is massandthecolour(Belletal.2003),andusingamatchingcrite-
911. riawitheitherasmaller∆M or∆0.1(g−r)willgreatlyreduce
star
InFigure1,weplot thestellarmass(M )distributionsof thenumberofmatchedSATs,especiallytowardsthemassiveend,
star
ourCENsampleasafunctionofgalaxycolourandhalomass.For becauseweuseavolume-limitedsampleanddon’tallowduplicate
each galaxy, the NYU-VAGC provides the Petrosian 0.1(g − r) matches. For CENswith log(Mhalo/h−1M⊙) < 11.0 we find a
colour,K+Ecorrectedtoz =0.1(seeY07fordetails),andwees- matchedSATusingtheabovecriteriamorethan90percentofthe
timateMstar usingthecolour-derivedM/LfromBelletal.(2003). time.Athigher masses(log(Mhalo/h−1M⊙) > 11.3), SATsbe-
AsshowninFigure1,ourrepresentativeCENselectionsamplesthe comerareandthefractionofmassiveCENswithamatchedSAT
sameM ,M and0.1(g−r)spaceasallCENswithz≤0.08 rapidlydropstolessthan10percent.Hence,weachieveSATsam-
star halo
inthegroupcatalogue(shownbythecontours). Wenotethatour plesof769(S1)and746(S2)matches.
selectionofCENsspansawiderangeofMstarrunningfrom109.8 InFigure2,weplotthestellarmassandcolourcomparisons
to1011.7h−2M⊙.Owingtotheexponentially decreasing number for our CEN-SATmatched samples as a function of CEN stellar
densityofhigh-masshaloesandtheMstar-MhalorelationofCENs mass.ThereisaslightbiasinthatSATsinbothsampleS1andS2
(Fig.1,rightpanel), our selectionofaconstant number ofgroups are less massive than their counterpart CENs with a median dif-
per Mhalo bin results in a CEN sample that is heavily-weighted ference(SAT-CEN)of-0.01dex,andSATsinS1areobviously
towardshigherstellarmassesandreddercolours. redder than their counterpart CENs. The difference of colour for
theSATsampleS2(lowerrightpanel)isalsosmall,withanalmost
zeromedianforlowmass(log(Mstar/h−2M⊙)<10.5)SAT-CEN
2.2 MatchedSatelliteGalaxySamples pairsandamedianof0.005for massive(log(Mstar/h−2M⊙) >
In addition to studying the structural properties of CENs, we 10.7)pairs.Inthelowerleftpanelweseeanobviousdifferencebe-
also want to investigate whether their central position in groups tweenthecolourofSAT-CENpairsinSATsampleS1,withame-
or clusters produces a distinctive structural difference com- diandifferenceof 0.03formassive(log(Mstar/h−2M⊙ > 10.7)
pared to non-CEN galaxies. Following a similar method as in pairsand0.3forlowmass(log(Mstar/h−2M⊙)<10.3)pairs.
vandenBoschetal. (2008), we construct two control samples of To evaluate whether the above biases arestatisticallysignif-
satellite(SAT)galaxies, one tomatch CENsinstellarmass only, icant or not, we match our CEN sample with mock samples cre-
and the other to match in both stellar mass and colour. For each atedfromitselfwithrandomchangesonM andcolouraccord-
star
CEN inour sample, we first randomly select from all SATswith ingtothemeasurementuncertainties.Thematchisdonewiththe
z ≤ 0.08 a similar-masscounterpart witha M within±0.08 same criteria used for constructing the SAT sample S2 and re-
star
dex, hereafter the SAT sample S1. We next find SATs likewise peated 20 times to produce a distribution of medians of ∆M
star
again matched to CENs in M , but further restricted to match and∆0.1(g−r)perM binbetweentheCENsampleandmock
star star
theircolourwithin∆0.1(g−r)=±0.03,hereaftertheSATsam- samples.WeplottheresultsinFigure2withcirclesanderrorbars
pleS2.OnceaSATismatchedtoaCEN,weremoveitfromthe showingthemeanand3σ deviationrespectively. Wecanseethat
poolsothatthereisnoduplicationineachSATsample.Thematch- thebiasesofourrealCEN-SATmatchesarewithin3σ deviations
ingcriteriaareequaltothemeasurementuncertaintiesofthestellar oftheself-matchingresults,except inthelowerleftpanel, where
(cid:13)c 2008RAS,MNRAS000,1–22
StructuralPropertiesofCentralGalaxies 5
0.1 0.1
matching M only matching M + color
N star N star
E E
C C

- -

T 0.05 T 0.05
A A
S S

= =

] ]
) )
⊙ ⊙
M 0 M 0
2 2
-h -h
( (

6ar 6ar
st st
M -0.05 M -0.05
[ [
g g
o o
l l
∆ ∆
-0.1 -0.1
0.4
0.02
N N
E 0.2 E
C C 0.01

- -

T T
A A
S 0 S 0

= =

) )
r r
- -
g g
( ( -0.01
1 -0.2 1
0. 0.

