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The Astrophysical Journal, 623:721 741, 2005 April 20
# 2005. The American Astronomical Society. All rights reserved. Printed in U.S.A.

THE MORPHOLOGY-DENSITY RELATION IN z $ 1 CLUSTERS
M. Postman, M. Franx,2 N. J. G. Cross,3 B. Holden,4 H. C. Ford,3 G. D. Illingworth,4 T. Goto,3 R. Demarco,3 ґi P. Rosati,5 J. P. Blakeslee,3 K.-V. Tran,6 N. BenIґ 3,7 M. Clampin,8 G. F. Hartig,1 N. Homeier,3 D. R. Ardila,3 tez, F. Bartko,9 R. J. Bouwens,4 L. D. Bradley,3 T. J. Broadhurst,10 R. A. Brown,1 C. J. Burrows,11 E. S. Cheng,12 P. D. Feldman,3 D. A. Golimowski,3 C. Gronwall,13 L. Infante,14 R. A. Kimble,8 J. E. Krist,1 M. P. Lesser,15 A. R. Martel,3 S. Mei,3 F. Menanteau,3 G. R. Meurer,3 G. K. Miley,2 V. Mot ta,14 M. Sirianni,1 W. B. Sparks,1 H. D. Tran,16 Z. I. Tsvetanov,3 R. L. White,1 and W. Zheng3
Received 2004 November 4; accepted 2005 January 12
1

ABSTRACT We measure the morphology-density relation ( MDR) and morphology-radius relation ( MRR) for galaxies in seven z $ 1 clusters that have been observed with the Advanced Camera for Surveys (ACS) on board the Hubble Space Telescope. Simulations and independent comparisons of our visually derived morphologies indicate that ACS allows one to distinguish between E, S0, and spiral morphologies down to z850 ј 24, corresponding to L /Lц ј 0:21 and 0.30 at z ј 0:83 and 1.24, respectively. We adopt density and radius estimation methods that match those used at lower redshift in order to study the evolution of the MDR and MRR. We detect a change in the MDR between 0:8 < z < 1:2 and that observed at z $ 0, consistent with recent work; specifically, the growth in the bulge-dominated galaxy fraction, fEЧS0 , with increasing density proceeds less rapidly at z $ 1than it does at z $ 0. At z $ 1 and ф ! 500 galaxies Mpcю2, we find h fEЧS0 i ј 0:72 ф 0:10. At z $ 0, an E+S0 population fraction of this magnitude occurs at densities about 5 times smaller. The evolution in the MDR is confined to densities ф k 40 galaxies Mpcю2 and appears to be primarily due to a deficit of S0 galaxies and an excess of Sp+Irr galaxies relative to the local galaxy population. The fE-density relation exhibits no significant evolution between z ј 1and 0. We find mild evidence to suggest that the MDR is dependent on the bolometric X-ray luminosity of the intracluster medium. Implications for the evolution of the disk galaxy population in dense regions are discussed in the context of these observations. Subject headingg galaxies: clusters: general -- galaxies: evolution -- galaxies: formation -- galaxies: structure s:

1. INTRODUCTION The study of the origin and evolution of the morphological distribution of galaxies in different environments can reveal important information about internal galactic stellar and gas dynamics and about the state of star formation activity as a function of time, as well as constrain the relative significance of the effects of environmental processes versus conditions at the epoch of their formation in establishing galactic structure. In standard hierarchical clustering models, galaxies in high-density regions of the universe, such as in the central regions of galaxy clusters, will collapse earlier and may evolve more rapidly than galaxies in low-density regions ( Kauffmann 1995; Benson et al. 2001; Heavens et al. 2004). In addition, galaxies in dense environments are subject to a variety of external stresses, which are, in general, not conducive to the maintenance of spiral structure. These

processes include ram pressure stripping of gas (Gunn & Gott 1972; Farouki & Shapiro 1980; Kent 1981; Fujita & Nagashima 1999; Abadi et al. 1999; Quilis et al. 2000), galaxy harassment via high-speed impulsive encounters ( Moore et al. 1996, 1999; Fujita 1998), cluster tidal forces ( Byrd & Valtonen 1990; Valluri 1993; Fujita 1998) that distort galaxies as they come close to the center, interaction /merging ( Icke 1985; Lavery & Henry 1988; Mamon 1992; Makino & Hut 1997; Bekki 1998), and removal and consumption of the gas due to the cluster environment ( Larson et al. 1980; Bekki et al. 2002). Two key relationships that must be understood in the context of the above processes are the relative population fraction of the different morphological classes as functions of the local galaxy density and their location within the local gravitational potential well. The morphology-density relation ( MDR) and the morphology-radius relation ( MRR) have been well studied at low z ( Dressler 1980, hereafter D80; Postman & Geller 1984, hereafter PG84; Whitmore & Gilmore 1991; Goto et al. 2003a)
Bartko Science and Technology, 14520 Akron Street, Brighton, CO 80602. Racah Institute of Physics, Hebrew University, Jerusalem 91904, Israel. MetaJiva Scientific, 12320 Scenic Drive, Edmonds, WA 98026. 12 Conceptual Analytics, LLC, 8209 Woburn Abbey Road, Glenn Dale, MD 20769. 13 Department of Astronomy and Astrophysics, Pennsylvania State University, 525 Davey Lab, University Park, PA 16802. 14 Departmento de Astronomґa y Astrof ґsica, Pontificia Universidad Cai i ґ tolica de Chile, Casilla 306, Santiago 22, Chile. 15 Steward Observatory, University of Arizona, Tucson, AZ 85721. 16 W. M. Keck Observatory, 65-1120 Mamalahoa Highway, Kamuela, HI 96743.
10 11 9

