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CAIRNS The Cluster And Infall Region Nearby Survey II. Environmental Dependence of Infrared

CAIRNS The Cluster And Infall Region Nearby Survey II. Environmental Dependence of Infrared
CAIRNS The Cluster And Infall Region Nearby Survey II. Environmental Dependence of Infrared

a r X i v :a s t r o -p h /0402242v 2 11 J u n 2004

Draft version February 2,2008

Preprint typeset using L A T E X style emulateapj v.21/08/00

CAIRNS:THE CLUSTER AND INFALL REGION NEARBY SURVEY II.ENVIRONMENTAL

DEPENDENCE OF INFRARED MASS-TO-LIGHT RATIOS

Kenneth Rines 1,2,Margaret J.Geller 3,Antonaldo Diaferio 4,Michael J.Kurtz 3,and

Thomas H.Jarrett 5

Draft version February 2,2008

ABSTRACT

CAIRNS (Cluster And Infall Region Nearby Survey)is a spectroscopic survey of the infall regions surrounding nine nearby rich clusters of galaxies.In Paper I,we used redshifts within ~10h ?1Mpc of the centers of the clusters to determine the mass pro?les of the clusters based on the phase space distribution of the galaxies.Here,we use 2MASS photometry and an additional 515redshifts to investigate the environmental dependence of near-infrared mass-to-light ratios.In the virial regions,the halo occupation function is non-linear;the number of bright galaxies per halo increases more slowly than the mass of the halo.On larger scales,the light contained in galaxies is less clustered than the mass in rich clusters.Speci?cally,the mass-to-light ratio inside the virial radius is a factor of 1.8±0.3larger than that outside the virial radius.This di?erence could result from changing fractions of baryonic to total matter or from variations in the e?ciency of galaxy formation or disruption with environment.The average mass-to-light ratio M/L K =53±5h implies ?m =0.18±0.03(statistical)using the luminosity density based on 2dFGRS data.These results are di?cult to reconcile with independent methods which suggest higher ?m .Reconciling these values by invoking bias requires that the typical value of M/L K changes signi?cantly at densities of 3ρc .

Subject headings:dark matter —galaxies:clusters:individual (A119,A168,A194,A496,A539,A576,

A1367,A1656(Coma),A2197,A2199)—galaxies:kinematics and dynamics —cosmology:observations —infrared:galaxies

1.introduction

The relative distribution of matter and light in the uni-verse is one of the outstanding problems in astrophysics.Clusters of galaxies,the largest gravitationally relaxed ob-jects in the universe,are important probes of the distri-bution of mass and light.Zwicky (1933)?rst computed the mass-to-light ratio of the Coma cluster using the virial theorem and found that dark matter dominates the clus-ter mass.Recent determinations using the virial theo-rem yield mass-to-light ratios of M/L B j ~250hM ⊙/L ⊙(Girardi et al.2000,and references therein).Equating the mass-to-light ratio in clusters to the global value pro-vides an estimate of the mass density of the universe (Oort 1958);this estimate is subject to signi?cant systematic error introduced by di?erences in galaxy populations be-tween cluster cores and lower density regions (Carlberg et al.1997;Girardi et al.2000).Indeed,some numerical simulations suggest that cluster mass-to-light ratios ex-ceed the universal value (Diaferio 1999;Kravtsov &Klypin 1999;Bahcall et al.2000;Benson et al.2000,but see also Ostriker et al.2003).

Determining the global matter density from cluster mass-to-light ratios therefore requires knowledge of the de-pendence of mass-to-light ratios on environment.Bahcall et al.(1995)show that mass-to-light ratios increase with scale from galaxies to groups to clusters.Ellipticals have larger overall values of M/L B than spirals,presumably a

result of younger,bluer stellar populations in spirals.At the scale of cluster virial radii,mass-to-light ratios appear to reach a maximum value.Some estimates of the mass-to-light ratio on very large scales (>10h ?1Mpc)are available (see references in Bahcall et al.1995),but the systematic uncertainties are large.

There are few estimates of mass-to-light ratios on scales between cluster virial radii and scales of 10h ?1Mpc (Eisen-stein et al.1997;Small et al.1998;Kaiser et al.2004;Rines et al.2000,2001a;Biviano &Girardi 2003;Katgert et al.2004;Kneib et al.2003).On these scales,many galax-ies near clusters are bound to the cluster but not yet in equilibrium (Gunn &Gott 1972).These cluster infall re-gions have received relatively little scrutiny because they are mildly nonlinear,making their properties very di?-cult to predict analytically.However,these scales are ex-actly the ones in which galaxy properties change dramati-cally (Ellingson et al.2001;Lewis et al.2002;G′o mez et al.2003;Treu et al.2003;Balogh et al.2004,and references therein).Variations in the mass-to-light ratio with envi-ronment could have important physical implications;they could be produced either by a varying dark matter fraction or by variations in the e?ciency of star formation with en-vironment.In blue light,however,higher star formation rates in ?eld galaxies compared to cluster galaxies could produce lower mass-to-light ratios outside cluster cores re-sulting only from the di?erent contributions of young and

1Yale Center for Astronomy and Astrophysics,Yale University,P.O.Box 208121,New Haven CT 06520-8121;krines@https://www.wendangku.net/doc/d111679649.html, 2Harvard-Smithsonian Center for Astrophysics,60Garden St,Cambridge,MA 021383Smithsonian Astrophysical Observatory;mgeller,mkurtz@https://www.wendangku.net/doc/d111679649.html, 4Universit`a degli Studi di Torino,Dipartimento di Fisica Generale “Amedeo Avogadro”,Torino,Italy;diaferio@ph.unito.it 5

IPAC/Caltech 100-22Pasadena,CA 91225;jarrett@https://www.wendangku.net/doc/d111679649.html,

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old stars to the total luminosity(Bahcall et al.2000). Because clusters are not in equilibrium outside the virial radius,neither X-ray observations nor Jeans analysis pro-vide secure mass determinations at these large radii.There are now two methods of approaching this problem:weak gravitational lensing(Kaiser et al.2004)and kinematics of the infall region(Diaferio&Geller1997;Diaferio1999, hereafter DG97and D99).Kaiser et al.(2004)analyzed the weak lensing signal from a supercluster at z≈0.4; the mass-to-light ratio(M/L B=280±40h for early-type galaxy light)is constant on scales up to6h?1Mpc.Wil-son et al.(2001)?nds similar results for weak lensing in blank?elds;Gray et al.(2002)obtain similar results for a di?erent supercluster.Recently,Kneib et al.(2003)used weak lensing to estimate the mass pro?le of CL0024+1654 to a radius of3.25h?1Mpc.Kneib et al.(2003)conclude that the mass-to-light ratio is roughly constant on these scales.

Galaxies in cluster infall regions produce sharp features in redshift surveys(Kent&Gunn1982;Shectman1982;de Lapparent et al.1986;Kaiser1987;Ostriker et al.1988; Reg¨o s&Geller1989).Early investigations of this infall pattern focused on its use as a direct indicator of the global matter density?m.Unfortunately,random mo-tions caused by galaxy-galaxy interactions and substruc-ture within the infall region smear out this cosmological signal(DG97,Vedel&Hartwick1998).Instead of sharp peaks in redshift space,infall regions around real clusters typically display a well-de?ned envelope in redshift space which is signi?cantly denser than the surrounding environ-ment(Rines et al.2003,hereafter Paper I,and references therein).

DG97analyzed the dynamics of infall regions with nu-merical simulations and found that in the outskirts of clus-ters,random motions due to substructure and non-radial motions make a substantial contribution to the amplitude of the caustics which delineate the infall regions(see also Vedel&Hartwick1998,and references therein).DG97 showed that the amplitude of the caustics is a measure of the escape velocity from the cluster;identi?cation of the caustics therefore allows a determination of the mass pro?le of the cluster on scales 10h?1Mpc.

DG97and D99show that nonparametric measurements of caustics yield cluster mass pro?les accurate to~50% on scales of up to10h?1Mpc.This method assumes only that galaxies trace the velocity?eld.Indeed,simula-tions suggest that little or no velocity bias exists on linear and mildly non-linear scales(Kau?mann et al.1999a,b). Geller et al.(1999,hereafter GDK),applied the kinematic method of D99to the infall region of the Coma cluster. GDK reproduced the X-ray derived mass pro?le and ex-tended direct determinations of the mass pro?le to a ra-dius of10h?1Mpc.The caustic method has also been applied to the Shapley Supercluster(Reisenegger et al. 2000),A576(Rines et al.2000,hereafter R00),AWM7 (Koranyi&Geller2000),the Fornax cluster(Drinkwa-ter et al.2001),A1644(Tustin et al.2001),A2199(Rines et al.2002),and six other nearby clusters(Paper I).Bi-viano&Girardi(2003)applied the caustic technique to an ensemble cluster created by stacking redshifts around43 clusters from the2dF Galaxy Redshift Survey.R00found an enclosed mass-to-light ratio of M/L R~300h within 4h?1Mpc of A576.Rines et al.(2001a)used2MASS pho-tometry and the mass pro?le from GDK to compute the mass-to-light pro?le of Coma in the K-band.They found a roughly?at pro?le with a possible decrease in M/L K with radius by no more than a factor of3.Biviano& Girardi(2003)?nd a decreasing ratio of mass density to total galaxy number density.For early-type galaxies only, the number density pro?le is consistent with a constant mass-to-light(actually mass-to-number)ratio.

Here,we calculate the infrared mass-to-light pro?le within the turnaround radius for the CAIRNS clusters (Paper I),a sample of nine nearby rich,X-ray luminous clusters.We use photometry from the Two Micron All Sky Survey(2MASS,Skrutskie et al.1997)and add sev-eral new redshifts to obtain complete or nearly complete surveys of galaxies up to1-2magnitudes fainter than M?K

s (as determined by Kochanek et al.2001;Cole et al.2001,

hereafter K01and C01).Infrared light is a better tracer of stellar mass than optical light(Gavazzi et al.1996;Zibetti et al.2002);it is relatively insensitive to dust extinction and recent star formation.Despite these advantages,there are very few measurements of infrared mass-to-light ratios in clusters(Tustin et al.2001;Rines et al.2001a;Lin et al. 2003).

Mass-to-light ratios within virial regions(where the masses are more accurate than in the infall regions)pro-vide interesting constraints on the distribution of dark matter and stellar mass(see also Lin et al.2003,here-after L03).The virial masses in our sample span an order of magnitude in mass.More massive clusters have larger mass-to-light ratios.

Cluster virial regions also provide potentially important constraints on the halo occupation distribution(e.g.,Pea-cock&Smith2000;Berlind&Weinberg2002;Berlind et al.2003,and references therein),the number of galax-ies in a halo of a given mass(see Cooray&Sheth2002, for a recent review).The motions of galaxies and hot gas yield estimates of the dynamical mass independent of the number of galaxies(provided enough galaxies are present to yield a virial mass).Our mass pro?les in Paper I are among the?rst to extend signi?cantly beyond r200. Thus,they should provide accurate estimates of r200.Also, the recent release of2MASS allows us to count galaxies based on their near-infrared light,which is close to select-ing galaxies by stellar mass.Thus,both the masses and galaxy numbers are better de?ned than the few previous direct estimates of the halo occupation function(Peacock &Smith2000;Marinoni&Hudson2002;Lin et al.2004). We describe the cluster sample,the near-infrared pho-tometry,and the spectroscopic observations in§2.We discuss the galaxy properties(luminosity functions and broadband colors)within and outside the virial radius and compare both populations to?eld galaxies in§4.We calculate the number density and luminosity density pro-?les in§5and compare them to simple theoretical mod-els.We compute radial pro?les of the mass-to-light ratio in§5.In§6we constrain the halo occupation distribu-tion for the CAIRNS clusters and explore the dependence of mass-to-light ratios on halo mass.We discuss possible systematic uncertainties and the implications of our re-sults in§7and conclude in§8.We assume a cosmology of H0=100h km s?1,?m=0.3,?Λ=0.7except as noted

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in §7.

2.observations

2.1.The CAIRNS Cluster Sample

We selected the CAIRNS parent sample from all nearby (cz <15,000km s ?1),Abell richness class R ≥1(Abell et al.1989),X-ray luminous (L X >2.5×1043h ?2erg s ?1)galaxy clusters with declination δ>?15?.Using X-ray data from the X-ray Brightest Abell Clusters catalog (Ebeling et al.1996),the parent cluster sample contains 14systems.We selected a representative sample of 8of these 14clusters (Table 1).The cluster properties listed in Table 1are from Paper I.The 6clusters meeting the selection criteria but not targeted in CAIRNS are:A193,A426,A2063,A2107,A2147,and A2657.The 8CAIRNS clusters span a variety of morphologies,from isolated clus-ters (A496,A2199)to major mergers (A168,A1367).The redshift limit is set by the small aperture of the 1.5-m Tillinghast telescope used for the vast majority of our spectroscopic observations.The richness minimum guar-antees that the systems contain su?ciently large numbers of galaxies to sample the velocity distribution.The X-ray luminosity minimum guarantees that the systems are real clusters and not superpositions of galaxy groups (cf.the discussion of A2197in Rines et al.2001a,2002).Three additional clusters with smaller X-ray luminosities (A147,A194and A2197)serendipitously lie in the survey regions of A168and A2199.A147and A2197lie at nearly identical redshifts to A168and A2199;their dynamics are proba-bly dominated by the more massive cluster (Rines et al.2002).A194,however,is cleanly separated from A168and we therefore analyze it as a ninth system.The inclusion of A194extends the parameter space covered by the CAIRNS sample.The X-ray temperature of A194listed in (Ebeling et al.1996)is an extrapolation of the L X ?T X relation;in Table 1we therefore list the direct temperature estimate of Fukazawa et al.(1998)from ASCA data.Fukazawa et al.(1998)lists X-ray temperatures for 6of the 8CAIRNS clusters which agree with those listed in Ebeling et al.(1996).