∆ ∆
-0.02
-0.4
-0.03
9.5 10 10.5 11 11.5 9.5 10 10.5 11 11.5
-2 -2
log[M 6 (h M )] of CENs log[M 6 (h M )] of CENs
star ⊙ star ⊙
Figure2.ThedifferenceofMstar(upperpanels)andcolour(lowerpanels)betweenmatchedCENsandSATsasafunctionofCENMstar.Theleftcolumn
showsthedifferencesfortheSATsampleS1,whichismatchedwithourCENsampleonlyinstellarmass,whiletherightcolumnshowstheSATsampleS2,
whichismatchedwithourCENsampleinbothstellarmassandcolour.Thesolidlineineachpanelshowsthemedianofthedifferenceforeach0.25dexwide
Mstarbin.Forcomparison,circleswitherrorbarsshowthemeanand3σdeviationofthebiasesineachmassbinfrommatchingtheCENsampleto20mock
samplescreatedfromitselfwithrandomchangesaccordingtomeasurementuncertainties(seetextfordetails).
thebiasatlog(Mstar/h−2M⊙)< 11aremuchlargerthanthe3σ sample,whiletheSATsfromsampleS1areonlymatchedinMstar
deviations.ThisresultsuggeststhattheM andcolourdistribu- andhaveasystematicreddercolourthantheCENsample.
star
tions of our SAT samples are not significantly different from the
distributionsof our CENsample, except forthecaseofcolour in
ourSATsampleS1,wherewefindthatSATsareredderthantheir
CEN counterparts as vandenBoschetal. (2008) finds. However, 3 MEASURINGTHESTRUCTUREOFGALAXIES
thecolourdifferencebetweenlowmassCENsandSATsinsample
S1 (∆0.1(g −r) ∼ 0.3) is larger than the average difference of Theprimaryaimofthispaperistoquantifythestructuralproperties
0.1inthesamestellarmassregionfoundbyvandenBoschetal. ofCENs.Inparticular,wemeasuretheshapeandsizeofthe2-D
(2008).Thereasonforthisdisagreementcouldbethesmallnum- luminosityprofileofeachgalaxyusingGALFIT(Pengetal.2002).
berstatisticsinourSATsample.WeconcludethattheSATsfrom Thiscodefitsaparametricmodeltothesurfacebrightnessprofileof
sampleS2iseffectivelymatchedinM andcolourwithourCEN agalaxyimageandoutputsasetofbest-fittingparameters.Forour
star
analysisweadopttheSe´rsic(1968)modeltodescribethesurface
(cid:13)c 2008RAS,MNRAS000,1–22
6 Guo etal.
brightnessatradiusrofagalaxy,Σ(r) = Σ e−bn[(r/r50)1/n−1], postagestampsarecuttoasizethatislargeenoughtoensurethat
e
where r is the half-light radius of a galaxy, Σ is the surface theouterlightprofilewillbefit.GALAPAGOSusesparametersin
50 e
brightness at r , n is the Se´rsic index, and b is coupled to the SExtractor catalogue to determine the X and Y dimension in
50 n
n such that half of the total flux of a galaxy is within r (for pixelsofthepostagestampsforeachobject:
50
0.5 < n < 10, b ≈ 2n − 0.327). In addition to r and n,
n 50 X =2.5×a×r ×(|sin(θ)|+(1−e)|cos(θ)|), (1)
GALFIT outputs the best-fitting total magnitude m , axis ratio Kron
tot
b/a,andpositionangleθ.TheSe´rsicprofileisroutinelyusedfor Y =2.5×a×r ×(|cos(θ)|+(1−e)|sin(θ)|), (2)
Kron
galaxy structure analysis to provide the half-light radius and the
wherea×r istheKronradiusalongthemajoraxisinunits
Se´rsicindexmeasuresthegalacticlightprofileshape;e.g.,n = 4 Kron
isthede Vaucouleurs’ r1/4 profileand n = 1 istheexponential ofpixels,θisthepositionangle,andeistheellipticity.