1 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218. 2 Leiden Observatory, Postbus 9513, 2300 RA Leiden, Netherlands. 3 Department of Physics and Astronomy, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218. 4 University of California Observatories / Lick Observatory, University of California, 373 Interdisciplinary Sciences, Santa Cruz, CA 95064. 5 European Southern Observatory, Karl-Schwarzschild-Strasse 2, D-85748 Garching, Germany. 6 Institute for Astronomy, ETH Zurich, Scheuchzerstrasse 7, CH-8093 Zurich, Ё Switzerland. 7 ґ Instituto de Astrofisica de Andalucia (CSIC ), Camino Bajo de Huetor, 24, Granada 18008, Spain. 8 NASA Goddard Space Flight Center, Code 681, Greenbelt, MD 20771.

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TABLE 1 Summary o f Spectroscop ic and HST Observations Mosaic Area (arcmin2) (5) 35.5 36.5 12.0 12.0 12.2 32.7 33.7 Filter ( Exposure Time in ks) (6) V606 (2.0), i775 (4.0), z850 (4.0) r625 (4.8), i775 (4.8), z850 (4.8) V606 (4.8), I814 (4.8) V606 (4.8), I814 (4.8) i775 (6.8), z850 (11.4) i775 (7.2), z850 (12.0) i775 (7.3), z850 (12.2)

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Cluster (1) MS 1054ю0321 ............... RX J0152ю1357 .............. CL 1604+4304 ................. CL 1604+4321 ................. RDCS J0910+5422 .......... RDCS J1252ю2927 ......... RX J0849+4452 ...............

Redshift (2) 0.831 0.837 0.900 0.921 1.101 1.235 1.266

Nz (3) 327 123 107 130 $10 180 90

Nz

; cl; ACS

(4) 143 93 20 31 $10 31 16

HST ID (7) 9290, 9919 9290 9919 9919 9919 9290 9919

and quantify many long-standing observations showing a preference for spheroidal systems to reside in dense regions (or perhaps better stated as a significant lack of spiral galaxies in dense regions). A full understanding of how such a cosmic arrangement came to be requires measuring the evolution of the MDR and MRR. Such an evolutionary study is only possible using the high angular resolution provided by the Hubble Space Telescope (HST ). Several pioneering works have now shed light on this evolution ( Dressler et al. 1997, hereafter D97; Fasano et al. 2000; Treu et al. 2003; Smith et al. 2005, hereafter S05). D97 and Fasano et al. (2000) find a significant decline in the fraction of lenticular galaxies ( fS0) when one looks back from the current epoch to an epoch 4 5 Gyr ago. The results presented by Treu et al. (2003) and S05 are perhaps the most enlightening: they find a smaller increase in the bulge-dominated galaxy ( E+S0) fraction ( fEЧS0 ) with increasing density at z k 0:4 than is seen at z < 0:1 but also find comparable fEЧS0 values for lowdensity regions (ф < 10 galaxies Mpcю2) at z k 0:4 and the current epoch. S05 propose a simple model to explain these observations in which high-density regions at z $ 1 would largely be comprised of elliptical galaxies with only a trace of lenticular galaxies (e.g., 0 fS0 < 0:1). They consider various processes to transform spiral galaxies into lenticular galaxies in order to increase fS0 with time to match the observed morphological population fractions at z $ 0:5. However, the S05 z $ 1 fS0 measurement was inferred from fEЧS0 rather than measured directly as S05 chose ( perhaps wisely) not to attempt to distinguish between S0 and E galaxies from the WFPC2 data used in their study. The deployment of the Advanced Camera for Surveys (ACS; Ford et al. 2003) on the HST has provided us with an opportunity to greatly expand our understanding of the physics behind the morphological evolution of galaxies in a wide variety of environments. The higher sensitivity and better angular sampling of the Wide Field Camera ( WFC) on ACS relative to WFPC2 enable the acquisition of high signal-to-noise ratio (S/ N ) morphological information for sub-Lц galaxies over projected areas of up to 10 Mpc2 in z $ 1 clusters, in a modest allocation of telescope time. This is a significant advantage over prior capabilities and enables us to sample more than three decades in local galaxy density using the same homogeneous data samples. As part of an extensive program to study the formation and evolution of clusters and their galaxy populations, the ACS Investigation Definition Team ( IDT) has implemented a 128-orbit program to observe seven distant clusters in the redshift range 0:83 z 1:27. In this paper we present new constraints on the form and evolution of both the MDR and the MRR in these clusters and their surroundings based on morphologies determined from the ACS WFC imagery coupled with extensive spec-