In Paper I,we applied a hierarchical clustering analysis (described in D99)to the redshift catalogs to determine the central coordinates and redshift of the largest system of galaxies in each cluster.Table 2lists these hierarchi-cal centers and their projected separations from the X-ray peaks.We adopt these hierarchical centers as the cluster centers.

2.2.2MASS Photometry

2MASS is an all-sky survey with uniform,complete pho-tometry (Nikolaev et al.2000)in three infrared bands (J,H,and K s ,a modi?ed version of the K ?lter truncated at longer wavelengths).We use photometry from the ?nal extended source catalog (XSC,Jarrett et al.2000).The 2MASS XSC computes magnitudes in the K s -band using several di?erent methods,including aperture magnitudes (using a circular aperture with radius 7′′),isophotal mag-nitudes which include light within the elliptical isophote corresponding to μK s =20mag/arcsec 2,Kron magnitudes,and extrapolated “total”magnitudes (Jarrett et al.2000).The sky coverage of the catalog is complete except for small regions around bright stars.

The 2MASS isophotal magnitudes omit ~15%of the to-tal ?ux of individual galaxies (K01).C01compare 2MASS photometry from the Second Incremental Data Release (2IDR)with deeper infrared photometry from Loveday (2000).They ?nd that Kron magnitudes are slightly fainter than the total magnitudes in deeper surveys (see also Andreon 2002a)and that 2MASS extrapolated total magnitudes are slightly brighter than Kron (roughly total)magnitudes from the deeper survey.2MASS is a relatively shallow survey and thus likely misses many low surface brightness galaxies Andreon (2002a);Bell et al.(2003).In this work we focus on bright galaxies (which typically have high surface brightness)so this bias is less important than,e.g.,estimates of the luminosity density or stellar mass density.

Except where stated otherwise,we use the K s -band sur-vey extrapolated “total”magnitudes.Galactic extinction is usually negligible in the near-infrared.We correct for Galactic extinction by using the value in the center of the cluster.We make K corrections and evolutionary correc-tions of <0.15magnitudes based on Poggianti (1997).Be-cause these corrections are small and not strongly depen-dent on the galaxy model at the redshifts of the CAIRNS clusters,we apply a uniform correction for all galaxies in a given cluster interpolated from the model Elliptical SED with solar metallicity and a star-formation e-folding time of 1Gyr.

We reprocess two galaxies in A576and two galaxies near A2199using the methodology of the 2MASS Large Galaxy Atlas (Jarrett et al.2003).The galaxies in A576(CGCG 261-056NED01and CGCG 261-056NED 02)are bright ellipticals near the cluster center and also close to a bright star.One of the galaxies near A2199,UGC 10459,is an extremely ?at edge-on disk galaxy.The other,NGC 6175,shows two nuclei aligned NW-SE.The SE component is brighter in K s band.

2.3.Spectroscopy

The 2MASS photometry allows selection of complete,near-infrared-selected samples extending ~1-2magnitudes

fainter than the M ?

K s

=?23.77+5log h determined for the ?eld galaxy luminosity function in 2MASS extrapo-lated magnitudes (C01).We de?ne K s -selected samples according to these magnitude limits within the smaller of the turnaround radius r t (the radius within which the av-erage density is 3.5ρc )or the limiting radius r max of the caustic pattern (our membership criterion)in each cluster (see Paper I).Table 4lists these radii and the apparent and absolute magnitude limits of these catalogs for the 9clus-ters.Our redshift catalogs are 99.7%complete for cluster galaxy candidates brighter than M K s =?23+5log h and

97.6%complete for candidates brighter than M ?

K s

+1.Most of the galaxies in these samples have redshifts in the redshift catalogs from the CAIRNS project (Pa-per I).Between 2002June and 2003September,we col-lected new redshifts for 515galaxies with the FAST spec-trograph (Fabricant et al.1998)on the 1.5-m Tilling-hast telescope of the Fred Lawrence Whipple Observatory (FLWO).FAST is a high throughput,long slit spectro-graph with a thinned,backside illuminated,antire?ection coated CCD detector.The slit length is 180′′;our observa-tions used a slit width of 3′′and a 300lines mm ?1grating.

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Table1

CAIRNS Parent Population

Cluster X-ray Coordinates cz⊙σp L X T X Richness

RA(J2000)DEC(J2000)km s?1km s?11043h?2ergs s?1keV

A194012550.4-0121545341495+41

?33

0.4 2.60

A119005610.1-011520132781294856

A168011500.7+0015311349313176239

A496043338.6-1315479831978624

A539051637.0+0626578648865033

A576072132.0+554521114871156116

A1367114449.1+1946036509683761

Coma130000.7+27565170967365153

A2199162847.0+3930229156918186

This setup yields spectral resolution of6-8?A and covers the wavelength range3600-7200?A.We obtain redshifts by cross-correlation with spectral templates of emission-dominated and absorption-dominated galaxy spectra cre-ated from FAST observations(Kurtz&Mink1998).The typical uncertainty in the redshifts is30km s?1.Table?? lists the new redshifts.The additional redshifts make no signi?cant di?erence to the locations of the caustics or to the resulting mass pro?les.We thus use the caustics and mass pro?les from Paper I.

An important di?erence between the FAST spectra col-lected for CAIRNS and those collected for other,larger redshift surveys(Colless et al.2001;Stoughton et al.2002) is that CAIRNS su?ers no incompleteness due to?ber placement constraints.

We calculate the maximum fraction f noz of light missing from our catalogs if we assume that all galaxies without redshifts and brighter than the magnitude limit are clus-ter members(Table4).In other words,we evaluate the potential observational bias which results if every galaxy without a redshift were a cluster member.For this extreme case,the total luminosity within r max is underestimated by the fraction f noz<0.10for all clusters.The new red-shifts in Table??contribute signi?cantly to the complete-ness of these catalogs.Because the galaxies without red-shifts are almost entirely faint galaxies at large distances from the cluster center,f noz is a very conservative upper limit on the fraction of light missing within the complete-ness limits(the surface number density of member galax-ies decreases with radius and the fraction of background galaxies increases with apparent magnitude).

Assuming that the luminosity function in clusters and infall regions is identical to that in the?eld(we test this assumption in§3.1),we calculate the fraction f L of total galaxy light contained in galaxies brighter than our com-pleteness limits.This fraction is greater than60%for all clusters.From repeated measurements,apparent magni-tudes in the2MASS XSC have an uncertainty of~0.14 magnitude at K s=13.4?13.5;the galaxy catalogs prob-ably su?er incompleteness fainter than K s≈14.Thus, the2MASS XSC provides accurate magnitudes for galax-ies within our completeness limits,but it is di?cult to use2MASS galaxy counts at much fainter magnitudes to estimate the contribution of fainter galaxies to the total cluster/infall region light.Note that the?eld luminosity function of C01that we adopt here has a steeper faint-end slope than the luminosity function calculated from Kron magnitudes.If we adopt the Kron magnitude faint-end slope of C01,f L increases by7-15%(the best sampled clusters have the smallest changes).We discuss this issue further in§3.1and§7.2.

Figure1shows the redshift completeness as a function of apparent and absolute magnitude(K s extrapolated mag-nitude)along with the total number of galaxies,the num-ber with redshifts,and the number of members versus magnitude.Note that,as in Paper I,we order the clusters by decreasing X-ray temperature from left to right and from top to bottom in this and all similar later?gures. The catalogs are complete for cluster galaxy candidates brighter than M K

s

=?23except for?ve candidates in the outskirts of A539which lie at high Galactic extinc-

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tion.It is not clear whether these objects are galaxies or extended Galactic infrared sources.The brightest of these sources,IRAS05155+0707,is an embedded Class 1protostar and likely the source of Herbig-Haro objects HH114and HH115(Reipurth et al.1997).We exclude IRAS05155+0707from the photometric catalog and the calculation of f noz in Table4.

Figure1also shows constraints on the luminosity func-tions in the clusters.The sets of dash-dotted lines show the limits from assuming that(1)all galaxies without redshifts are members or(2)none are.We discuss the luminosity functions in more detail in§4,but we note here that the faint-end slope of the luminosity function in infall regions is poorly constrained without deep,complete spectroscopy.

3.properties of galaxies inside and outside the

virial region

Galaxy properties such as morphology and star forma-tion rate are strongly correlated with their local and global environments(e.g.,Ellingson et al.2001;Lewis et al.2002; G′o mez et al.2003;Treu et al.2003;Balogh et al.2004, and references therein).Di?erences in galaxy properties with environment may lead to apparent changes in the observed mass-to-light ratio even if the ratio of dark mat-ter to stellar mass remains constant(e.g.Bahcall et al. 2000).The CAIRNS2MASS selected galaxies provide a well-de?ned population with which to investigate these en-vironmental e?ects.The environments considered range from cluster centers with densities~1000ρc to the edges of infall regions with densities~3ρc at the turnaround radius r t.These environments are all denser than the universal average density?mρc,but they cover the density range where galaxy morphologies,optical colors,and star for-mation rates change dramatically(Ellingson et al.2001; Lewis et al.2002;G′o mez et al.2003;Treu et al.2003; Balogh et al.2004).We investigate the near-infrared pho-tometric properties of galaxies inside and outside the virial regions of the CAIRNS clusters and compare them to?eld galaxies.

3.1.Luminosity Functions

Many investigators have sought to determine the en-vironmental dependence of the luminosity function(e.g., Balogh et al.2001;Beijersbergen et al.2002;De Propris et al.2003,and references therein).Using the2dF Galaxy Redshift Survey,De Propris et al.(2003)?t their cluster data to the Schechter(1976)luminosity function(LF), N(M)∝100.4(α+1)(M??M)e?100.4(M??M)(1) and?nd that the cluster LF in the b J band has a brighter characteristic magnitude M?and steeper faint-end slope αthan the?eld LF.Although di?erences between cluster and?eld luminosity functions exist at other wavelengths (e.g.,Trentham1998a,b;Mobasher et al.2003;Sabatini et al.2003),the cluster LF in the K s band is quite similar to the?eld LF(e.g.,Mobasher&Trentham1998;de Pro-pris et al.1998;Andreon&Pell′o2000;Tustin et al.2001; Balogh et al.2001),perhaps indicating a universal stellar mass function(Andreon2004).Balogh et al.(2001)com-bine data from2MASS and the Las Campanas Redshift Survey and?nd that the cluster LF in the J band has a brighter characteristic magnitude and a steeper faint-end slope than the?eld LF;similar di?erences are seen at K s band but the parameters di?er by<3-σ.Andreon(2004)?nds that the cluster and?eld LFs are indistinguishable at red wavelengths in the optical(see also Christlein& Zabludo?2003),suggesting that much of the di?erence at bluer wavelengths is due to star formation.

Figure2shows the near-infrared luminosity functions of each of the CAIRNS clusters including all galaxies within the infall regions.We use the caustics from Paper I to de?ne membership.In magnitude bins without complete redshifts,we compute a completeness correction by assum-ing that the membership fraction of galaxies without red-shifts is the same as the membership fraction of galaxies with redshifts.Galaxies without redshifts tend to be at larger projected clustrocentric distances than those with redshifts.One might thus expect that these galaxies are more likely to be non-members because the ratio of clus-ter members to background galaxies decreases with radius. Counteracting this e?ect,galaxies without redshifts tend to have lower surface brightnesses than those with red-shifts(because of observational bias towards higher sur-face brightness galaxies);because of the correlation be-tween absolute magnitude and surface brightness,galaxies of a given apparent magnitude with lower surface bright-nesses should be intrinsically fainter and are thus more likely to be cluster members(Conselice et al.2002;Ko-ranyi&Geller2000).

We count the number of bright galaxies(those with M K

s≤M?K s+1)in each cluster and use this number to calculate relative normalizations for each cluster.Fig-

ure2shows the Schechter LF for?eld galaxies from C01 scaled by this number of bright galaxies with an arbitrary overall normalization.