GALFIT Inputs: For running GALFIT, GALAPAGOS pro-
diskprofile.WechooseGALFITasourfittingtoolbecauseitcan
duces an input file of initial parameter guesses for the fit-
simultaneouslyfitSe´rsicprofilestoseveralgalaxiesinoneimage,
ting parameters based on the SExtractor output as follows:
whichisadvantageous forgalaxiesindenseenvironments, where
m =MAG BESTfortheapparentr-bandmagnitude,r =
galaxies have a high chance to be overlapping withone other. In tot,i 50,i
0.162r1.87,wherer isFLUX RADIUS;b/a =1−e,where
whatfollows,weoutlineourimagefittingpipeline,testitwithsim- flux flux i
e is ELLIPTICITY; and θ = THETA IMAGE. We start with
ulated galaxies, discuss technical issues, and estimate the effects i
an initial Se´rsic index of n = 1.5. We note that for this analy-
thatbackgroundskyestimationhasonparameteruncertainties.
sis,wedonotusethehigherfittingmodes,suchasdiskynessand
boxiness,offeredwiththeGALFITsoftware.Nearbycompanions
within1.5timestheSExtractorKronapertureofthetargetgalaxy
3.1 TheGalaxyFittingPipeline:ModifiedGALAPAGOS arefitsimultaneouslywithaSe´rsicmodelusinginitialparameters
alsodeterminedasdescribedabove.Companionsfurtherawayare
TorunGALFIToneachgalaxyinoursample,werequireapostage
maskedoutusingthemasksprovidedbySExtractor.Inadditionto
stampimagewithanappropriatesizetomeasurestructureoverthe
theinputfile,GALFITrequiresaPSFimagetoconvolvewiththe
fullextentofanobject,thepointspreadfunction(PSF),theinitial
modelimage.ThePSFatthecentreofthetargetgalaxyisextracted
guessforthefittingparameters,andanestimateofthebackground
fromtheSDSSphotopipelinebyemployingaSDSSpublishedtool
skylevel.Inourpipeline,westartfromthefully-processedSDSS
readAtlasImages1.
imagingframes,whichhaveasizeof2048×1042pixels.Weem-
Background Sky Estimation: The background sky level is a
ployGALAPAGOS(Bardeninprep.)toprocessthewholeimage
criticallyimportantingredientingalaxyimagefitting.Forexample,
frameandtoprovidetheneededinformationtoGALFIT.GALA-
anoverestimationoftheskycanresultinflux,size,andSe´rsicin-
PAGOS was originally designed to facilitate fitting large galaxy
dexunderestimation. GALAPAGOSincludesasophisticated way
datasetsbasedonHST/ACSimages.Wehavemodifiedthisrou-
to measure the local sky around a galaxy, which is demonstrated
tine to work on SDSS images. In brief, GALAPAGOS takes the
to be successful for ACS images (Ha¨ussleretal. 2007). How-
followingsteps: (1) itdetectsneighbouring sources and produces
ever,GALAPAGOSusesahierarchical iterationforfittinggalax-
imagemasks;(2) itcutsoutpostage stampsfor detectedsources;
ies,from bright tofaint, over the wholeframetoisolatesky pix-
(3)itpreparesaninputfileforGALFIT;and(4)itestimateslocal
els. Rather than using this CPU-intensive approach, we rely on
skyvaluesfortargetgalaxies.Weoutlinethedetailsofthesesteps
the SDSS, which provides useful and well-tested sky estimates.
below.
The SDSS global sky is considered to be a good measure of the
Source DetectionandInitialFitParameterGuesses:Weuse
background skylevelforstudyingthestructureofSDSSgalaxies
SExtractor (Bertin&Arnouts 1996) to detect and mask nearby
(vonderLindenetal.2007).Wetreatthebackgroundskyasafixed
companionsourcesintheSDSSimageofeachgalaxythatwede-
fluxpedestalduringthefittingtoreducedegeneraciesbetweenthe
siretofit, and toprovide initial fitparameter guesses for the pri-
skyandtheouterisophotesofhigh-nmodels.
marygalaxyandanycloseneighboursthatwillbesimultaneously
fit.SExtractorprovidesusefulestimatesofgalaxyproperties(mag-
nitude, size, axis ratio, position angle) for calculating the initial
3.2 TestingthePipelinewithSimulations
guessesfortheGALFITparameters.Asetofconfigurationparam-
etersdefineshowSExtractordetectssources.Aftertuning,wefind WetestourSDSSimagefittingpipelinebyrunningiton850sim-
that for SDSS r-band images the following configuration works ulatedgalaxies.Thegoalsofthistestaretwofold:(1)toestimate
best:DETECT MINAREA=25,DETECT THRESH=3.0andDE- random and bias of the structural parameters returned by our fit-
BLEND MINCONT=0.003. This configuration provides a good ting pipeline; and (2) to confirm that using the SDSS global sky
trade off between detecting and deblending most bright and ex- does not produce bias. Wecompare the actual properties that de-
tendedsourceswithoutartificiallydeblendinggalaxieswithstrong fine each simulated galaxy (input) to the corresponding fit result
substructuresintomultiplesources.Sinceourgoalistostudybright (output)followingFigure9inBlantonetal.(2005).