troscopic data and X-ray observations. This paper is organized as follows: In x 2 we give a brief summary of the space- and ground-based observations used in this study, in x 3we present a detailed discussion of our morphological classification procedure and an assessment of the reliability of these classifications, in x 4 we present the methods used to estimate the local projected density, and in x 5 we present our derived MDR and MRR. An assessment of the implications of these results is given in x 6, and a summary of the essential results is provided in x 7. Two appendices discuss details associated with the computation of population fractions that are suitably corrected for contamination and incompleteness, the robustness of our density estimators, and the validity of using composite samples to enhance the S/ N in the derived MDR and MRR. We adopt H0 ј 70 km sю1 Mpcю1, m ј 0:3, and ц ј 0:7 for the computation of all intrinsic quantities unless specifically indicated otherwise. 2. OBSERVATIONS The clusters included in this study, along with a summary of the ACS observations, are listed in Table 1. The average cluster redshift, based on all available spectroscopically confirmed cluster members, is given in column (2) of this table. The number of redshifts acquired for galaxies in the region of each cluster (both members and nonmembers and including galaxies outside the ACS mosaic boundaries) is listed in column (3). Column (4) lists the number of spectroscopically confirmed cluster members that also lie within the ACS mosaic boundaries. The details of the HST ACS observations are given in columns (5) (7). The sample selection process was limited by the small number of spectroscopically confirmed clusters at z > 0:8. However, we were able to include clusters with a range of X-ray luminosities, from LX; bol < 1044 ergs sю1 to LX; bol ј 1:9 ; 1045 ergs sю1. Table 2 is a compilation of the derived X-ray properties and velocity dispersions of these clusters. Two of the seven clusters (the two at R:A: ј 16 hr) are optically selected systems, while the rest are X-ray selected, although R X J0849+ 4452 is a binary cluster system in which the less massive component (CL J0848+4453) was IR selected (Stanford et al. 1997). 2.1. ACS Observations We used the WFC on the ACS to image each cluster. For MS 1054ю0321, R X J0152ю1357, RDCS J1252ю2927, and R X J0849+4452 multiple pointings were used to construct larger mosaics covering $35 arcmin2. For the first three of these clusters, the pointings form a 2 ; 2 pattern with all four pointings overlapping the central 10 region of each cluster; hence, the exposure time in the central regions of these systems is 4 times as long as the values given in Table 1. For R X J0849+4452, we used a 3 ; 1 pattern in order to obtain images of both components

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TABLE 2 Su mmary of Clus ter X-Ray and Kine mati c Data

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Cluster MS 1054ю0321 ............... RX J0152ю1357 .............. CL 1604+4304 ................. CL 1604+4321 ................. RDCS J0910+5422 .......... RDCS J1252ю2927 ......... RX J0849+4452 ...............

(10

44

LX hю2 ergs sю1) 70

(10

44

LX; bol hю2 ergs sю1) 70 0.8 1.9 0.3 0.3 1.1 0.6

TX ( keV )
Ч2 5 8:0ю1::5 6:46Ч1::7 ю1 2 2:51Ч1::05 ю0 69 ... 7:20Ч2::2 ю1 4 6.50 ф 0.5 5:80Ч2::8 ю1 7

(km sю1) 1153 ф 80 919 ф 168 989Ч98 ю76 649Ч59 ю46 .. . Ч117 760ю69 .. .

r200 (hю1 Mpc) 70 1.79 1.42 1.48 0.95 0.99a 0.94 0.91a

X-Ray Data References 1, 2 2, 3 4 5 6, 7 8, 9

Velocity Dispersion References 1 10 11 11 12

7.78 ф 0.4 5.74 ф 0.6 0.86 ф 0.13 <0.7 0.78 ф 0.09 1.90 ф 0.3 1.41 ф 0.3

16.43 ф 18.57 ф 2.01 ф ... 2.14 ф 6.60 ф 2.85 ф

a Parameter r200 based on assumed ј 750 km sю1. References.--(1) Gioia et al. 2004; M. Donahue 2004, private communication; (2) Romer et al. 2000; (3) Della Ceca et al. 2000; (4) Lubin et al. 2004; (5) Stanford et al. 2002; (6) Rosati et al. 2004; (7) Lombardi et al. 2005; (8) Rosati et al. 1999; (9) Stanford et al. 2001; (10) Demarco et al. 2004b; (11) Gal & Lubin 2004; (12) Demarco et al. 2004a.