We compute the luminosity functions separately for the virial regions and the infall regions taking R200(rδis the radius within which the enclosed mass density isδtimes the critical density,Rδ=rδis the projected radius)as the dividing radius.Some galaxies projected inside R200 lie outside r200,but no galaxies projected outside R200 lie inside r200;thus the luminosity functions inside R200 will be contaminated by galaxies outside the virial region. Figure3shows the luminosity functions within R200;Fig-ure4shows the luminosity functions outside this radius. In each panel,we plot the best-?t Schechter(1976)lumi-nosity function for?eld galaxies from C01scaled by the number of bright galaxies with an arbitrary overall nor-malization.Figure5shows the combined CAIRNS LFs inside and outside R200as well as the total LF.The LFs in the virial regions and infall regions are very similar.

At the bright end,the LFs in both the virial regions and the infall regions are poorly?t by a Schechter func-tion(Figure5);the observed LFs contain more galax-ies brighter than M K

s

=?25and fewer galaxies at ?25

s

?25)than the virial region LF, but there is very little di?erence within the Poissonian un-certainties.Also,it is worth noting that extremely bright

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galaxies are present in six of the nine infall regions (Coma,A119,A2199,A576,A168,and A194),demonstrating that these bright galaxies do not reside exclusively in cluster centers.Many of these galaxies likely occupy the centers of galaxy groups in the infall regions (Rines et al.2001b).A χ2test shows that the LF ratios for all bright galaxies (M K s ≤?23.7)are consistent with a constant value at the 95%con?dence level.

At magnitudes fainter than the completeness limit,the LF in the infall region (excluding the virial region)consis-tently exceeds that inside the virial region,suggesting that the faint-end slope might be steeper in the infall region.The uncertainties in Figure 6are Poissonian.Because the correction for galaxies without redshifts may be biased,these uncertainties may be signi?cantly underestimated.A deeper complete spectroscopic survey of the infall re-gions is necessary to determine the reality of e?ects at these faint luminosities.

We calculate the best-?t luminosity function of the Schechter (1976)form for M K s ≤?22.1+5log h for all the clusters combined.This limit corresponds to the 2MASS completeness limit of K s =13.5for the most dis-tant CAIRNS clusters.We ?t the LF for galaxies within R 200,outside R 200,and all galaxies combined.We do not account for measurement uncertainties in the ?ts.Ta-ble 5lists the best-?t parameters (from minimizing χ2)as well as determinations of the ?eld luminosity function (K01,C01).The uncertainties are 68%con?dence limits for two interesting parameters.We list two di?erent es-timates from C01,one using extrapolated magnitudes (as used here)and one using 2IDR Kron magnitudes converted to ’total’magnitudes by subtracting -0.20mag (see C01).The LF parameters di?er by 2-3σfrom the ?eld values,and agree well with previous determinations (Balogh et al.2001,L03).However,the ?ts to the CAIRNS LFs are not very good;the probability of obtaining a larger value of χ2from a sample drawn from the Schechter LF is <0.7%for the total LF.The best-?t characteristic magnitude of the virial region LF is brighter than the ?eld LF,similar both in sign and magnitude to the di?erence found by Balogh et al.(2001);the faint-end slope of the CAIRNS virial re-gions is slightly steeper than the ?eld values.The LFs in the infall regions are intermediate between the ?eld LFs and the virial region LFs.

We repeat the ?ts using the completeness limit of the redshift catalogs M K s

It is interesting that the characteristic magnitude of the CAIRNS virial region LF agrees well with that of the clus-ter LF constructed by L03without spectroscopy.This agreement suggests that statistical background subtrac-tion produces little bias in the resulting LF parameters.Both L03and CAIRNS use 2MASS photometry which pro-vides only a limited probe of the faint-end slope.It would be instructive to compare the LFs of individual clusters constructed with spectroscopic membership to those con-structed with statistical background subtraction.A de-tailed comparison is outside the scope of the present work,but in §5we will show that LFs constructed with statis-tical background subtraction (L03)yield mass-to-light ra-tios consistent with our results for clusters with complete spectroscopy.

The best-?t LF parameters signi?cantly a?ect the esti-mates of the fraction of light f L contained in faint galaxies (see Table 4).However,for ?xed LF parameters,the ra-tio of the maximum to the minimum values of f L for the clusters varies by less than 10%;thus,the relative values of f L are robust.Because the CAIRNS LF parameters are consistent with the ?eld LF but have larger uncertainties,we continue to use the ?eld LF to estimate the fraction of light contributed by faint galaxies.Note that the ?eld LF we adopt (C01extrapolated magnitudes)has both a brighter characteristic magnitude and a steeper faint-end slope than the LF of C01from Kron magnitudes.

We repeat this analysis in the J band,which extends deeper in 2MASS and thus has smaller statistical uncer-tainties.Figure 7shows the J band LF for all galaxies within r t ,Figure 8shows the luminosity functions within R 200,and Figure 9shows the luminosity functions outside this radius.We combine the LFs to produce an average cluster LF in Figure 10.We scale the LF inside and out-side R 200to have the same normalization at M ?

J for ?eld galaxies.As in K s band,the cluster LF has a very sim-ilar shape to the ?eld LF except for an excess of bright galaxies.We repeat the non-parametric test of comput-ing the LF ratios (Figure 11).Table 5lists the best-?t Schechter function parameters.These parameters di?er by no more than 3-σfrom the ?eld values determined by

C01.The characteristic magnitude M ?

J for cluster virial regions is brighter than the ?eld value by about 0.5mag-nitudes,consistent with the results of Balogh et al.(2001).There is remarkably little di?erence between the two LFs across the entire range of magnitudes,although at faint magnitudes there is room for signi?cant di?erences which could be explored with deep,complete spectroscopy.

To summarize,we see marginal evidence for di?erences between the cluster LF and the ?eld LF.The cluster LF is slightly brighter and has a steeper faint-end slope than the ?eld LF.We obtain similar results in both J and K s bands.Our data sample only giant galaxies,so signi?-cant di?erences may exist in the cluster and ?eld LFs in the dwarf galaxy regime.For the purposes of comput-ing mass-to-light ratios,the systematic uncertainty intro-duced by possible di?erences in the cluster and ?eld LFs is 15%.Note that,as expected,the LF in the infall region is intermediate between the ?eld LF and the cluster LF.

3.2.Luminosity Segregation

Dynamical friction could lead to luminosity segregation in galaxy clusters.Some investigators have claimed evi-dence for luminosity segregation in compilations of cluster data (e.g.Adami et al.1998;Andreon 2002b,and refer-ences therein).Figure 12shows the distribution of abso-lute magnitude versus (projected)distance R p from the cluster center.If luminosity segregation were signi?cant,

7

we would see more bright galaxies near cluster centers.The brightest cluster galaxy is typically very close to the cluster center,consistent with a bright central cD galaxy increasing in mass through accretion of smaller galaxies.However,there are also many comparably bright galaxies in the outskirts of the clusters.In A2199,many of the extremely bright galaxies outside the virial region are at the centers of infalling groups (Rines et al.2001b,2002).There is little evidence for luminosity segregation in the CAIRNS clusters,consistent with earlier results for A576(Rines et al.2000).This result is not surprising given the similarity of the LFs inside and outside R 200(Figure 5).Again,note that the CAIRNS samples do not extend into the dwarf galaxy regime,where luminosity segregation might be present (Andreon 2002b).

3.3.Broadband Galaxy Colors

Star formation rates depend on environment (e.g.,Ellingson et al.2001;Lewis et al.2002;G′o mez et al.2003;Treu et al.2003;Balogh et al.2004,and refer-ences therein).Because stellar populations in ?eld galax-ies are on average younger than those in cluster galax-ies,more blue light is emitted per unit mass in ?eld-like environments than in cluster environments.As a conse-quence,mass-to-blue-light pro?les might decrease with ra-dius (Bahcall et al.2000)even if the ratio of gravitational mass to stellar mass were constant.

Because young stars are both hotter and bluer than older stars,the di?erence in stellar mass-to-light ratios decreases toward longer wavelengths (see the synthesized stellar population models of Bruzual &Charlot 2003).For example,studies of near-infrared mass-to-light ratios in galaxies suggest that the mass-to-light ratio at these wave-lengths is insensitive to the current star formation rate in either disk galaxies (Gavazzi et al.1996)or early-type galaxies (Zibetti et al.2002).Unfortunately,the color dif-ferences between J and K bands are not very large because these wavelengths primarily trace Population II stars (Jar-rett et al.2003),making this e?ect di?cult to detect with 2MASS data alone.

For A576,our 9square degrees of photometric CCD ob-servations in R band (Rines et al.2000)allow a measure-ment of R ?K s colors.Optical-infrared colors enable us to investigate stellar population e?ects.Although both the 2MASS magnitudes used here and the R band magnitudes in Rines et al.(2000)are supposed to be close to total,a systematic di?erence in the magnitude de?nitions could introduce an arti?cial color gradient.We reprocess the R band images using SExtractor (Bertin &Arnouts 1996)to obtain aperture magnitudes within a circular aperture of radius 14′′in R band and radius 15′′in 2MASS.This slight mismatch in apertures produces a small bias towards redder colors,but clustrocentric gradients,if any,should still be evident.We calculate R ?J and R ?K s colors for all of the galaxies in both catalogs.Figure 13displays the R ?K s colors versus projected radius.There is no obvious radial gradient in either R ?J or R ?K s colors for bright galaxies.There may be a radial gradient in R ?K s col-ors for galaxies fainter than M K s =?22.77,but we lack complete spectroscopy at these magnitudes.In a photo-metric study of clusters using SDSS,Goto et al.(2004)?nd small but signi?cant radial gradients in the fraction

of blue galaxies with radius (the fraction increases with radius).The trends are weakest in the most nearby clus-ters which are the most similar to the CAIRNS clusters.Note that the CAIRNS catalogs are selected at K s rather than r ,which may account for the lack of a gradient in A576.Also,the trends may be weaker in R ?K s colors than in,e.g.,u ?r colors,which are much more sensitive to the presence of young stars.A multiwavelength study of several clusters with spectroscopically determined mem-bership would clarify the importance of color gradients in clusters.

We plot the R ?K s color versus K s magnitude in Figure 14.There is little evidence for a color-magnitude relation.Galaxies inside and outside R 200occupy the same parts of the diagram,indicating that there is no large di?erence in the two populations.The galaxies appear to have very similar stellar https://www.wendangku.net/doc/d111679649.html,paring the colors to the models of Bruzual &Charlot (2003)indicates metallici-ties greater than solar.The degeneracy between age and metallicity e?ects prevents further conclusions.3.4.Near-Infrared Colors and the Color-Magnitude

Relation Signi?cant variations in the stellar mass-to-light ratio might be indicated by radial gradients in J ?K s colors.Unfortunately,identifying such gradients is di?cult be-cause variations in galaxy J ?K s colors are relatively small and because unlike optical colors,galaxies with the reddest J ?K s colors may contain younger stellar populations and are red as a result of emission from hot dust (Hunt et al.2002;Barton Gillespie et al.2003).We observe no radial color gradients in J ?K s (see Figure 15,which highlights the lack of trends in the outlying points).Figure 16shows that the distributions of J ?K s colors of bright galaxies inside and outside R 200are extremely similar.There is a possible excess of galaxies in the red tail of the distri-bution in the sample outside R 200(Figure 15);some of these are edge-on disk galaxies while others are probably AGN (Jarrett 2000;Jarrett et al.2003).Because of the morphology-density relation,we expect more disk galaxies in cluster outskirts.

We plot J ?K s color (computed within the ellipti-cal isophote K s =20mag arcsec ?2)versus absolute mag-nitude M K s (from the extrapolated K s magnitude)of CAIRNS members in Figure 17.The most striking re-sult is that the outlying data points are galaxies both inside and outside R 200,which suggests that the stellar populations of galaxies in these regions are similar.There is tentative evidence for a color-magnitude relation (i.e.,fainter galaxies are bluer,see,e.g.,Terlevich et al.2001,and references therein)in the near-infrared,but the slope (≈?0.01mag mag ?1)is much shallower than at optical wavelengths,e.g.,the slope is ?0.14±0.01in U ?V versus V in Coma (Terlevich et al.2001).We obtain a similar color-magnitude relation when the colors and magnitudes are determined from aperture photometry,suggesting that the relation does not result from systematic e?ects in 2MASS.The variations in the colors can be explained by variations in the metallicities of the stellar populations.The most re-cent stellar population models of Bruzual &Charlot (2003)indicate that 10Gyr old stellar populations (formed in-stantaneously according to a Chabrier (2003)initial mass

8

function)with metallicities [F e/H ]=?0.64→+0.56have rest-frame J ?K s =0.75→1.1.As at optical wave-lengths,there is degeneracy between age and metallicity e?ects;bluer colors result from either lower metallicities or younger ages (Worthey 1994).Accurate spectral informa-tion is required to break this degeneracy (e.g.,Concannon et al.2000).

The scatter in the observed near-infrared color-magnitude relation is larger for fainter galaxies;the fainter galaxies have more varied stellar populations and/or larger uncertainties.Note that galaxies in clusters at low galactic latitude (A539and A496)have larger scatter than those in clusters near the galactic poles (Coma and A1367).This observation suggests that a signi?cant part of the scatter may result from uncertainties in Galactic extinction.A full accounting of the color-magnitude relation is beyond the scope of this paper.Instead,we note that the near-infrared properties of galaxies do not change dramatically with radius.This result implies that the stellar mass-to-light ratios do not change dramatically with radius;thus,measuring near-infrared mass-to-light ratios is a good ap-proximation to a measurement of the ratio of total mass to stellar mass.