galaxies in groups or clusters, we keep this configuration to al- For our tests, we use the SDSS-based simulations of
lowahighsuccessrateonbrightgalaxies.Todistinguishwhether Blantonetal.(2005).Briefly,eachsimulatedgalaxyisanaxisym-
companions arestarsorgalaxies,allsourceswithSExtractorflag metricSe´rsicmodel. The simulation sample has arange of input
STAR CLASS<0.9 are classified as galaxies. However, a small parametersmatchingtheNYU-VAGCLarge-ScaleStructure(LSS)
fraction of sources may be misclassified using this criterion, and samplefromSDSSDR4.Eachsimulatedgalaxyisconvertedtoraw
wewilldiscusstheeffectofthismisclassificationonourfittingre- dataunits,scaledtotheSDSSpixel size,and convolved withthe
sultsin§3.3. PSFatitsposition.AfteraddingPoissonnoise,theresultingimage
PostageStampImages:GALAPAGOSproducesarectangular
postagestampcentredoneachgalaxyofinterest.Thepurposeof
postagestampsistoreducetheCPUtimeforfittingonegalaxy.The 1 http://www.sdss.org/dr4/products/images/read psf.html
(cid:13)c 2008RAS,MNRAS000,1–22
StructuralPropertiesofCentralGalaxies 7
0.4
t
u
p
n 0.2
i
-
t
u
p
t 0
u
o
=
g -0.2
a
m
∆
-0.4
1.4
1.2
n
,i
0
5
r
/ 1
t
u
o
,
0
5 0.8
r
0.6
2
1.5
t
u
p
n 1
i
-
t
u
0.5
p
t
u
o 0
=
n
∆
-0.5
-1
0 1 2 3 4 5 0 0.5 1 14 15 16 17 18
n log(r /arcsec) mag
in 50,in in
Figure3.AcomparisonbetweeninputandoutputparameterswhenusingGALFITtofitSe´rsicmodelsto850simulatedSe´rsicgalaxies.Weplotthedifference
(output-input)asafunctionofinputforthreeimportantSe´rsicparameters:theindexn,thehalf-lightradiusr50,andthetotalmagnitude.Ineachpanel,grey
pointsrepresentindividualsimulatedgalaxies.Thesolidlinesshowthe3rdquartile,medianand1stquartile(fromtoptobottom).
isplacedintoanactualSDSSimageatarandomlocation.Gener- smallscatter.Forhalfofthesimulationsamplethepipelinereturns
ally,about60simulatedgalaxieswereaddedtoeach2048×1024 structuralmeasurementswithin10percentofthetruevalue.Asex-
pixelimage. pected,thereisalargerparameteroffsetscatterforsimulatedgalax-
ieswithn > 4thanforthosewithn < 4(seeHa¨ussleretal.
TheresultsofapplyingourpipelinetotheSDSSsimulations in in
(2007)).Weseeaslightlyincreasedscatterwithmagnitudeowing
areshowninFigure3.Weplottheoutput-inputoffsetasafunction
tothelowerS/Noffaintergalaxies.Wenotethatthegoodagree-
ofinputforthreeimportantparameters:thetotalmagnitudem ,
tot mentbetweeninputandoutput parametersalsodemonstratesthat
thehalf-lightradiusr ,andtheSe´rsicindexn.Theresultsdemon-
50 theSDSSglobalskyisagoodchoiceforgalaxyimagefitting.We
stratethatourpipelinesuccessfullyrecoversthesestructuralparam-
addresstheeffectsofskyuncertaintiesonourstructuralproperties
etersofsimulatedSe´rsicgalaxieswithalmostnooffsetandonlya
(cid:13)c 2008RAS,MNRAS000,1–22
8 Guo etal.
measurementsinmoredetailin§3.4.TothedegreethatSe´rsicpro- sky isdifficult tomeasure especially for CENsindense environ-
filesprovideareasonablefittothetruelightdistributionofgalax- ments.Inthissubsection,weestimatetheuncertaintyintheSDSS
ies,thegoodperformanceofourpipelineonsimulatedgalaxiesis globalskyvaluesandevaluatehowthisuncertaintytranslatesinto
promisingfortheanalysisofrealgalaxies. fitparametererrors.