of this binary cluster system. All the remaining targets were observed using a single WFC pointing centered on the cluster. The filters are chosen to approximately straddle the restframe 4000 8 break in order to facilitate the identification of bulge-dominated galaxies in the red sequence of the clusters. This sequence, which is populated mostly by elliptical and lenticular galaxies with a strong 4000 8 break, is well separated from the color-magnitude relation (CMR) for late-type cluster galaxies, as well as that for most field galaxies. In all cases, we have at least one filter that samples part of the rest-frame B band. We use the ACS images taken in those filters to perform our morphological classifications so that we can readily compare our results with morphological information obtained at lower redshifts (e.g., Fabricant et al. 2000). The filters used are explicitly listed in Table 1. Hereafter we use V606 to denote the F606W bandpass, r625 to denote F625W, i775 to denote F775W, I814 to denote F814W, and z850 to denote F850LP. 2.2. Object Photometry and Classification Object detection and analysis are performed using the ACS IDT pipeline (a.k.a. APSIS; Blakeslee et al. 2003a). APSIS photometry is on the AB system and is corrected for Galactic extinction using the Schlegel et al. (1998) 100 m map. Object detection and star-galaxy discrimination are performed using the dual-image mode in SExtractor ( Bertin & Arnouts 1996). The detection image is an inverse variance weighted combination of the ACS exposures from all available passbands. The inverse variance weighting preserves information about the structural characteristics of the galaxies ( for details see Benґtez i et al. 2004). In this paper we count as galaxies all objects with SExtractor stellarity parameter CLASS STAR 0:50. The automated image structure analysis of detected objects in our ACS data includes the determination of the luminosity-weighted moments, the ellipticity, and the 180 rotational asymmetry and image concentration parameters (e.g., Abraham et al. 1994; Conselice et al. 2000). All magnitudes cited in this study are based on the SExtractor MAG_ AUTO magnitude as it provides a reasonable estimate of the total flux. 2.3. Spectroscopic Observations and Photometric Redshifts Spectroscopic redshifts have been obtained for the clusters in our survey, by us and others, using multiobject spectrographs on the Keck, VLT, or Magellan observatories. The total number of redshifts and the number of confirmed cluster members within each ACS mosaic are listed in Table 1. The publications containing some or all of the redshift data include K. Tran et al.

(2005, in preparation) for MS 1054ю0321, Demarco et al. (2004b) for R X J0152ю1357, Postman et al. (1998b, 2001) and Gal & Lubin (2004) for the CL 1604+43 system, Stanford et al. (2002) for RDCS J0910+5422, R. Demarco et al. (2005, in preparation) for RDCS J1252ю2927, and Rosati et al. (1999) for R X J0849+4452. The target selection criteria for the redshift surveys of MS 1054ю0321 and the CL 1604+43 clusters were based on a single red flux limit. The target selection for R X J0152ю1357 includes a color selection criterion (see Demarco et al. 2004b). The spectra are of moderate resolution (R $ 500 1200), and most have sufficient S/ N to measure the prominent spectral features [e.g., (O ii) line widths]. Our photometric redshifts are derived using the Bayesian method (a.k.a. BPZ) described in Benґtez (2000) and are based i on a minimum of three passbands, including all available ACS photometry. We have reliable photo-z's for R X J0152ю1357 (z ј 0:837), MS 1054ю0321 (z ј 0:831), and RDCS J1252ю 2927 (z ј 1:235). Photo-z's for R X J0152ю1357 are based on the ACS r625, i775, and z850 photometry. Photo-z's for MS 1054ю0321 are based on the ACS V606, i775, and z850 photometry. Photo-z's for RDCS J1252ю2927 are based on ACS i775 and z850 photometry and ground-based BVJK photometry (Toft et al. 2004). For the two z ј 0:83 clusters, the rms scatter in (zspec ю zph )/(1 Ч zspec ), ph , is 0.05. For RDCS J1252ю2927, ph is 0.10. Only objects that have a BPZ confidence level of 0.90 or greater are selected for analysis. Figure 1 shows the distribution of galaxies with photometric redshifts within 2ph of the mean cluster redshift and galaxies with 2ph < jzcl ю zph j /(1 Ч zcl ) < 6ph . The cluster overdensity is clearly seen only when we select galaxies close to the actual mean cluster redshift, indicating that our photo-z's are useful in significantly suppressing fore/ background contamination and isolating most of the actual cluster members. 3. MORPHOLOGICAL CLASSIFICATION We visually classified the morphologies of all galaxies in each field with i775 23:5( for the z < 1 clusters) or z850 24 (for the z > 1 clusters) regardless of their position or color. For reference, the characteristic magnitude, mц , for cluster galaxies is i775 ј 22:3 at z ј 0:83 (Goto et al. 2005) and z850 ј 22:7 at z ј 1:24 ( Blakeslee et al. 2003b). For all our cluster observations, we have at least one filter that samples part of the restframe B band (see Table 1) so that morphological classifications can be readily compared with those at lower redshifts. We classify galaxies using the common Hubble sequence: E, E/S0, S0, S0/Sa, Sa, Sb, Sb/Sc, Sc/Sd, Irr. However, for the purposes of

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Fig. 1.--Right: Projected distribution of galaxies with photometric redshifts that lie within ф2ph of the mean cluster redshift for RX J0152ю1357, MS 1054ю0321, and RDCS J1252ю2927. Left: Distribution of galaxies with photometric redshifts in the range 2ph < jzcl ю zph j /(1 Ч zcl ) < 6ph . Different symbols denote different morphological classifications: black filled circles are elliptical galaxies, gray filled circles are S0 galaxies, and stars are Sp+Irr galaxies. The dashed lines denote the boundaries of the ACS mosaics. The RDCS J1252ю2927 photo-z's are available over less area than the full ACS mosaic because they rely on nearIR photometry that covers a smaller region. The overdensities associated with the clusters are easily seen in the right panels and are dominated by E and S0 galaxies.