4.near-infrared luminosity and number density

profiles

4.1.Number Density Pro?les

Because our catalogs are essentially complete within their respective magnitude limits,we can count the num-ber of bright galaxies to compare cluster richness.We adopt M K s =?22.77+5log h as our limiting magnitude because all clusters are complete to this depth (Table 4).

This limit is equivalent to M ?

K s

+1for ?eld galaxies.Ta-ble 6lists the number of galaxies inside and outside R 200(“outside R 200”means the projected radius R p satis?es r 200

Figure 18shows the surface number density pro?les of the CAIRNS clusters.We choose radial bins spaced loga-rithmically by 0.25;the outermost bin contains the maxi-mum radius r max of the caustics.We ?t the number den-sity pro?les of the CAIRNS clusters to three simple ana-lytic models.The simplest model of a self-gravitating sys-tem is a singular isothermal sphere (SIS).The volume den-sity of the SIS decreases with radius according to ρ∝r ?2;the projected number density of objects Σdecreases as

Σ(R p )∝R ?1

p .Navarro et al.(1997)and Hernquist (1990)propose two-parameter models based on CDM simulations of haloes.These density pro?les are

ρ(r )∝[r

a

)?α](2)

where a is a scale radius and α=2for the NFW pro?le and α=3for the Hernquist pro?le.At large radii,the NFW density pro?le decreases as r ?3and the density of the Hernquist model decreases as r ?4(implying a ?nite total mass).The NFW surface number density pro?le is

Σ(

N (a )

πa 2(s 2

?1)2

[(2+s 2)X (s )?3]

(5)

where a is the scale radius and M is the total mass.Note that M (a )=M/4.We minimize χ2and list the best-?t parameters a N for the NFW and Hernquist models in Ta-ble 7.We perform the ?ts on all data points within the maximum radii listed in Table 4.We plot the surface num-ber density pro?les and the best-?t NFW (solid lines)and Hernquist (dash-dotted lines)models in Figure 18.The SIS (dashed lines)is not normalized and is shown only for comparison.

The best-?t scale radii a N for both the NFW and Hern-quist models are larger than the best-?t scale radii a M of the mass pro?les in Paper I for all clusters except A539,where the NFW scale radius is the same.In individual clusters,a N and a M di?er only at 1-3σsigni?cance.How-ever,a K-S test indicates that the distributions of a N and a M are not drawn from the same population at the 99.6%con?dence level for the NFW model and at 99.95%con?-dence for the Hernquist model.These di?erences suggest that mass is more concentrated than light.

Two clusters,A168and A1367,are poorly ?t by Hern-quist and NFW pro?les.They both could be ?t by these pro?les within R 200,but the surface number density out-side R 200exceeds the predicted pro?le.This result sug-gests that these clusters are not isolated from surrounding large-scale structure and that we may be observing them at an early stage of their evolution.In fact,both these clusters contain major mergers.Furthermore,they are the only CAIRNS clusters currently undergoing major merg-ers.Excluding these clusters from the comparison of scale radii only reduces the signi?cance of the K-S test to 99.5%for both models.Thus,the di?erence in distribution of scale radii is not solely a result of these merging systems.Similarly,A2199has a large core component.Excluding the innermost bin slightly increases the best-?t value of a N and slightly decreases the best-?t value of N (a ).

Biviano &Girardi (2003)?nd similar results from a Jeans analysis of an ensemble cluster constructed from the 2dFGRS:the ratio of mass density to galaxy (deprojected)number density decreases with radius.Similarly,Lin et al.(2004)?nd that the concentration of galaxies is smaller than the expected concentration of mass,i.e.,the galaxies are more extended than expected.From our results and the independent analyses of these other authors,we thus conclude that the di?erence is a real physical e?ect.

4.2.Luminosity Pro?les

Because the cluster LF is not signi?cantly di?erent from the ?eld LF,the estimates of the fraction f L of the total cluster light contained in galaxies brighter than the magni-tude limits in Table 4(which assume the LF parameters of

9

the ?eld LF)are justi?ed.We estimate the total light by adding the luminosity in galaxies brighter than the magni-tude limits,then dividing by f L .We make no corrections for the small incompleteness in our spectroscopic catalogs (f noz in Table 4).This omission could lead to slight under-estimates of the luminosity in the outskirts of the clusters.The photometric uncertainties in the luminosity pro?les are 10%.Because we compute the luminosity pro?les only from relatively bright galaxies,the uncertainties are dominated by counting statistics (Kochanek et al.2003).We ?t the luminosity density pro?les of the CAIRNS clusters to the simple analytic models described in the previous section,replacing N (a )with L (a ),the luminos-ity contained within the sphere of radius a L .Figure 19shows the surface luminosity density pro?les and the best-?t NFW (solid lines)and Hernquist (dash-dotted lines)models.The scale radii a L of the light distributions are close to a N and larger than a M ,again implying that the light in galaxies is more extended than the mass.A K-S test indicates that the distributions of a L and a M are not drawn from the same population at the 98.1%con?dence level for the NFW model and at 99.95%con?dence for the Hernquist model.A K-S test detects no di?erences in the distributions of a L and a N for either model.Again we conclude that the mass is more concentrated than the light.

5.near-infrared mass-to-light profiles

We next compute M (

One notable feature of Figure 20is the variety in the shapes of the mass-to-light pro?les in individual clusters.Some clusters have ?at pro?les while others have strongly peaked pro?les.There is no obvious cause of these di?er-ences (e.g.,presence of a bright cD galaxy,presence of a major merger).Indeed,signi?cant variation in the shapes of mass-to-light pro?les obtained with the caustic tech-nique is expected from projection e?ects along di?erent lines of sight (D99).

Obviously,it is preferable to compute both the mass and the light in either spheres or cylinders but not one of each.Because mass and light are never negative,L K s (

rather than attempting to deproject the noisy luminosity pro?les.In particular,we assume that the mass distribu-tion is well-described by one of the simple mass models.Because the Hernquist pro?le has a ?nite total mass,the best-?t Hernquist pro?les have smaller densities than the best-?t NFW pro?les at large radii.Thus,the projected Hernquist pro?le is more centrally concentrated than the NFW pro?le.These projection e?ects will thus be larger if the true pro?le is a Hernquist pro?le.We show these projected M H (

We quantify the size of this e?ect for NFW mass pro-?les.For NFW pro?les with concentrations c =5?20(in Paper I we measured c =5?17for the CAIRNS clusters),the projected mass within a cylinder of radius R 200is a factor of 1.15-1.25larger than the mass in a sphere of radius r 200(the factor increases with decreas-ing concentration).Projection e?ects are less dramatic for cylindrical shells compared to spherical shells at large radii because some light/mass outside the spherical shell is pro-jected into the cylindrical shell;some light/mass within the spherical shell is projected into cylindrical shells at smaller radii.For NFW halos with concentrations c =5?20,the projected mass in the cylindrical shell bounded by R 200and R max is 1–5%greater than the mass in the spherical shell bounded by r 200and r max .Thus,if the CAIRNS clusters are well-described by NFW pro?les with c ≈5,the mass-to-light ratio inside the cylinder R 200is larger by a factor of 1.15-1.25than the measured quan-tity M (

M (>r 200)/L (>R 200)

≈2.2±0.4.

(6)

The projection e?ects therefore aggravate the di?erence in mass-to-light ratios between cluster virial regions and their outskirts.

The preceding calculation used the nonparametric mass pro?les from Paper I.We repeat the calculations of Ta-ble 8using the best-?t (parametric)NFW mass pro?les from Paper I projected into cylinders.The mean mass-to-light ratio inside r 200is M NF W /L |r 200=77±7h and the mean mass-to-light ratio outside r 200is 48±5h .The ratio of these is 1.6±0.2,very similar to the ratio 1.8±0.3calculated above with no corrections for geometric projec-tion e?ects.We note here that the best-?t NFW param-eters do not vary signi?cantly if the ?ts are restricted to r <1.5h ?1Mpc;at these radii,the mass pro?les agree with X-ray and virial mass estimates (see Paper I).

We now calculate the mass-to-light pro?le in individual shells.The enclosed mass-to-light pro?les calculated above decrease with radius.Because these pro?les are dominated by the mass-to-light ratio in the core,the mass-to-light ra-

10

tio in the outer shells must generally be smaller than the enclosed mass-to-light ratio at that radius.The uncer-tainties in individual shells are su?ciently large that we must bin several shells to obtain a signi?cant signal.These mass-to-light ratios are the mass in spherical shells divided by the light in cylindrical shells.As noted above,for spher-ically symmetric NFW models,the projection e?ects de-crease with radius and lead to underestimates of the mass-to-light ratio inside r 200.Open squares (Figure 20)show the mass-to-light ratios of these shells.Indeed,there is a general trend for lower mass-to-light ratios in shells at larger radii,but the uncertainties are quite large.Note that the enclosed mass-to-light pro?les M (

X-ray mass estimates provide an independent check of our mass-to-light ratios within r 500.As shown in Paper I,the caustic mass pro?les evaluated at r 500agree quite well with X-ray mass estimates from the mass-temperature relation.Thus,it is no surprise that the mass-to-light ra-tios calculated from the X-ray mass M 500and the lumi-nosity evaluated at L 500yield similar values.Note that,again,the luminosity estimates include all galaxies pro-jected within R 500.An NFW pro?le with concentration c =5appropriate for clusters (Navarro et al.1997)would have a deprojected mass-to-light ratio (M/L )(

Our results are in excellent agreement with Lin et al.(2003,hereafter L03),who ?nd a mass-to-light ratio M/L K s =76±4h (statistical)at r 500for hot (T X ≥3.7keV)clusters using X-ray masses and 2MASS photom-etry from a larger cluster sample.We include only galax-ies within the caustics in our luminosity estimates;L03use statistical background subtraction to correct their lu-minosity estimates.The close agreement shows that the methods L03use to subtract background galaxies do not introduce a bias in the luminosity estimates.

Previously,we have used the caustic technique to calcu-late mass-to-light pro?les in R band for A576(Rines et al.2000)and in K s band for Coma (Rines et al.2001a).In A576,we found a steeply decreasing mass-to-light pro?le in R band.In Coma,we found a ?at pro?le but noted that the systematic e?ects allowed for a decreasing pro?le.The results we derive here for these clusters are consistent with these earlier determinations.

Other investigators have applied Jeans analysis to en-semble clusters to test for variations in the mass-to-light ratio.This e?ort is complicated by the fact that one needs to assume an orbital distribution to measure variations in M/L .Carlberg et al.(1997)and van der Marel et al.(2000)?nd that light traces mass in the CNOC1ensemble cluster (composed of massive clusters at z =0.2?0.5)to a radius of 2r 200.Biviano &Girardi (2003)construct an ensemble cluster from poor clusters in the 2dFGRS.They ?nd that the ratio of the mass density to the galaxy number density decreases with radius to 2r 200,similar to our result for the CAIRNS clusters.When they exclude late-type galaxies from the galaxy number density,the ra-tio is roughly constant.Katgert et al.(2004)construct an ensemble cluster from the ESO (European Southern Observatory)Nearby Abell Cluster Survey and ?nd that the mass-to-light ratio decreases with radius in the range 0.2?1.5r 200,although the mass-to-light ratio is roughly constant when late-type galaxies are excluded.

Weak lensing provides an independent estimate of mass-to-light ratios on large scales that does not depend on the dynamical state of the system.Kaiser et al.(2004)and Gray et al.(2002)estimate the mass-to-light ratios of su-perclusters with weak lensing.Kaiser et al.(2004)?nd M/L B =280±40h for light in early-type galaxies.As-suming a typical early-type color of B ?K s =3.7(Jarrett 2000),this value corresponds to M/L K s ≈64±9h .In-cluding late-type galaxies would decrease this ratio.Wil-son et al.(2001)?nd similar results from weak lensing in blank ?elds.Gray et al.(2002)?nd M/L B ~200h (early-type light only)for individual clusters;when they cross-correlate mass and light they ?nd M/L B =130h (early-type light only),but they caution that there are many systematic uncertainties in this estimate.Recently,Kneib et al.(2003)used weak lensing to estimate the mass pro?le of CL0024+1654to a radius of 3.25h ?1Mpc.Kneib et al.(2003)conclude that the K band mass-to-light ra-tio is roughly constant on these scales.Assuming passive evolution,their mass-to-light ratio corresponds to 65±9h (74±10h for red sequence galaxies only)at z =0,inter-mediate between our estimates of the mass-to-light ratio inside and outside r 200.

Bahcall et al.(2000)use simulations to show that clus-ter mass-to-light ratios in B band exceed the global value due to the older,less luminous stellar populations found in clusters.Cluster mass-to-light ratios measured in K s band should then be much closer to the global value be-cause K s band light has a much weaker dependence on stellar population ages (e.g.,Bell &de Jong 2001).If stel-lar populations are the primary cause of the decreasing mass-to-light pro?les in the simulations of Bahcall et al.