WeusethedifferencebetweentheSDSSglobalskyandmean
skytocharacterisetheuncertaintyintheskymeasurement.SDSS
measurestheglobalskyasthemediandatacounts(ADUs)fromev-
3.3 Se´rsicFittingoftheCENSample
erypixelofthesource-subtractedframeaftersigma-clipping.Be-
Weapplyour pipelinetofiteachgalaxyintheCENsamplewith sidestheglobalsky,SDSSalsoprovidesameanskyforeachframe
a Se´rsic model. To evaluate the fit quality we visually checked a andalocalskyforeachdetectedobjectintheframe.SDSSmea-
randomsubsampleof200CENsandfindthatabout15percentof suresthebackground insub-frameboxesofof256×256 pixels
our fitssuffer fromavariety of technical issues. These issuesin- centredevery128pixels.Thelocalskyofeachobject inaSDSS
cludestarsmisclassifiedasgalaxiesandunreliablefitstocompan- frame is an interpolation of the sub-frame background values at
ionsources.Herewediscusswhatportionofourfittingresultsare thepositionoftheobjectcentre.Themeanofallsub-framesisthe
affectedbytheseissuesandhowwecancorrectforthem. meanskyforaframe.
The accuracy of star/galaxy classification affects the fitting Inthe leftpanel of Figure4, weplot thedifference between
quality.AlthoughCENgalaxiescanalwaysbecorrectlyclassified, theSDSSglobalskyandmeanskyforourCENsample.Themean
a small portion of their companions may suffer from misclassifi- skyissomewhatlargerthantheglobalskyonaveragebecauseindi-
cation.Somegalaxiesaremisclassifiedasstarsandsomestarsare vidualsub-framesmaysuffercontaminationfromlargeandbright
misclassified as galaxies, but only the latter has a severe impact sources.WealsoplotthedifferencebetweentheSDSSglobaland
on our fitting. Fitting a Se´rsic model to a stellar profile typically localskymeasurementsforoursampleintheleftpanel.Thesedif-
resultsinaverylargenwithanoverestimatedextentandanover- ferencesaremuchlargerthanthatbetweentheglobalandmeansky
estimated flux. As a result, this false extension takes light away becausethelocalskyisheavilycontaminatedbylargeandbright
fromthewholeimageandhencecausesanunderestimateofmtot, sources. Furthermore, in the middle panel of Figure 4, we show
r50 and n for the target galaxy. Conversely, companion galaxies thattheoverestimatesofthelocalskyarehalo-massdependentfor
misidentified as stars and fit by a PSF are spatially compact and CENs. The local sky at the centre of massive haloes tends to be
faint, thus their improper treatment has littleimpact on the mea- higher than that in less massive haloes. Since the real sky back-
sured structure or flux of the target galaxy. Weestimate that less groundshouldbeindependentofthepropertiesofhaloes,thisde-
than5percentofourCENsample(inarandomsense)sufferfrom pendenceimpliesthatlocalskymeasuresforCENssufferfromin-
theissueofcompanionstarsbeingmisclassifiedasgalaxies. creasedcontaminationfromthehigherdensityofgalaxiesinlarger
Adrawbacktofittingseveralsourcessimultaneouslyisthatan haloes. In contrast, SATsdisplay littledependence on halo mass,
unrealisticmodelfitforacompanionwillspoilthefittingqualityof eventhoughtheirlocalskyisalsooverestimated,asshowninthe
thetargetgalaxy.Wedevelopanempiricalsetofcriteriaforiden- rightpanelofFigure4.Weattributethislackofhalodependenceto
tifyingbadcompanionssuchthatanycompanionbeingfittedwith thefactthatSATsarefoundoverarangeofhalo-centricpositions
σ /a > 0.3 and n > 8.0 is identified as a bad companion, andhenceatvariousgalaxydensities.Itisalsopossiblethatintra
a50 50
wherea isthesemi-majoraxisa =r /pb/a,b/aistheaxis clusterlight(ICL)atthecentreofmassivehaloescancontributeto
50 50 50
ratio,andσ istheinternalGALFITerrorofa .Suchbadcom- thedifferencebetweenCENandSATskyestimatesasweshowin
a50 50
panions are usually small and/or low surface brightness galaxies Figure 4. Given the large overestimates and the halo dependence
andtendtobefitwithanoverestimatedsize,Se´rsicindexandmag- oftheSDSSlocalsky,wewillnotuseitasameasurementofthe
nitude,resultinginasevereunderestimateofthesamequantitiesfor skybackground. Moreover,weconcludethattheSDSSmeansky
thetargetgalaxies.WeexamineSExtractormagnitudedifferences notonlyprovidesarobustalternativemeasurementoftheskyback-
betweenbadcompanions(m )andtargetgalaxies(m )andfind groundbutitalsotellsusinwhichdirectiontheskymeasurement
BC T
thatbadcompanions,asdefinedhere,aremostlyfainterthantheir mightbebiased.