the present analyses, we bin these finer classifications into just three broad morphological categories: E (elliptical; ю5 T ю3), S0 ( lenticular; ю2 T 0), and Sp+Irr (spiral + irregular; 1 T 10). The FWHM of the point-spread function in our co-added ACS images is $0B09 (1.8 WFC pixels), corresponding to a projected proper distance of 684 pc at z ј 0:831 and 752 pc at z ј 1:27. We are thus able to resolve subkiloparsec structure in all cluster members. At i775 ј 23:5, the typical galaxy subtends an isophotal area of $400 WFC pixels or 125( FWHM)2, making visual classification (or for that matter any classification method) quite feasible. At fainter magnitudes, however, classification rapidly becomes difficult and systematic errors increase both because galaxies are becoming smaller (e.g., Roche et al. 1998; Bouwens et al. 1998; Ferguson et al. 2004; Trujillo et al. 2004) and because there is insufficient area over which the integrated S/ N is sufficient for accurate classification. Examples of the ACS image quality and our corresponding classifications are shown in Figures 2 and 3. The morphological classification was performed on the full sample of 4750 galaxies (in seven clusters) by one of us ( M. P.). Three other team members ( N. C., M. F., B. H.) classified a subset of $400 of these galaxies to provide an estimate of the

uncertainty in the classifications. All classifiers used a common reference set of morphologies from a low-redshift B-band galaxy sample as a guide. Exact or majority agreement between all four classifiers in the overlap sample was typically achieved for 75% of the objects brighter than i775 ј 23:5. Furthermore, there was no significant systematic offset between the mean classification for the three independent classifiers (as determined using the voting scheme from Fabricant et al. 2000) and the classification by M. P., giving confidence that the full sample was classified in a consistent manner. The overall population fractions between the four independent classifiers exhibit only a relatively small variance. Figure 4 shows the E+S0 fraction for each classifier as a function of z850 magnitude for a color-selected [(i775 ю z850 ) ! 0:5] subset of galaxies in the RDCS J1252ю2927 field. The average rms scatter in the E+S0 population fraction between classifiers is 0.06. The average rms scatter in the S0 population fraction between classifiers is about 2 times higher, 0.11. The rms in the E population fraction is the same as that for the S0 galaxies, 0.11. In other words, the population fractions are fairly robust and the variance in these fractions is significantly less than the $20% 25% disagreement level between classifiers on the

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Fig. 2.--Color postage stamp cutouts of the brightest 49 spectroscopically confirmed members of CL 1604+4321 (z ј 0:92) and CL 1604+4304 (z ј 0:90) and their corresponding visually derived morphological classifications. The ``Pos Disk'' classification stands for ``possible disk'' galaxy. It is given to objects that appear to have a disk structure but the precise nature of that disk could not established. Galaxies with the ``Pos Disk'' classification are counted as spiral galaxies in our derivation of the MDR. The first 29 cells show galaxies from CL 1604+4321, and the rest contain galaxies from CL 1604+4304. The galaxies from each cluster are shown in increasing apparent magnitude order and span the range 20:91 i775 23:50. Each cutout subtends a 6B4 ; 6B4 area.

morphological classification of any individual galaxy. Not surprisingly, the combined E+S0 fraction is more robust than either the E or the S0 fractions, a quantitative demonstration that detecting spiral structure is a more robust skill than detecting disks. Most importantly, there are no significant systematic differences between the classifiers. The scatter in the S0 population fraction is comparable with N 1/2 uncertainties in any given value, and while counting statistics do not suggest the minimum scatter one might expect between different classifiers, this level of scatter indicates that our classification errors are small enough for the task at hand, providing a uniform set of classifications. If our visual morphological classifications are robust, there should be noticeable differences in the distributions of the objectively derived ``form'' parameters (ellipticity, asymmetry, concentration) for the E, S0, and Sp+Irr categories. Figure 5 shows the histograms of these three form parameters for each of the three morphological bins. Clear differences between the distributions exist. For example, the ellipticity distribution of visually classified elliptical galaxies differs from that for visu-

ally classified S0 galaxies at greater than the 99.999% confidence level. We use this fact later on as a key part of our analysis. Elliptical galaxies as a class have, as expected, a lower median ellipticity and asymmetry and a higher median concentration than the other two morphological classes. Elliptical galaxies also exhibit less scatter about the mean values of these form parameters. The Sp+Irr class exhibits a higher mean ellipticity and asymmetry than either the E or S0 class. The S0 galaxies have form characteristics that are, on average, intermediate between the E and Sp+Irr distributions. Two key concerns when performing galaxy morphological classification, visually or via machine algorithms, are the effect of surface brightness dimming and the shorter rest-frame wavelength being imaged with increasing redshift. The latter effect, sometimes referred to as the ``morphological k-correction,'' has been studied fairly well ( Bunker et al. 2000; Abraham & van den Bergh 2001; Windhorst et al. 2002; Papovich et al. 2003). In general, over the redshift range being studied here, the morphological k-correction has been shown to be important only in a small fraction (P20%) of the galaxy population, and in those