11

(2000),the CAIRNS clusters should have roughly?at K s band mass-to-light pro?les.Thus,the similarity of the decreasing K s band mass-to-light pro?les of the CAIRNS clusters to the simulations of Bahcall et al.(2000)shows that the decreasing pro?les in their simulations may not result primarily from di?erences in the stellar populations but from di?erences in the relative distribution of dark matter and galaxies.

The CAIRNS sample is unique in both the completeness of the individual cluster catalogs and in the near-infrared digital photometry used to avoid stellar population e?ects. The mass-to-light ratios of the CAIRNS clusters decrease with radius and the mass-to-light ratios inside the virial regions agree with other estimates at optical and near-infrared wavelengths(see also Rines et al.2000,2001a). The decreasing mass-to-light pro?les are consistent with results from other cluster studies.We discuss these re-sults in more detail in§7.

6.properties of the virial regions

6.1.The Halo Occupation Distribution

The halo occupation distribution(see the review by Cooray&Sheth2002)is an important input for convert-ing the results of numerical simulations into observables (e.g.,Peacock&Smith2000;Berlind&Weinberg2002; Berlind et al.2003,and references therein).The simplest prediction is that the number of galaxies formed is directly proportional to the available baryonic mass.Thus,the number of galaxies N(brighter than some minimum mass or luminosity)contained in a halo of mass M is given by N∝M(i.e.,the e?ciency of galaxy formation is a uni-versal constant for su?ciently massive haloes).If galaxy formation is more e?cient in the most massive haloes,then the relation might be N∝Mμwithμ>1.Conversely, if galaxy formation is less e?cient in massive haloes(e.g., if the gas is heated by the halo potential and is unable to collapse into galaxies)or galaxy disruption is more ef-?cient(e.g.,dynamical friction and tidal stripping),then the relation might be N∝Mμwithμ<1.Models of the halo occupation distribution suggest that,for cluster mass halos,the relation is close to a power law with slope μ<1.Semi-analytic models predictμ~0.8?0.9(Sheth &Diaferio2001;Berlind et al.2003).A smoothed particle hydrodynamics simulation of aΛCDM cosmological model predicts halo occupation distributions withμ~0.56?0.74 for cluster mass halos,similar to the values for a di?erent set of semi-analytic models(Berlind et al.2003).Springel &Hernquist(2003)show that numerical simulations pre-dict suppression of galaxy formation in the most massive halos because gas cannot cool and collapse into galaxies. One of the few previous determinations of the relation between virial masses and galaxy numbers is that of Mari-noni&Hudson(2002),who compute masses and(blue)lu-minosities of virialized objects in the Nearby Optical Cata-log.Marinoni&Hudson(2002)?nd N∝M0.55±0.03,simi-lar to the semi-analytic models.Kochanek et al.(2003)use a constrained numerical simulation of2MASS to develop a matched?lter algorithm to study cluster properties in the 2MASS catalog and heterogeneous auxiliary observations from the literature(e.g.,redshifts and X-ray properties). Their best-?t relation between cluster mass and number of members is N∝M1.10±0.09.Pisani et al.(2003)?nd N∝M0.70±0.04in a sample of groups,although mass es-timates of groups are very uncertain.Recently,Lin et al. (2004)analyzed the halo occupation distribution for clus-ters with2MASS photometry and X-ray mass estimates. They?nd N∝M0.84±0.04,steeper than Marinoni&Hud-son(2002)but still in reasonable agreement with models. We can constrain the halo occupation distribution with the CAIRNS clusters,which cover roughly an order of magnitude in mass and have both accurate photometry and complete spectroscopy.Our results have the advan-tages of uniform sky coverage,greater redshift complete-ness,and galaxy selection at near-infrared wavelengths, which is a better tracer of stellar mass and su?ers less dust extinction than blue light.Conveniently,the mag-nitude limit we adopt(M K

s≤M?K s+1)is very similar to the luminosity threshold used in Berlind&Weinberg

(2002)and one of the thresholds used in Berlind et al. (2003),L 0.5L?.Figure21shows the number of galax-ies N200projected within R200versus M200,the mass of the halo.We do not attempt to deproject the number density pro?les to obtain a deprojected estimate of N200 because the number density pro?les are too noisy.If all haloes have similar concentrations,then the fraction of interlopers should be constant with mass.If the halo concentration decreases with mass(as expected for NFW models),then the fraction of interlopers should increase with mass.In this case,the?t toμwould be an over-estimate.The bisector of the two ordinary least-squares

?ts(Feigelson&Babu1992)yields N200∝M0.70±0.09

200

, 3.3σshallower than a linear relation(shown by a dashed line in Figure21).This result is not driven by A194, the least massive cluster;excluding this cluster yields a

least squares?t N200∝M0.74±0.15

200

.This result agrees well with previous determinations as well as with expecta-tions from semi-analytic models for galaxy formation(e.g., Kau?mann et al.1999a;Sheth&Diaferio2001;Marinoni &Hudson2002;Berlind et al.2003;Pisani et al.2003;Lin et al.2004).We speculate that the signi?cant di?erence from Kochanek et al.(2003)is due to the systematic un-certainties from the process of matching their simulation to the observations.Kochanek et al.(2003)use a matched ?lter algorithm which is?nely tuned to reproduce the ex-pected properties of clusters based on simulations(where galaxies trace the dark matter distribution).Systematic e?ects can arise both from mismatches in the assumed and true cosmology and recipes for galaxy formation as well as unknown systematics in the heterogeneous auxiliary ob-servations.

The comparison with Lin et al.(2004)is especially in-teresting because both datasets use2MASS photometry. Lin et al.(2004)use a much larger sample of clusters but they use only statistical background subtraction whereas we study fewer clusters but use complete spectroscopic in-formation to assign cluster membership.A detailed com-parison of these two methods would be instructive but it lies beyond the scope of this paper.In particular,there are few clusters in both samples,so cluster-to-cluster vari-ations could signi?cantly a?ect the comparisons.We refer the reader to Lin et al.(2004)for an excellent discussion of the physical signi?cance of a non-linear HOF as well as the observational implications for clusters.

12

6.2.Mass Dependence of Mass-to-Light Ratios Figure22shows the mass-to-light ratio within r200ver-

sus M200for the CAIRNS clusters.The scatter is large, but the CAIRNS clusters show an increase in M/L(evalu-ated at r200)with increasing mass.Lin et al.(2003,here-after L03)found a similar correlation between X-ray mass and near-infrared mass-to-light ratios;more massive clus-ters have larger mass-to-light ratios with a best-?t relation

(M/L K

s )(

M500

13

Figure 24,i.e.,the most discrepant clusters are those with the highest masses.Substituting a higher (M/N )|r 200in-creases the amplitude of the predicted VDPs and brings the predicted and observed VDPs into better agreement.Outside r 200,galaxies are not relaxed.At these radii,VDPs do not necessarily contain information about the orbital distribution.Thus,the VDPs outside r 200should not be considered strong constraints on the mass and or-bital distributions.

The most straightforward predictions of VDPs based on the assumption that light traces mass disagree with the observed VDPs.In contrast,the VDPs predicted by the caustic mass pro?les agree well with the observed VDPs.Thus,the decrease in the e?ciency of galaxy formation (and/or the increase in the e?ciency of galaxy disruption)for haloes with larger virial temperatures is not an arti-fact of the caustic technique.Velocity dispersion pro?les,a more traditional tool of galactic dynamics,also indicate a discrepancy between the distribution of galaxies and mass (although subject to possible biases from the orbital dis-tribution and/or the dynamical state of galaxies outside r 200).It is interesting that Katgert et al.(2004)also ?nd a decreasing mass-to-light pro?le for an ensemble cluster using Jeans analysis to compute the mass pro?le.Their results strengthen our conclusion that the decreasing mass-to-light pro?les are physical e?ects.

7.2.Morphological Gradients

Because of the well-known correlation between morphol-ogy and density,we expect larger fractions of late-type galaxies with increasing clustrocentric radius (decreasing density).If the LFs of early-type and late-type galaxies di?er signi?cantly,the total LF should vary with clustro-centric radius.That is,the LF in cluster centers should closely resemble the early-type LF,whereas at larger radii it should resemble the late-type LF.K01separate the LF into early-type and late-type LFs and ?nd that ?ts to

Schechter functions yield a brighter M ?

K s

for the early-type LF;the faint-end slope is slightly shallower for the late-type LF (but see Bell et al.2003,who ?nd that 2MASS misses many blue low surface brightness galaxies present in SDSS).

Because our spectroscopic surveys extend to ?xed abso-lute magnitudes,the correction for light in galaxies fainter than our limiting magnitudes changes with radius.Adopt-ing the type-dependent LFs of K01,the correction be-comes larger with radius provided the limiting magni-tude is M K s ?10(note that the type-dependent LFs are only constrained for M K s ,iso ≤?20.5).That is,a magnitude-limited survey misses more light at large clus-trocentric radii.If the fraction of early-type galaxies changes from 1to 0(a huge overestimate),the correc-tion changes by ~20%(~10%)for a magnitude limit of M K s ,iso =-22.5(-21.5),approximately the magnitude lim-its for the CAIRNS clusters.Correcting for this e?ect in §5would add even more light to the cluster outskirts and lead to more steeply decreasing pro?les.Thus,the de-creasing mass-to-light pro?les in §5cannot be explained by the morphology-density relation.

7.3.Stellar Populations and Correcting for Faint

Galaxies

Pro?les of the ratio of dark matter to stellar mass can be used both to estimate ?m and to constrain prescrip-tions for galaxy formation.If K s -band light traces stellar mass exactly,the results of §5indicate that the e?ciency of star formation is reduced in dense cluster environments.However,the properties of galaxies change rapidly with in-creasing distance from cluster centers (Balogh et al.2004,and references therein).In particular,the stellar mass-to-light ratio is smaller in late-type galaxies than in early-type galaxies by up to a factor of https://www.wendangku.net/doc/d111679649.html,te-type galaxies are much more common in the ?eld than in clusters.Thus,the mean stellar mass-to-light ratio should decrease with radius.

Because stellar populations are younger at larger clus-trocentric radii,mass-to-optical-light pro?les might de-crease with radius (Bahcall et al.2000)even if the ratio of gravitational mass to stellar mass is constant.Thus,the total-to-stellar mass pro?les of the CAIRNS clusters may decrease less steeply than the mass-to-light pro?les.Here,we test for radial gradients in the stellar mass-to-light ra-tio in A576and estimate the magnitude of this e?ect in K s band.

7.3.1.A Test in A576and the Importance of Faint

Galaxies We showed above (§3.3)that there are no obvious gra-dients in the R ?K s colors of galaxies in A576.We test for gradients in the stellar mass-to-light ratio directly by comparing the mass-to-light pro?les in an optical band (R)and near-infrared bands.If there were a signi?cant gradi-ent in stellar mass-to-light ratios,the near-infrared pro?le would be ?atter than at optical wavelengths.

Indeed,the K s band mass-to-light pro?le (thick solid line in Figure 25)decreases more slowly than the R band pro?le (dash-dotted line).The cumulative mass-to-light ratio decreases by a factor of ~2in R band and by a fac-tor of ~1.4in K s band.This result suggests that the e?ect of star formation gradients on mass-to-light pro?les is signi?cant in the R band as well as in the B band (e.g.,Bahcall et al.2000).However,there is no obvious change in the average R ?K s color with radius in A576(§3.3).Thus,the steeper decrease in the cumulative mass-to-light pro?le in the R band is not readily explained by a simple color gradient.

Another explanation for the di?erence in R and K s band M/L pro?les is the corrections for faint galaxies without redshifts.The R band catalog has complete spectroscopy to R=16.5and complete photometry to R=18.0.Rines et al.(2000)used several techniques to estimate the (as-sumed constant)?ux surface density contributed by back-ground galaxies.Here,by contrast,we correct for faint galaxies by assuming a universal luminosity function in all environments.Under this assumption,the total luminos-ity in all galaxies is simply a constant factor multiplied by the luminosity contained in bright galaxies.

Because 2MASS is a shallow survey,it is di?cult to es-timate magnitudes (and hence number counts)of galaxies fainter than our spectroscopic completeness limit (these number counts are necessary to make a background cor-rection similar to Rines et al.2000).However,it is interest-ing that the 2MASS galaxy counts indicate a steeply rising LF in the outskirts of A576fainter than the spectroscopic

14

completeness limit(Figure4).The number counts there-fore suggest that applying a constant background subtrac-tion to the2MASS data would lead to better agreement between the two mass-to-light pro?les.The presence of a background group or cluster behind A576(Rines et al. 2000)shows that the true background is non-uniform. Fortunately,it is straightforward to apply the assump-tion of a universal luminosity function to the mass-to-light pro?le in the R band.Under this assumption,the two mass-to-light pro?les are in quantitative agreement; the decrease in the mass-to-light ratio between the inner 1h?1Mpc and the outskirts is a factor of~1.4at both wavelengths.Figure25shows that the shapes of the mass-to-light pro?les(thick solid and dashed lines)agree well under this assumption(except at R p 0.5h?1Mpc where the photometry of two bright galaxies is uncertain;see §2.2).Thus,the apparent disagreement between the R-band and K s-band shapes of the cumulative mass-to-light pro?les in A576is not due to radial gradients in the stellar mass-to-light ratio but is simply a result of using di?erent methods to account for the luminosity contributed by faint https://www.wendangku.net/doc/d111679649.html,ing consistent methods produces both qualita-tive and quantitative agreement in the mass-to-light pro-?les calculated at optical and near-infrared wavelengths. Because the same caustic mass pro?le is used for both wavelengths,this comparison tests the relative shapes of the light pro?les calculated at di?erent wavelengths.The agreement between the two pro?les should therefore gen-eralize to all clusters with similar galaxy populations;the fact that A576has one of the most strongly peaked mass-to-light pro?les(Figure22)should not a?ect this gener-alization.This result demonstrates the importance of us-ing consistent corrections for faint galaxies when compar-ing mass-to-light ratios or pro?les at di?erent wavelengths and/or for di?erent clusters.This result also suggests that a complete census of cluster light requires deep,complete spectroscopy.