corresponding targets. Actually, the majority of bad companions TostudytheeffectofskyuncertaintiesontheSe´rsicfittingof
have ∆m = m −m > 2.5 and the distribution of ∆m is actualgalaxies,wefirstselectarepresentativesubsetof45CENs
BC T
peakedat∆m∼3.5.Thuswesimplymaskoutall∆m>2.5bad from our sample that span a 3 × 3 matrix in Mhalo-n space as
companionsandrefittheimage.Weiteratethisprocedureuntilall follows:
thetargetshavenomorebadcompanions.About8percentofour
CENsamplestartwithbadcompanionsandwecorrectallofthem • for log(Mhalo/h−1M⊙)=[12.0:12.5], n=[1.8:2.2], [3.3:3.7],
asdescribedabove.SomeofthetargetCENshave∆m<2.5bad [4.8:5.2]
companions within afew arcseconds and any masking might ad- • for log(Mhalo/h−1M⊙)=[13.0:13.5], n=[2.8:3.2], [4.3:4.7],
verselyaffectthefit.Henceinsteadweopttoexcludethosetarget [6.3:6.7]
galaxiesfromourCENsample.ThefractionofCENshavingsuch • for log(Mhalo/h−1M⊙)=[14.0:14.5], n=[3.8:4.2], [4.8:5.2],
bad companions depends on halo mass: from 7 percent at high- [6.3:6.7]
massesto3percentatlow-masses.Intotal,32CENsareexcluded
fromoursampleowingtoproblemswithbadcompanions. Next,werandomlyselectfivegalaxiesfromeachbinoftheabove
matrix. For each galaxy, we Monte-Carlo sample 50 values from
thedistributionofthemean-globaldifferenceshownbytheredline
intheleftpanelofFigure4.Thesevaluesareaddedtotheglobal
3.4 SkyUncertaintyandParameterCovariance
skyandthegalaxyisrefitusingthesenewbackgroundlevels.This
AlthoughtheSDSSglobalskyworksasagoodchoiceofskyback- procedure provides a distribution of fitting parameters caused by
groundforfittingisolatedgalaxies,asthesimulationsshow,thereal theuncertaintyinmeasuringthesky.Forthissubset of45CENs,
(cid:13)c 2008RAS,MNRAS000,1–22
StructuralPropertiesofCentralGalaxies 9
0.2
mean-global [12.0:13.0] [12.0:13.0]
local-global [13.0:14.0] [13.0:14.0]
[14.0:15.0] [14.0:15.0]
0.15
n
o
ti 0.1
c
a
r
F
0.05
0
-4 -3 -2 -1 0 1 2 3 -4 -3 -2 -1 0 1 2 3 -4 -3 -2 -1 0 1 2 3 4
∆sky (ADU) sky -sky (ADU) sky -sky (ADU)
local global local global
Figure4.Distributionsofdifferencesbetweenvariousskymeasurements.Left:TheredlineshowsthedifferencebetweentheSDSSmeanandglobalsky
valuesforourCENsampleandthegreenlineshowsthedifferencebetweentheSDSSlocalandglobalmeasurements.Middle:Thelocal-globaldifferencefor
CENsdividedintohalomassbins.Right:Sameasthemiddlepanel,butforSATs.
weplotdistributionsaroundthemeanvalueofthreeimportantfit
parameters(m ,nanda )inFigure5. 10
tot 50
ThedistributionsinFigure5clearlydemonstrateacovariance
between best-fitting parameter values and the choice of sky. The
8
boxes represent our original results using the SDSS global sky.
Theseriesof(50)crosses,whichformashortandnearlystraight
linethrougheachbox,representthefittingresultsusingtheMonte
6
Carlosamplingoftheskybackgroundasdescribedabove.Thecor-
relationsbetweenm anda (bottom)andm andn(top)show n
tot 50 tot
thestrongdegeneracyoftheseparametersintheSe´rsicmodel.Ifwe 4
increasetheskybackground,thebest-fittingfluxdecreasestokeep
thetotal(galaxy+sky)fluxconstant,whilethebest-fittingnand
a decrease.Conversely,decreasingtheskybackgroundlevelre- 2
50
sultsinlargerbest-fittingvaluesform ,n,anda .Wefindthat
tot 50
thecovarianceismoresevereforgalaxieswithhighern.Thiseffect
0
showsthattheskyestimateisverycrucialforproducingaccurate
Se´rsicprofilefits.Thisisespeciallytrueforgalaxieswithn > 4
becausetheflat,extendedwingsoftheprofilearesensitivetosky 100
uncertainties.Thestrengthanddirectionofthesecovariancesmust
beaccountedforwhenanalysingthesize-luminosityrelation,aswe
willdiscussin§4.2 )
x
pi
(
0
5
a
4 THESTRUCTUREOFCENS
10
In this section we explore the r-band structural properties of our
CEN sample. CENs are the most massive members of the SDSS
groupsandclusters,andarepresumedtobelocatedatthedynami-
calcentreofthehosthalo.Wefocusonthestructuralshape(char-
acterisedbytheSe´rsicindexn)andthesize(characterisedbythe 12 13 14 15 16 17
half-lightradiusr )oftheSe´rsicprofileof CENs.Westudythe
50 mag
relationships between these parameters and galaxy stellar masses
andhosthalomassestoinvestigatewhichfactorismorerelatedto
Figure5.Thecovariancesamongbest-fittingtotalmagnitude,Se´rsicindex
thestructureofCENs.Wealsocomparethestructuralparameters
anda50 asaresultofskyuncertainty for45representative CENs.Boxes
of CENs and SATsusing our two matched SAT samples (see §2 representtheGALFITresultusingtheSDSSglobalsky.Foreachgalaxy,
fordetails)andstudywhetherthecentralhalolocationimpactsthe theseriesof(50)crossesrepresentfitsusingskybackgroundlevelstaken
shapeorsizeofagalaxy. fromMonteCarlosamplingsoftheskyasdescribedinthetext.