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Fig. 3.--Color postage stamp cutouts of the brightest 49 spectroscopically confirmed members of MS 1054ю0321 (z ј 0:831). The galaxies are displayed in increasing apparent magnitude order and span the range 20:14 i775 22:15.

cases, it is often more of an issue of how one characterizes any existing spiral structure and not usually a case of missing spiral structure altogether (see references above for details). Furthermore, the bluest wavelengths we use for our morphological classifications correspond to the blue end of the restframe B band, which is where many lower redshift studies have been done. Our classifications are never performed in the restframe U band. The effects of surface brightness (SB) dimming are potentially of greater concern as the ability to distinguish between adjacent categories (e.g., E vs. S0, S0 vs. Sa) may be compromised at higher redshift. To test how sensitive our visual classification scheme is to SB dimming, we performed two simulations. In the first test, we ``redshift'' our ACS image of the z ј 0:33 cluster MS 1358+6245 to z ј 0:83 and perform visual classifications on both the original and redshifted versions. In the second test, we redshifted our ACS image of MS 1054ю0321 to z ј 1:24 and compared the classifications derived for the original and redshifted versions. The redshifting involved dimming the objects appropriately, resampling the images to account for the smaller angular scale, and adjusting the noise levels to correspond to those appropriate for our exposure times used in the more distant cluster observations. Reclassification of the red-

shifted galaxy images was done in a random order and at least 3 months after the initial classifications to minimize ``memory'' of the initial classifications by the classifier. Some examples of the original and redshifted MS 1054ю0321 galaxies are shown in Figure 6. The results of the comparisons between the morphological classifications of the original and redshifted objects are shown in Figure 7. The population fractions obtained using the redshifted images are completely consistent with those in the original images: the differences are comparable to or less than the N 1/2 uncertainties. Thus, our increased exposure times for the more distant clusters coupled with the high angular sampling and sensitivity of the ACS WFC successfully mitigate the effects of SB dimming and allow us to distinguish between our three primary morphological categories ( E, S0, and Sp+Irr) uniformly across the redshift range under study. 3.1. Classification of Mergers and External Morphology Comparisons As we wish to measure the MDR be compared to previous work, we a Hubble type classification ( E, S0, above our flux limits. We do make the object appears to be undergoing and MRR in forms that can ttempt to provide a standard or Sp+Irr) for all galaxies a separate note on whether a merger or tidal disruption,

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Fig. 4.--Top: E+S0 population fraction as a function of z850 magnitude for each of the four independent visual classifiers. The sample used in this comparison is a color-selected sample that favors inclusion of bulge-dominated galaxies, hence the relatively high overall early-type population fraction. The values for each classifier are horizontally offset slightly from one another for clarity. The error bars shown represent the N 1/ 2 uncertainties. The dashed line shows the mean E+S0 population fraction averaged over all classifiers. Bottom: The rms scatter in the E+S0 ( four-point stars) and S0 (diamonds) population fractions as a function of z850 magnitude between the four classifiers. The dashed lines represent the average rms scatter.

important exercise to provide a set of morphological classifications that are as similar as possible to the low-z studies. We also agree, however, that quantifying the frequency of mergers at higher redshift reveals fundamental information about the evolution of cluster galaxies. The assessments of the early-type population component of MS 1054ю0321 by us and vD00 are ultimately consistent, however, if one accounts for the observation that the majority of the close pairs in MS 1054ю0321 include at least one bulge-dominated member. We compare our Hubble classifications with those galaxies that vD00 did classify as E, S0, or Sp/ Irr (i.e., excluding the merger/peculiar objects). We find exact agreement with their Hubble classification (when binned into these three categories) 71% of the time. We swapped E or S0 classifications 11% of the time (i.e., they called it E and we called it S0 or vice versa) and we swapped S0 and Sp classifications 10% of the time. The remaining 8% were cases in which either we or they could not make a definitive classification. This translates to a ф0.1 scatter between our respective fE or fS0 values, which is consistent with the scatter estimated from our comparisons between our ACS team classifiers. As a further external validation of our morphological classifications, M. P. classified all galaxies from our ACS exposure of MS 1358+6245 (z ј 0:33) that were in common with the extensive study of this system performed by Fabricant et al. (2000). Agreement between the M. P. classifications and those from Fabricant et al. (2000) was achieved $80% of the time with no systematic bias seen in the discrepant classifications (see Fig. 7). We thus conclude that our E, S0, and Sp+Irr classification scheme is robust and produces Hubble types that are comparable in accuracy to visual morphological data used in other studies. 3.2. Field Morphological Population Fractions Figure 9 shows the E, S0, and Sp+Irr fractions as a function of z850 for field galaxies. The data points are the fractions derived from our ACS data and our visual classifications. The results in this figure are based exclusively on galaxies with spectroscopic or photometric redshifts that are incompatible with their being cluster members. The gray bands show the typical range in lowdensity population fractions derived from local galaxy redshift surveys (e.g., PG84; D97; Goto et al. 2003a). The local (z < 0:1) and distant (0:5 P z P 1) field ( i.e., low density) galaxy populations appear to have similar fractions of E, S0, and Sp+Irr systems. 4. LOCAL PROJECTED GALAXY DENSITY ESTIMATION We compute the local projected galaxy density in two different ways to ensure robustness: the nearest N neighbors approach used by D80 and D97 and a friends-of-friends ( FoF ) algorithm. Both methods yield consistent results, and we therefore present our results in terms of the nearest N neighbors based density unless otherwise specified. Appendix A provides a demonstration of the consistency of these two density estimation techniques. In the nearest neighbor method, one computes the area of the region containing the N nearest neighbors and then derives the corresponding projected density at each galaxy location from the expression ( ) N Ч1 i fcorr ПMcl ; Mref ч Xh ю1 ю а wПmk ; ck ч ю Nbkgd ; П1ч фi ј N D2 A k ј1 where фi is the projected galaxy density about a given galaxy, fcorr(Mcl, Mref) is a correction factor that ensures that the density