7.3.2.Estimating the Total-to-Stellar Mass Pro?les Although we showed above(§3)that there is no obvious evidence from near-infrared photometry or R?K s colors for dramatic changes in the stellar populations with clus-trocentric radius,the degeneracy between age and metal-licity and the weak dependence of near-infrared colors on these properties might obscure a real gradient.Here we estimate the potential size of this e?ect.

Because the galaxies we sample are relatively bright, the color-magnitude relation implies that these galaxies should have red colors.We estimate the fraction of light in early-type galaxies at large radii using the type-dependent LFs of https://www.wendangku.net/doc/d111679649.html,ing their estimates of the type-dependent LFs,early-type galaxies contribute roughly half of the to-tal light in bright galaxies(M K

s≤?22.77+5log h)av-eraged over all environments.The K s band mass-to-light

ratio is a factor of1.8±0.3times larger in virial regions than in infall regions(§5).Thus,the ratio of total matter to stellar matter(in galaxies)could be roughly constant on scales up to~10h?1Mpc if the K s band stellar mass-to-light ratio in early-type galaxies is~2.6times larger than in late-type galaxies.Bell&de Jong(2001)and Bell et al. (2003)?nd that the stellar mass-to-light ratio measured in K s band varies by no more than a factor of2over a wide range of star formation histories.Such a large di?erence would probably produce signi?cant R?K s color gradients, contradicting Figure13.The age-metallicity degeneracy and/or complicated star formation histories could conceiv-ably mask these gradients,but these e?ects are generally small at K s band.

A second method of quantifying the changes in stellar mass-to-light ratios is to use the relation between stellar mass-to-light ratio and galaxy color(Bell&de Jong2001; Bell et al.2003).The range of galaxy colors in the SDSS is 0.4 g?r 1.0,although little stellar mass is contained in the bluest galaxies(e.g.,Kau?mann et al.2003).If the average galaxy g?r color changed from0.9in cluster cen-ters to0.4in the outskirts(an extreme assumption),the corresponding change in stellar mass-to-light ratio is only a factor of1.3.A more realistic estimate is that early-type red galaxies comprise roughly half the light in bright galaxies.Then,the average K s band stellar mass-to-light ratio in cluster outskirts is at most20%smaller than in cluster centers.Thus,gradients in stellar populations do not account for the radially decreasing mass-to-light ratios of the CAIRNS clusters.

7.4.Intracluster Light

Another explanation for the decreasing mass-to-light pro?les is that we do not account for light outside of galax-ies.The existence of intracluster red giant branch stars (Durrell et al.2002),planetary nebulae(Ciardullo et al. 1998;Feldmeier et al.1998;Durrell et al.2002;Arnaboldi et al.2003;Feldmeier et al.2003),globular clusters(West et al.1995;Jord′a n et al.2003),di?use light(Zwicky1951; Melnick et al.1977;Uson et al.1991;Bernstein et al.1995; Gregg&West1998;Trentham&Mobasher1998;Gonzalez et al.2000;Feldmeier et al.2002),and supernovae(Smith 1981;Gal-Yam et al.2003)not associated with individual galaxies all suggest that stars are stripped from cluster galaxies and form di?use intracluster light(Moore et al. 1999;Gnedin2003).Numerical simulations of clusters inΛCDM cosmologies show that processes such as tidal stripping and dynamical friction disrupt cluster galaxies (Kravtsov&Klypin1999;Col′in et al.1999).

Surveys of the above tracers of intracluster stars indicate that intracluster light constitutes~5-50%of the total light in the virial regions.The decreasing mass-to-light pro?les found here may be?at if intracluster light is taken into account.Thus,the most secure conclusion we can draw is that the number of galaxies per unit mass is smaller in cluster virial regions than in infall regions.The star formation e?ciency could be constant in all environments with the observed dependence resulting from more e?cient galaxy disruption in environments with larger virial tem-peratures.A prediction of this scenario is that the fraction of intracluster light should increase with cluster mass.A similar trend has recently been noted in simulated clusters (Murante et al.2004).

7.5.Uncertainties in the Caustic Mass Pro?les

D99used numerical simulations to investigate the sys-tematic uncertainties in the caustic technique.D99found that the uncertainties in individual cluster pro?les are large(~50%)but unbiased.We extend this work to ob-servations in Paper I.Surprisingly,the contrast between

15

the caustic envelope and the background is larger in the CAIRNS clusters than in the simulations of D99.This di?erence may indicate a mismatch between the cosmo-logical model used in D99(standardΛCDM)and the true model and/or de?ciencies in the recipe for star formation and galaxy formation used in the simulations.

D99anaylze only Coma-size clusters.It is possible that the caustic technique is less accurate and/or biased for less massive halos.Further high-resolution simulations with di?erent cosmological models and/or di?erent recipes for star and galaxy formation may clarify this issue.

The masses obtained with the caustic technique agree very well with virial masses and X-ray estimates at small radii(Paper I).Thus,the mass-to-light ratios at these radii are reasonably secure(if corrected for projection e?ects). The caustic mass pro?les in Paper I agree very well with both NFW and Hernquist models,with each model pro-viding a slightly better?t on roughly half of the clusters. The NFW pro?le predicts more mass at large radii than the Hernquist pro?le,and it produces better?ts to halos in CDM simulations(Navarro et al.1997).The extrapola-tion of the NFW pro?le beyond the virial radius provides a reasonable description of clusters in simulations(Tasit-siomi et al.2004).We therefore calculate the mass-to-light ratios assuming that the NFW pro?les inside r200extend to r t and that the caustic diagrams indicate cluster/infall region membership.This calculation yields results similar to those found using the caustic mass pro?les.

Caustics are a good but not perfect indicator of clus-ter/infall region membership.Galaxies outside the caus-tics are outside the infall region,but there may be inter-lopers in the caustic diagram.In cluster cores,only~1% of galaxies are interlopers(van der Marel et al.2000).The number of interlopers should increase at roughly the same rate as the area sampled.Indeed,detailed numerical sim-ulations of clusters indicate that the fraction of interlopers increases with radius(Cen1997).To estimate this e?ect in Coma,we estimate the contribution of interlopers to be the background luminosity density times the volume within the caustics,which scales roughly with the area on the sky.The luminosity contained in possible interlop-ers in each radial bin is less than10%of the luminosity in that bin.Thus,although the luminosity of interlopers could lead to an overestimate of the luminosity of infall region members at large radii,the overestimate is likely 10%.

Finally,§7.1shows that the observed VDPs(a better es-tablished tool of galactic dynamics)di?er from those pre-dicted by the galaxy distributions under the assumption of isotropic orbits.The above discussion indicates that the decreasing mass-to-light pro?les are probably not caused by(currently unknown)systematic e?ects in the caustic technique.

7.6.Cosmological Implications

Two groups have used the Second Incremental Data Release(2IDR)of2MASS to measure the near-infrared galaxy luminosity function(K01,C01).Both groups?nd acceptable?ts with the functional form proposed by Schechter(1976).Further,their estimates of the near-infrared luminosity density and the best-?t parameters of the LF agree within the uncertainties.Assuming that the cluster luminosity function is identical to the?eld luminosity function of C01(calculated using2MASS K s extrapolated magnitudes,the same magnitude de?nition used here),the average mass-to-light ratio within the turnaround radius(M/L K

s

)tot implies?m=0.18±0.04 (statistical).If the global value of M/L K

s

is closer to the value in cluster infall regions than the value in cluster virial regions,the best estimate of?m is from(M/L K

s

)inf(the average mass-to-light ratio between r200and r t),which yields?m=0.13±0.03(statistical).Note that these es-timates become~20%smaller if we adopt the C012IDR Kron magnitude LF with a-0.20magnitude adjustment for converting2IDR Kron magnitudes to2MASS extrapo-lated magnitudes(the best-?t LF parameters for the Kron LF have a fainter M?K

s

and a shallower faint-end slope). We explicitly use the luminosity function of C01(for extrapolated magnitudes)to estimate the completeness corrections for faint galaxies.This constraint means that our results are independent of the faint-end slope of the luminosity function in clusters.Provided the luminosity functions are similar at the bright end(as shown in§3.1), the estimate of?m is independent of the properties of dwarf galaxies.Similarly,any unusual systematic e?ects in the measured photometric properties of the galaxies are present in both our sample and that of C01.Thus, any such e?ects should cancel out in the estimate of?m. In particular,2MASS misses faint,low surface brightness (LSB)galaxies(Andreon2002a;Bell et al.2003).Be-cause these galaxies are missing in both the CAIRNS cat-alogs and in the estimates of the?eld LF,the omission of these galaxies leads to an overestimate of M/L K

s

but does not a?ect the estimate of?m.If these LSB galaxies were substantially more numerous in low-density environments than in cluster environments,a bias could result,but An-dreon(2002a)shows that these LSB galaxies are present in clusters.Furthermore,most of these LSB galaxies are fainter than the portion of the LF sampled in the CAIRNS 2MASS catalogs(M K

s

?22).

Some investigators suggest that the local universe is sub-stantially underdense with respect to the global average density(e.g.,Busswell et al.2003;Frith et al.2003,and references therein).In particular,galaxy number counts indicate that the region surveyed by the2dFGRS is signi?-cantly underdense(Frith et al.2003).The presence of such an underdensity obviously has important implications for estimating?m using the mass-to-light ratio.

Wright(2001)suggests that the near-infrared luminos-ity density estimated by C01is a factor of2.3smaller than the value obtained by extrapolating the z band Sloan Digital Sky Survey LF using typical spiral galaxy colors. However,Blanton et al.(2003)recently released a cor-rected version of the SDSS LF(including evolutionary K-corrections)which yields di?erent LF parameters and a z band luminosity density smaller by a factor of1.29.From a comparison of galaxies in both SDSS and2MASS,Blan-ton et al.(2003)?nd that the mean di?erence between the0.1i SDSS band(the notation means that the band-pass is the rest-frame bandpass of a galaxy at z=0.1as observed in the SDSS i band,i.e.,0.1i is slightly blueward of0.0i,the observed bandpass)and the2MASS K s band is0.1i?K s≈2.52.The0.1i band luminosity density can then be extrapolated to K s band(using M⊙,0.1i=4.58and

16

M ⊙,K s =3.39)to obtain j (K s )≈7.22×108hL ⊙Mpc ?3.We thus obtain ?m ≈0.14±0.05using the total (virial plus infall region)mass-to-light ratio (M/L K s )tot ,and ?m ≈0.10±0.03using the mass-to-light ratio (M/L K s )inf in the infall region only.

Huang et al.(2003),using a smaller but deeper sur-vey,suggests that the infrared luminosity density is signif-icantly larger (but see Bell et al.2003,who note that this estimate ignores evolutionary corrections).Using his lumi-nosity density yields ?m =0.23±0.04from M/L K s (

Table 9list several recent estimates of ?m from a variety of techniques.The estimates in Table 9typically assume a ?at universe dominated by dark energy.A detailed dis-cussion of the systematic uncertainties and potential biases in the various techniques lies outside the scope of this pa-per.In general,estimates of ?m from cluster abundances and dynamics and weak lensing yield low values;estimates from supernovae and from the combination of microwave background with large-scale structure yield higher values of ?m .Our estimates are smaller than the currently pop-ular value of ?m ≈0.27,but within the range of estimates from other techniques.It is curious that our estimates agree with other estimates based on mass-to-light ratios both inside and outside of clusters.