Toevaluatetheaccuracyofourmeasurementsofgalaxystruc-
tural parameters and total flux using our GALFIT pipeline, we
(cid:13)c 2008RAS,MNRAS000,1–22
10 Guoet al.
compare our fit results with the one-dimensional (1D) Se´rsic fit- bars in Figure 6 show the median and the 1st and 3rd quartile
tingparametersbasedontheNYU-VAGCanalysis(Blantonetal. of the n distribution in M bins with a 0.25 dex width. From
star
2005, hereafter ’NYU-VAGC’).TheNYU-VAGC Se´rsicparame- the plot we see that the median Se´rsicindex is a strong function
tershavebeenwidelyusedinthestudyofgalaxymorphologyand ofstellarmass: low-massCENshavelow n(disk-like) and high-
size(e.g.Shenetal.2003;Blantonetal.2005;Malleretal.2008). massCENshavehighn(spheroid-like).Yet,thereislargescatter
WefindthatforhighSe´rsicindex(ourGALFITn>3.0)galaxies, in the relation between n and M , especially for CENs with
star
NYU-VAGCunderestimatestheSe´rsicindexbyabout1.3andun- 3×1010 <Mstar/h−2M⊙ <1011,wheretheSe´rsicindexranges
derestimatesthetotalmagnitudebyabout0.4magcomparedtoour from1<n<6orlarger.Higher-massCENstendtohaven>3.
results.Therearetworeasonsfortheseunderestimates:(1)NYU- WealsoshowhowtheuncertaintyandcovarianceoftheGAL-
VAGC’s1DprofilefittingsystematicallyunderestimatestheSe´rsic FITnvaluesaffectthen-M relationintheupperleftpanelof
star
indexandtotalmagnitudeforhighngalaxies,asshownbyFigure9 Figure 6 (green symbols). The red symbols in the plot only take
ofBlantonetal.(2005);(2)NYU-VAGCusestheSDSSlocalsky, intoaccountofthescatterfromourfits.However,asweshowedin
whichoverestimatesthebackgroundskylevelandhenceresultsin §3.4,thereisastrongcovariancebetweenthefitparametersnand
underestimatesofnandthetotalmagnitude.Furthermore,forlow m andtheskyuncertainty,andweusem toestimatestellar
tot tot
Se´rsicindex(ourGALFITn < 3.0)galaxies,NYU-VAGCover- mass. To evaluate how this covariance may change the above n-
estimatestheSe´rsicindexbutstillunderestimatesthetotalmagni- M relation, were-calculatetherelationusing theresultsfrom
star
tudebyabout0.2mag.Besidesusingthelocalsky,NYU-VAGC’s therepresentativesubsetof45CENsin§3.4.ForeachCENinour
azimuthally-averaged 1D fitting procedure systematically overes- sample we randomly select one CEN from the nearest five in n
timates the Se´rsic index for highly inclined galaxies, which are space among the representative subset, and we assume that each
mostlydisks. Wealsocompare bothour GALFITresultsand the CEN has the same n and m covariance as its matched com-
tot
NYU-VAGC resultswith the Petrosianquantities from the SDSS panion. In this way, we construct a probability distribution of n
photometricpipeline.ByfollowingtheformalismofGrahametal. andM (fromm )forall911CENs.Themedian,1stand3rd
star tot
(2005),wefindthatunderourworkingassumptions(aSe´rsicmodel quartilesofthisdistributionareshownbythegreensymbolsander-
and a global sky), our GALFIT fitting pipeline more accurately rorbarsintheupperleftpanelofFigure6.Thenewrelationshows
measures the structural properties of SDSS galaxies then NYU- littledifferencecomparedwiththeoriginalbecausetheparameter
VAGC’s.ThedetailsofthiscomparisonareinAppendixA. uncertaintiesowingtoskyaresmallerthantheintrinsicscatterin
oursample(redsymbols).Forexample,theaveragerelativescatter
betweenthe1stand3rdquartilesofnowingtothebackgroundsky
4.1 TheSe´rsicIndexofCENs
leveluncertaintyisonly∆n/n ∼ 0.2,whilethemeasuredscatter
Withreliableandaccuratemeasurementsofgalaxystructuralprop- is∆n/n∼0.75andhencedominates.