and the analyses of the distribution and frequency of such systems will be presented in a separate paper ( F. Bartko et al. 2005, in preparation). However, for the present work, we do not classify galaxies as merger/peculiar systems (as done by van Dokkum et al. 2000, hereafter vD00) if one of the above standard morphological categories can indeed be applied to the individual objects involved in the merger. Nonetheless, the WFPC2 study of MS 1054ю0321 by vD00 provides an additional check on the robustness of our morphological classifications. There are a total of 79 galaxies in common that have morphological classifications by us and by vD00. Of these, 16 are classified as merger/peculiar by vD00. We classify 13 of them as bulge-dominated systems ( E, S0, or S0/Sa) and 3 as later type spiral galaxies. The ACS cutouts of these 16 objects are displayed in Figure 8. As can be seen from this figure, the morphology of most of the systems classified as merger / peculiar by vD00 can also reasonably be placed into one of the E / S0/ Sp + Irr bins. While this confirms the vD00 conclusion that MS 1054ю 0321 hosts a significant fraction of early-type mergers, it does yield one difference (albeit perhaps a semantic one) in the conclusions reached regarding the overall early-type populations in MS 1054ю0321. By counting merger/peculiar systems as a separate category, vD00 concluded that early-type systems comprise a lower population fraction (44%) than in comparably rich clusters at lower redshift. We conclude that the early-type fraction, fEЧS0 , in MS 1054ю0321 is higher, about 73%, when one attempts to classify cluster members (including merger components) as E, S0, or Sp+Irr. Of course, the factor is a function of local density and the above value is averaged over densities in the range 15 galaxies Mpcю2 < ф 1000 galaxies Mpcю2 . Given that the merger/peculiar category has not routinely been used in the classification of low-z clusters, we feel that it is an

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Fig. 5.--Image concentration, rotational asymmetry, and ellipticity distributions for galaxies visually classified as elliptical, S0, and Sp+Irr. The top row shows the distributions for Sp+Irr. The middle row shows the S0 distributions. The bottom row shows the distributions for elliptical galaxies.

is always measured with respect to a common fiducial luminosity that corresponds to that used in low-redshift studies of the MDR, N is the number of nearest neighbors, w(mk , ck)isthe selection function (which can depend on magnitude and color; see Appendix B for details), Nbkgd is a background contamination correction (if needed), N is the solid angle of the region containing the N nearest neighbors (a rectangular region in our implementation), and DA is proportional to the angular diameter distance to the cluster (essentially the conversion between arcsec and projected Mpc). The correction factor is R f
corr Mref

ПMcl ; Mref ч ј Rю1 Mcl
ю1

х(M ) dM х(M ) dM

;

П 2ч

where Mref is the absolute magnitude limit to which we measure all densities, Mcl is the available limit for the cluster being anaц lyzed, and х(M ) is the galaxy luminosity function [with MV (z ј 0) ј ю21:28 and ј ю1:22]. We choose Mref to match that of the original D80 study at z ј 0(MV ј ю19:27 for our adopted cosmological parameters), but as we are sampling look-back times over which significant evolution in the characteristic magnitude of a Schechter luminosity function is detected, we allow Mref to vary with redshift as Mref (z) ј Mref (z ј 0) ю 0:8z. For our data, fcorr lies in the range [1.2, 3.0]. We use the density derived from the N ј 7 nearest neighbors, but the results are not sensitive to this choice in the range 5 N 10. The background correction is applied only when we are using samples requiring a statistical background subtraction.

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Fig. 6.--Image cutouts of 21 original (z ј 0:83) and redshifted (z ј 1:24) MS 1054ю0321 galaxies and their corresponding morphological classifications. The original image is on the left. The galaxies shown here are spectroscopically confirmed cluster members. The redshifted images are constructed to match the exposure level used for our z850 mosaic of RDCS J1252ю2927 (see Table 1).