However,we ?nd a signi?cantly smaller value than es-timates based on the cluster baryon fraction.In particu-lar,L03(see also Mohr et al.1999)calculate the baryon fraction within r 500and estimate ?m =0.28±0.03(sta-tistical).Comparing this estimate with the mass-to-light ratios of hot clusters in their sample,they conclude that the mass-to-light ratio in hot clusters (kT X ≥3.7keV)is a factor of 0.68±0.10smaller than the global value.This conclusion disagrees with our result that the mass-to-light inside r 200is a factor of 1.8±0.3larger than the mass-to-light ratio outside r 200(which should better approximate the global value).Note that departures from hydrostatic equilibrium of intracluster gas due to nonthermal pres-sure would aggravate this problem by decreasing the true cluster baryon fraction (e.g.,Sadat &Blanchard 2001).At least two explanations may account for the discrep-ancy between L03and the decreasing mass-to-light pro-?les.First,if baryons in hot gas avoid cluster centers due to,e.g.,shock heating,the baryon fraction within r 500may be smaller than the global value (see the compari-son of many simulations by Frenk et al.1999).Detailed observations with ROSAT and ASCA showed that the gas mass fraction increases with radius in some nearby clusters (David et al.1995;Markevitch &Vikhlinin 1997;Ettori &Fabian 1999),but little data exist beyond r 500.Even with Chandra and XMM-Newton ,warm/hot gas is presently not observable at large radii because its temperature and den-sity are too low.If the baryon fraction continues to in-crease outside r 500,the baryon fraction within r 500leads to an overestimate of ?m .Thus,it may be possibile to reconcile these results,but at present,the baryon frac-tion outside r 500remains unconstrained by observations.Second,cluster infall regions and low-mass clusters (which L03and §6.2show have smaller mass-to-light ratios than more massive clusters)may provide a uniquely favorable environment for star formation where the baryon density is high enough to encourage gravitational collapse but not so high that virial temperatures prevent collapse.Under this scenario,the mass-to-light pro?le of a cluster would peak in the center,decrease in the infall region,then rise again to the global value.

The latter explanation is intriguing,and might lead to consistency with Turner (2002),who notes that ?m =0.33is signicantly larger than previous determinations based on the mass-to-light ratios in clusters and concludes that the di?erence results from variations in the mass-to-light ra-tio with environment.The mass-to-light pro?les presented here disagree with this conclusion both qualitatively and quantitatively to densities as small as ≈3ρc .The mass-to-light ratio decreases with radius,and there are no obvious systematic e?ects in the caustic technique that can rec-oncile these results.Thus,the scale dependence of the mass-to-light ratio on scales 10h ?1Mpc cannot be the resolution of this profound problem.

Some recent simulations suggest that galaxies form pref-erentially in overdense regions of the universe (Blanton et al.1999;Ostriker et al.2003).These simulations im-ply that the estimates of ?m from the mass-to-light ratio in cluster virial regions may underestimate the true value by a factor of ~1.25.We ?nd instead that the mass-to-light ratio decreases in cluster infall regions.It is possible,however,that the global mass-to-light ratio is signi?cantly higher than in cluster infall regions and low-mass clusters.Although somewhat arbitrary,such a scenario is consis-tent with all the constraints found in this paper and other investigations.Future studies of bulk ?ows are the most likely candidate to test this scenario.

8.conclusions

We discuss some of the ?rst estimates of radial variations in mass-to-light ratios on scales of 1-10h ?1Mpc using near-infrared photometry from 2MASS and mass pro?les from the kinematics of infalling galaxies.Because cluster infall regions contain the transition from cluster galaxies to ?eld galaxies (Ellingson et al.2001;Lewis et al.2002;G′o mez et al.2003;Treu et al.2003;Balogh et al.2004,and refer-ences therein),mass-to-light ratios in infall regions should closely resemble the global value.To summarize our results:

?Infall regions contain more bright galaxies (to a ?xed absolute magnitude limit)than cluster virial regions.?The near-infrared luminosity functions for bright galaxies (M K s ?22+5log h )in the CAIRNS cluster virial regions and infall regions do not di?er signi?cantly from the ?eld galaxy luminosity function.Clusters contain an excess of extremely bright galaxies above the predictions of a Schechter function.?Optical-near-infrared colors in A576show no radial dependence.This lack of a color gradient shows that the stellar populations do not change

17

dramatically with radius.It is likely that the mild gradients found in the photometric study of Goto et al.(2004)may be enhanced in optically selected samples as compared to near-infrared selected samples such as CAIRNS.

?Galaxies in cluster virial regions and infall regions exhibit a near-infrared color-magnitude relation with a shallower slope than at optical wavelengths.These galaxies also exhibit little scatter in J ?K s colors,indicating that the stellar populations are fairly homogeneous and that internal dust extinction and/or emission is important for only a few galaxies.?Both the surface number density pro?les and surface luminosity density pro?les of CAIRNS members indicate that galaxies and stellar light are more extended than mass.?Near-infrared mass-to-light ratios generally

decrease with radius by a factor of 1.8±0.3in the infall regions of the CAIRNS clusters.This result agrees with previous results based on individual clusters and optical photometry.The presence of decreasing mass-to-light pro?les even at K s band suggests that the decrease is not due to changes in stellar populations.?Near-infrared mass-to-light ratios calculated at r 200using caustic mass estimates agree quite well with mass-to-light ratios calculated at r 500from X-ray mass estimates.This agreement suggests that the decreasing mass-to-light pro?les are not monotonic;the mass-to-light ratio is roughly constant inside r 200.?We derive some of the ?rst constraints on the halo occupation function using cluster masses and near-infrared selected galaxy samples.The number of bright galaxies N 200projected within

R 200increases as N 200∝M 0.70±0.09

200,signi?cantly shallower than N 200∝M 200.Earlier studies of the halo occupation distribution suggest that a halo occupation distribution shallower than N 200∝M 200is necessary to reproduce the observed clustering properties of galaxies (e.g.,Berlind &Weinberg 2002;Berlind et al.2003).?No such non-linear relation is evident between N 200and L 200,the K s band luminosity inside R 200.This result shows that the non-linearity of the halo occupation function is not driven by variations in the luminosity function.?More massive virialized halos have larger mass-to-light ratios.This result follows logically from the two prior points.Our M/L ?M relation agrees with previous determinations (Bahcall &Comerford 2002,L03).These results signify that the e?ciency of galaxy formation decreases (and/or that the e?ciency of galaxy disruption increases)with increasing halo mass and/or virial temperature.

?We investigate possible systematic e?ects and conclude that dark matter is more concentrated than stellar mass contained in galaxies .This result could arise either from di?erent clustering properties of dark matter and baryonic matter or from variations in the e?ciency of converting baryonic matter into galaxies.The cluster environ-ment seems to be either less e?cient at converting baryons into galaxies or more e?cient at disrupting galaxies than less dense environments.Such a di?erence is predicted by simulations of ΛCDM cosmologies where processes such as tidal stripping and dynamical friction disrupt galaxies in clusters (Kravtsov &Klypin 1999;Col ′in et al.1999)and supported by observations of signi?cant numbers of intergalactic stars in clusters.Alternatively,the heating of the intracluster medium may cut o?the supply of cold material needed to form stars (e.g.,Blanton et al.1999;Balogh et al.2000,and references therein),thus lowering the star formation e?ciency in cluster galaxies.?Assuming the mass-to-light ratios at large radii are similar to the global value,we estimate

?m =0.10±0.03(1-σstatistical uncertainty)using the SDSS luminosity density with appropriate color corrections or ?m =0.13±0.03(1-σstatistical uncertainty)from the 2dFGRS.We suggest that the 2dFGRS and the CfA/SSRS2surveys sample local underdensities.Uncertainties in the luminosity density,especially at infrared wavelengths,contribute a signi?cant amount of the systematic uncertainty in estimating ?m .These estimates of ?m are small compared with other recent estimates from the microwave background,the galaxy power spectrum,and supernovae.However,they agree well with other estimates based on cluster mass-to-light ratios (Carlberg et al.1996,1997;Bahcall et al.2000;Girardi et al.2000;Bahcall &Comerford 2002),cluster abundances (Reiprich &B¨o hringer 2002;Bahcall et al.2003,but see Schuecker et al.2003)and weak lensing (Kaiser et al.2004;Wilson et al.2001;Hoekstra et al.2001;Gray et al.2002).We discuss possible systematic e?ects that could cause our result to be anomalously low.Reconciling these estimates of ?m by invoking bias requires that the typical value of M/L K at the smallest densities we probe ≈3ρc is a factor of 2-3smaller than the global value.For instance,if galaxy formation occurs nearly exclusively above a density threshold δ~10,the mass-to-light ratios in cluster outskirts may underestimate the global value.One promising future direction is to study clusters at moderate redshifts where weak lensing provides an inde-pendent mass estimate (Kneib et al.2003).Comparing lensing mass pro?les to caustic mass pro?les will constrain unknown systematics in both techniques.For instance,a sheet of mass of uniform density produces no lensing signal (the mass-sheet degeneracy),but this mass should be evi-dent in the galaxy kinematics.Conversely,foreground and

18

background structures may produce a weak lensing signal but would not a?ect the kinematics of the infall region. Infall regions are interesting environments for studying the evolution of galaxy populations.We show here that in-fall regions are important in constraining models of galaxy bias or antibias and?m.If other methods yield a precise measurement of?m,the changes in mass-to-light ratios with environment provide important clues to the forma-tion and evolution of galaxies.

We once again thank the hard work of Perry Berlind and Michael Calkins,the remote observers at FLWO,and Susan Tokarz,who processed the spectroscopic data.We thank Andi Mahdavi,Dan Fabricant,Je?Kenney,Scott Kenyon,Stefano Andreon,and Ken Nagamine for help-ful discussions.We thank the referee for many sugges-tions which improved the clarity of the paper.MJG and MJK are supported in part by the Smithsonian Institu-tion.We thank the Max-Planck-Institut f¨u r Astrophysik in Garching for allowing us to use some of their computing resources.We thank the entire2MASS team(in particular J.Huchra,M.Skrutskie,T.Chester,R.Cutri,J.Mader, and S.E.Schneider).This publication makes use of data products from2MASS,a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center,funded by NASA and NSF.

REFERENCES

Abell,G.O.,Corwin,H.G.,&Olowin,R.P.1989,ApJS,70,1 Adami,C.,Biviano,A.,&Mazure,A.1998,A&A,331,439 Andreon,S.2002a,A&A,382,495

—.2002b,A&A,382,821

—.2004,A&A,416,865

Andreon,S.&Pell′o,R.2000,A&A,353,479

Arnaboldi,M.et al.2003,AJ,125,514

Bahcall,N.A.&Bode,P.2003,ApJ,588,L1

Bahcall,N.A.,Cen,R.,Dav′e,R.,Ostriker,J.P.,&Yu,Q.2000, ApJ,541,1

Bahcall,N.A.&Comerford,J.M.2002,ApJ,565,L5

Bahcall,N.A.,Lubin,L.M.,&Dorman,V.1995,ApJ,447,L81 Bahcall,N.A.et al.2003,ApJ,585,182

Balogh,M.et al.2004,MNRAS,348,1355

Balogh,M.L.,Christlein,D.,Zabludo?,A.I.,&Zaritsky,D.2001, ApJ,557,117

Balogh,M.L.,Navarro,J.F.,&Morris,S.L.2000,ApJ,540,113 Barton Gillespie,E.,Geller,M.J.,&Kenyon,S.J.2003,ApJ,582, 668

Beijersbergen,M.,Hoekstra,H.,van Dokkum,P.G.,&van der Hulst,T.2002,MNRAS,329,385

Bell,E.F.&de Jong,R.S.2001,ApJ,550,212

Bell,E.F.,McIntosh,D.H.,Katz,N.,&Weinberg,M.2003,ApJS, 149,289

Benson,A.J.,Cole,S.,Frenk,C.S.,Baugh,C.M.,&Lacey,C.G. 2000,MNRAS,311,793

Berlind,A.A.&Weinberg,D.H.2002,ApJ,575,587

Berlind,A.A.et al.2003,ApJ,593,1

Bernstein,G.M.,Nichol,R.C.,Tyson,J.A.,Ulmer,M.P.,& Wittman,D.1995,AJ,110,1507

Bertin,E.&Arnouts,S.1996,A&AS,117,393

Biviano,A.&Girardi,M.2003,ApJ,585,205

Blanton,M.,Cen,R.,Ostriker,J.P.,&Strauss,M.A.1999,ApJ, 522,590

Blanton,M.R.et al.2003,ApJ,592,819

Bridle,S.L.,Lahav,O.,Ostriker,J.P.,&Steinhardt,P.J.2003, Science,299,1532

Bruzual,G.&Charlot,S.2003,MNRAS,344,1000

Busswell,G.S.,Shanks,T.,Outram,P.J.,Frith,W.J., Metcalfe,N.,&Fong,R.2003,ArXiv Astrophysics e-prints astro-ph/0302330

Carlberg,R.G.,Yee,H.K.C.,&Ellingson,E.1997,ApJ,478,462 Carlberg,R.G.,Yee,H.K.C.,Ellingson,E.,Abraham,R.,Gravel, P.,Morris,S.,&Pritchet,C.J.1996,ApJ,462,32

Cen,R.1997,ApJ,485,39

Chabrier,G.2003,PASP,115,763

Christlein,D.&Zabludo?,A.I.2003,ApJ,591,764

Ciardullo,R.,Jacoby,G.H.,Feldmeier,J.J.,&Bartlett,R.E. 1998,ApJ,492,62

Col′in,P.,Klypin,A.A.,Kravtsov,A.V.,&Khokhlov,A.M.1999, ApJ,523,32

Cole,S.et al.2001,MNRAS,326,255

Colless,M.et al.2001,MNRAS,328,1039

Concannon,K.D.,Rose,J.A.,&Caldwell,N.2000,ApJ,536,L19 Conselice,C.J.,Gallagher,J.S.,&Wyse,R.F.G.2002,AJ,123, 2246