erties from our fitting pipeline in hand, we turn to the study of
how theSe´rsicindex of CENsisrelatedtotheir stellarmass and
theirenvironment.TheSe´rsicindexiswidelyusedtocharacterise
4.1.2 TheDependenceonHostHaloMass
the profile and concentration of galaxies in both observational
(e.g., Grahametal. 1996; Blantonetal. 2005; MacArthuretal. IntheupperrightpanelofFigure6,weshowthedependenceofthe
2003; deJongetal. 2004; Allenetal. 2006) and numerical (e.g., Se´rsicindexofCENsontheirhosthalomass.RecallthatMhalois
Naab&Trujillo2006;Acevesetal.2006)studies.Somearguethat calculatedbymatchingtherankofthetotalstellarmassofgroups
themorphology-densityrelationimpliesthatthestructureofgalax- andclusterswiththatofdarkmatterhaloesfromnumericalsimu-
iesisaffectedbytheenvironment. Othersarguethatthestructure lations(seeY07fordetails).Wefindthatndependsonlyweakly
of galaxies depends strongly on stellar mass but only weakly on onMhalo andthatthescatterofthen-Mhalo relationislarge.For
the environment (e.g., Hoggetal. 2004; Kauffmannetal. 2004; CENsinhaloeswithlog[Mhalo/h−1(M⊙)]<12.5,wefindame-
vanderWel2008).In thissection, weexplore the dependence of dian value of n = 3 and a relative scatter of ∆n/n ∼ 1.3. For
theSe´rsic-indexdistributionofCENgalaxiesonbothMstar and massive haloes with log[Mhalo/h−1(M⊙)]>14.0 the median is
M . n=5andtherelativescatteris∆n/n∼0.6.
halo
Then-M relation, although weak, suggests that the halo
halo
mass may also affect the structure of CENs. However, from the
4.1.1 DependenceonStellarMass rightpanelofFigure1weknowthatthestellarmassofCENsalso
IntheupperleftpanelofFigure6,weplottheSe´rsicindexofCENs dependsonthehalomassinthesensethatCENsinmassivehaloes
asafunctionoftheirstellarmass.TheM valuesforourCEN tend to have larger stellar masses than CENs in smaller haloes.
star
samplearecalculatedfollowingtheformulafromBelletal.(2003): Given this dependence and the strength of the n-M relation,
star
it is tempting to rule out any dependence of n on halo mass. To
log[Mstar/M⊙]=−0.306+1.0970.0(g−r)−0.15−0.4(0.0Mr−4.67),(3) addressthis,weattempttoremoveanyM -M dependence
star halo
where the constant 0.15 corrects to a Kroupa (2001) IMF, and fromboththen-M andn-M relations.
star halo
0.0(g−r)isthePetrosiancolourfromtheNYU-VAGCshiftedto First,inthelowerleftpanelofFigure6,weplotthen-M
star
thez =0rest-frameusingtheBlantonetal.(2003)K-corrections relationsforCENsinfivehalomassbins,each0.5dexinwidth.All
and correcting for Milky Way extinction using the Schlegeletal. thebinswithlessthansixCENsareexcludedtogetbetterstatis-
(1998) dust maps. The absolute r-band magnitude 0.0M is ex- tics.TheroughlyM -independentrelationsallhaveaslopeand
r halo
tinction and K-corrected in the same manner, but we use the to- amplitudethatissimilartothesinglen-M relationforthefull
star
talfluxfromourfittingforthisquantityratherthanthePetrosian sample (red symbols in the upper left panel). There is some evi-
magnitude in the SDSS pipeline. We show in Appendix A that dencethattherelationsfordifferentM binsaresomewhatoff-
halo
ourfittingprocedurebetterrecoversthetotalmagnitudeofgalax- setalongtheM directioninthesensethatCENsinlessmassive
star
ies than the Petrosian photometry. The red symbols with error- haloestendtohavelargernthantheircounterpartsinmoremassive
(cid:13)c 2008RAS,MNRAS000,1–22