Cooray,A.&Sheth,R.2002,Phys.Rep.,372,1

David,L.P.,Jones,C.,&Forman,W.1995,ApJ,445,578

de Lapparent,V.,Geller,M.J.,&Huchra,J.P.1986,ApJ,302,L1 de Propris,R.,Eisenhardt,P.R.,Stanford,S.A.,&Dickinson,M. 1998,ApJ,503,L45

De Propris,R.et al.2003,MNRAS,342,725

Diaferio,A.1999,MNRAS,309,610Diaferio,A.&Geller,M.J.1997,ApJ,481,633

Drinkwater,M.J.,Gregg,M.D.,&Colless,M.2001,ApJ,548,

L139

Durrell,P.R.,Ciardullo,R.,Feldmeier,J.J.,Jacoby,G.H.,& Sigurdsson,S.2002,ApJ,570,119

Ebeling,H.,Voges,W.,Bohringer,H.,Edge,A.C.,Huchra,J.P., &Briel,U.G.1996,MNRAS,281,799

Eisenstein,D.J.,Loeb,A.,&Turner,E.L.1997,ApJ,475,421 Ellingson,E.,Lin,H.,Yee,H.K.C.,&Carlberg,R.G.2001,ApJ, 547,609

Ettori,S.&Fabian,A.C.1999,MNRAS,305,834

Fabricant,D.,Cheimets,P.,Caldwell,N.,&Geary,J.1998,PASP, 110,79

Feigelson,E.D.&Babu,G.J.1992,ApJ,397,55

Feldmeier,J.J.,Ciardullo,R.,&Jacoby,G.H.1998,ApJ,503,109 Feldmeier,J.J.,Ciardullo,R.,Jacoby,G.H.,&Durrell,P.R.2003, ApJS,145,65

Feldmeier,J.J.,Mihos,J.C.,Morrison,H.L.,Rodney,S.A.,& Harding,P.2002,ApJ,575,779

Finoguenov,A.,Reiprich,T.H.,&B¨o hringer,H.2001,A&A,368, 749

Frenk,C.S.et al.1999,ApJ,525,554

Frith,W.J.,Busswell,G.S.,Fong,R.,Metcalfe,N.,&Shanks,T. 2003,MNRAS,345,1049

Fukazawa,Y.,Makishima,K.,Tamura,T.,Ezawa,H.,Xu,H., Ikebe,Y.,Kikuchi,K.,&Ohashi,T.1998,PASJ,50,187

G′o mez,P.L.et al.2003,ApJ,584,210

Gal-Yam,A.,Maoz,D.,Guhathakurta,P.,&Filippenko,A.V. 2003,AJ,125,1087

Gavazzi,G.,Pierini,D.,&Boselli,A.1996,A&A,312,397 Geller,M.J.,Diaferio,A.,&Kurtz,M.J.1999,ApJ,517,L23 Girardi,M.,Borgani,S.,Giuricin,G.,Mardirossian,F.,&Mezzetti, M.2000,ApJ,530,62

Gnedin,O.Y.2003,ApJ,589,752

Gonzalez,A.H.,Zabludo?,A.I.,Zaritsky,D.,&Dalcanton,J.J. 2000,ApJ,536,561

Goto,T.,Yagi,M.,Tanaka,M.,&Okamura,S.2004,MNRAS,348, 515

Gray,M.E.,Taylor,A.N.,Meisenheimer,K.,Dye,S.,Wolf,C.,& Thommes,E.2002,ApJ,568,141

Gregg,M.D.&West,M.J.1998,Nature,396,549

Gunn,J.E.&Gott,J.R.I.1972,ApJ,176,1

Hernquist,L.1990,ApJ,356,359

Hoekstra,H.et al.2001,ApJ,548,L5

Huang,J.-S.,Glazebrook,K.,Cowie,L.L.,&Tinney,C.2003, ApJ,584,203

Hunt,L.K.,Giovanardi,C.,&Helou,G.2002,A&A,394,873 Jarrett,T.H.2000,PASP,112,1008

Jarrett,T.H.,Chester,T.,Cutri,R.,Schneider,S.,Skrutskie,M., &Huchra,J.P.2000,AJ,119,2498

Jarrett,T.H.,Chester,T.,Cutri,R.,Schneider,S.E.,&Huchra, J.P.2003,AJ,125,525

Jord′a n,A.,West,M.J.,C?o t′e,P.,&Marzke,R.O.2003,AJ,125, 1642

Kaiser,N.1987,MNRAS,227,1

Kaiser,N.,Wilson,G.,Luppino,G.,Kofman,L.,Gioia,I.,Metzger, M.,&Dahle,H.2004,ApJ,submitted(astro-ph/9809268) Katgert,P.,Biviano,A.,&Mazure,A.2004,ApJ,600,657

Kau?mann,G.,Colberg,J.M.,Diaferio,A.,&White,S.D.M. 1999a,MNRAS,303,188

—.1999b,MNRAS,307,529

Kau?mann,G.et al.2003,MNRAS,341,33

Kent,S.M.&Gunn,J.E.1982,AJ,87,945

Kneib,J.-P.et al.2003,ApJ,598,804

19

Knop,R.et al.2003,ApJ,598,102

Kochanek,C.S.,White,M.,Huchra,J.,Macri,L.,Jarrett,T.H., Schneider,S.E.,&Mader,J.2003,ApJ,585,161

Kochanek,C.S.et al.2001,ApJ,560,566

Koranyi,D.M.&Geller,M.J.2000,AJ,119,44

Kravtsov,A.V.&Klypin,A.A.1999,ApJ,520,437

Kurtz,M.J.&Mink,D.J.1998,PASP,110,934

Lewis,I.et al.2002,MNRAS,334,673

Lin,Y.,Mohr,J.J.,&Stanford,S.A.2003,ApJ,591,749

—.2004,ApJ,in press(astro-ph/0402308)

Loveday,J.2000,MNRAS,312,557

Mahdavi,A.,Geller,M.J.,B¨o hringer,H.,Kurtz,M.J.,&Ramella, M.1999,ApJ,518,69

Marinoni,C.&Hudson,M.J.2002,ApJ,569,101

Markevitch,M.&Vikhlinin,A.1997,ApJ,491,467

Melnick,J.,Hoessel,J.,&White,S.D.M.1977,MNRAS,180,207 Mobasher,B.&Trentham,N.1998,MNRAS,293,315 Mobasher,B.et al.2003,ApJ,587,605

Mohr,J.J.,Mathiesen,B.,&Evrard,A.E.1999,ApJ,517,627 Moore,B.,Lake,G.,Quinn,T.,&Stadel,J.1999,MNRAS,304, 465

Murante,G.et al.2004,ApJ,607,L83

Navarro,J.F.,Frenk,C.S.,&White,S.D.M.1997,ApJ,490,493 Nikolaev,S.,Weinberg,M.D.,Skrutskie,M.F.,Cutri,R.M., Wheelock,S.L.,Gizis,J.E.,&Howard,E.M.2000,AJ,120, 3340

Oort,J.1958,in La Structure et L’′Evolution de L’Univers, Onzie‘me Conseil de Physique,ed.R.Stoops(Brussels:Solvay Institute),163

Ostriker,E.C.,Huchra,J.P.,Geller,M.J.,&Kurtz,M.J.1988, AJ,96,1775

Ostriker,J.P.,Nagamine,K.,Cen,R.,&Fukugita,M.2003,ApJ, 597,1

Peacock,J.A.&Smith,R.E.2000,MNRAS,318,1144

Pisani,A.,Ramella,M.,&Geller,M.J.2003,AJ,126,1677 Poggianti,B.M.1997,A&AS,122,399

Reg¨o s,E.&Geller,M.J.1989,AJ,98,755

Reiprich,T.H.&B¨o hringer,H.2002,ApJ,567,716

Reipurth,B.,Bally,J.,&Devine,D.1997,AJ,114,2708 Reisenegger,A.,Quintana,H.,Carrasco,E.R.,&Maze,J.2000, AJ,120,523

Rines,K.,Geller,M.J.,Diaferio,A.,Mahdavi,A.,Mohr,J.J.,& Wegner,G.2002,AJ,124,1266

Rines,K.,Geller,M.J.,Diaferio,A.,Mohr,J.J.,&Wegner,G.A. 2000,AJ,120,2338

Rines,K.,Geller,M.J.,Kurtz,M.J.,&Diaferio,A.2003,AJ,126, 2152

Rines,K.,Geller,M.J.,Kurtz,M.J.,Diaferio,A.,Jarrett,T.H., &Huchra,J.P.2001a,ApJ,561,L41Rines,K.,Mahdavi,A.,Geller,M.J.,Diaferio,A.,Mohr,J.J.,& Wegner,G.2001b,ApJ,555,558

Sabatini,S.,Davies,J.,Scaramella,R.,Smith,R.,Baes,M.,Linder, S.M.,Roberts,S.,&Testa,V.2003,MNRAS,341,981

Sadat,R.&Blanchard,A.2001,A&A,371,19

Schechter,P.1976,ApJ,203,297

Schombert,J.M.1988,ApJ,328,475

Schuecker,P.,B¨o hringer,H.,Collins,C.A.,&Guzzo,L.2003,

A&A,398,867

Shectman,S.A.1982,ApJ,262,9

Sheth,R.K.&Diaferio,A.2001,MNRAS,322,901

Skrutskie,M.F.et al.1997,in ASSL Vol.210:The Impact of Large Scale Near-IR Sky Surveys,25

Small,T.A.,Ma,C.,Sargent,W.L.W.,&Hamilton,D.1998, ApJ,492,45

Smith,H.A.1981,AJ,86,998

Spergel,D.et al.2003,ApJS,148,175

Springel,V.&Hernquist,L.2003,MNRAS,339,312 Stoughton,C.et al.2002,AJ,123,485

Tasitsiomi,A.,Kravtsov,A.V.,Gottloeber,S.,&Klypin,A.A. 2004,ApJ,607,125

Tegmark,M.et al.2003,Phys.Rev.D,(astro-ph/0310723) Terlevich,A.I.,Caldwell,N.,&Bower,R.G.2001,MNRAS,326, 1547

Tonry,J.L.1987,in IAU Symp.127:Structure and Dynamics of Elliptical Galaxies,89–96

Tonry,J.L.et al.2003,ApJ,594,1

Trentham,N.1998a,MNRAS,293,71

—.1998b,MNRAS,294,193

Trentham,N.&Mobasher,B.1998,MNRAS,293,53

Treu,T.,Ellis,R.S.,Kneib,J.,Dressler,A.,Smail,I.,Czoske,O., Oemler,A.,&Natarajan,P.2003,ApJ,591,53

Turner,M.S.2002,ApJ,576,L101

Tustin,A.W.,Geller,M.J.,Kenyon,S.J.,&Diaferio,A.2001, AJ,122,1289

Uson,J.M.,Boughn,S.P.,&Kuhn,J.R.1991,ApJ,369,46

van der Marel,R.P.,Magorrian,J.,Carlberg,R.G.,Yee,H.K.C., &Ellingson,E.2000,AJ,119,2038

Vedel,H.&Hartwick,F.D.A.1998,ApJ,501,509

West,M.J.,Cote,P.,Jones,C.,Forman,W.,&Marzke,R.O. 1995,ApJ,453,L77

Wilson,G.,Kaiser,N.,&Luppino,G.A.2001,ApJ,556,601 Worthey,G.1994,ApJS,95,107

Wright,E.L.2001,ApJ,556,L17

Zibetti,S.,Gavazzi,G.,Scodeggio,M.,Franzetti,P.,&Boselli,A. 2002,ApJ,579,261

Zwicky,F.1933,Helv.Phys.Acta,6,110

—.1951,PASP,63,61

Table4

CAIRNS Near-Infrared Spectroscopic Completeness

Cluster r200r t r max K lim f noz A K

s KE K

s

(z)M K

s,lim

f L1

h?1Mpc h?1Mpc h?1Mpc mag mag mag mag

A1940.69 3.3 3.312.20.0440.015-0.052-21.420.844

20

00.20.40.60.81-26-25-24-23-22-26-25-24-23-22-26-25-24-23-22

110

100

00.20.40.60.81110

100

-26-25-24-23-22

0.20.40.60.81-26-25-24-23-22

-26-25-24-23-22

1

10

100

Fig.1.—Completeness of the CAIRNS spectroscopic catalogs versus absolute magnitude M K s (falling thick solid lines and scales on left).Vertical bars indicate the spectroscopic completeness limits.The scales on the right show the number of galaxies per 0.2magnitude bin (rising thin solid lines).The dashed lines show the number of galaxies with redshifts and the dash-dot lines show the number of cluster galaxies with the upper and lower lines indicating the maximum and minimum number of members.The scales are identical in all panels.Clusters are ordered left to right,top to bottom,in decreasing X-ray temperature.

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