For samples based on spectroscopic or photometric redshifts, the background subtraction (if needed at all) is computed using the prescriptions described in Appendix B. Our statistical background correction, Nbkgd , is derived from a combination of ACS and ground-based data. We use ACS observations of the Hubble Deep Field and Tadpole galaxy ( Benґtez et al. 2004) to i generate the surface density of field galaxies when i775 > 23:0. For i775 23:0, we transform the number counts from the large I-band survey of Postman et al. (1998a) to the required ACS bandpasses. Density estimation is most accurate when using galaxy samples that are based on spectroscopic or photometric redshift information as fore / background objects are effectively excluded from the analyses. In cases in which sufficient redshift in-

formation is not available, one can use statistically subtracted background-corrected density estimates. Such estimates are only reliable in dense regions (>80 galaxies Mpcю2) where the cluster population dominates the counts. For reference, the 1 error in the field galaxy surface density at z850 ј 24 is 5.4 galaxies arcminю2, which corresponds to a projected density of 26 and 22 galaxies Mpcю2 at z ј 0:83 and 1.27, respectively. The statistically subtracted background-corrected population fractions and densities can be biased if there happens to be a significant overdensity in the line of sight to the cluster. Thus, the most reliable results are those based on samples with complete or nearly complete spectroscopic or photometric redshift information. In Appendix A we demonstrate that a reliable composite MDR or MRR can be derived from a combination of spectroscopic

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Fig. 7.--Left: Population fractions of E and S0 galaxies as a function of i775 magnitude for the cluster MS 1358+6245 at z ј 0:33. The population fractions shown are from Fabricant et al. (2000; based on their WFPC2 mosaic) and this paper ( based on the i775 ACS WFC image and a redshifted version of this image out to z ј 0:83). There are no obvious systematic offsets between our fractions and those in Fabricant et al. (2000) nor any systematic changes as we redshift the data out to z ј 0:83. The dashed lines show the population fractions obtained by averaging the results of all classifiers. Right : Population fractions in the original MS 1054ю0321 ACS image and in a version redshifted to z ј 1:24. The population fractions at each magnitude are horizontally offset from one another by a small amount for clarity.

samples, photo-z samples, and samples with statistically subtracted background corrections providing that each such sample is limited to its optimal density regime. 5. THE MORPHOLOGY-DENSITY AND MORPHOLOGY-RADIUS RELATIONS AT z $ 1 We present our MDR and MRR results in Figures 10 15. Figure 10 shows the composite MDR derived from all clusters in the sample using the best available data. The composite MDR

is derived from the spectroscopic samples for MS 1054ю0321 and R X J0152ю1357 for densities below 1000 galaxies Mpcю2 and their photo-z selected samples for densities above 1000 galaxies Mpcю2, the photo-z sample for RDCS J1252ю2927 ( for all densities), and the statistically subtracted background results for CL 1604+4304, CL 1604+4321, RDCS J0910+5422, and R X J0849+4452. The statistically subtracted background results are used only when ф ! 80 galaxies Mpcю2 (roughly 3 times the amplitude of the typical fluctuations in the surface

Fig. 8.--Color composite images of the 16 galaxies in common between our morphological sample for MS 1054ю0321 and those classified as merger/peculiar by vD00. Our morphological classification of the object centered in each cutout is indicated in the lower left corner. The pictures here are made from the V606, i775, and z850 ACS WFC images.

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Fig. 9.--Population fractions of E, S0, and Sp+Irr of field galaxies (in our survey) as a function of z850 magnitude. The horizontal lines show the mean values over the range 20 z850 24. The gray shaded regions denote the local (z P 0:15) population fractions at low density (ф P 0:1 galaxies Mpcю2 ). The open circles in the top panel show the fraction of galaxies for which classifications could not be readily made.

density of fore / background galaxies; see x 4). As in S05, we find that the MDR exists at z $ 1. The z $ 1 MDR results from S05 are shown for comparison. Our fEЧS0 versus local density results are consistent with those of S05 to within the 1 uncertainties: we also find a less rapid increase in fEЧS0 with increasing density than is seen at low redshift. However, the elliptical fraction, fE , shows no significant departures from the low-redshift fE-density relation, although, as demonstrated in Figure 4, the classification uncertainties in our fE and fS0 values are about twice as high as the uncertainties in our fEЧS0 and fSpЧIrr values. The most notable difference between our current results and those at z P 0:2 (see, e.g., Fig. 9 in Fasano et al. 2000) is the significantly lower fraction of S0 galaxies: averaged over all densities with ф ! 30 galaxies Mpcю2, our mean fS0 ј 0:20 ф 0:12, where the error includes both the uncertainties from counting statistics (ф0.035) and classification errors (ф0.11). The typical low-z fS0 value, when averaged over the same density range, is 0:46 ф 0:06 ( D80; D97; PG84), a factor of $2 higher than what is found at z $ 1. A significant decline in the S0 population, relative to that seen in the current epoch, has previously been reported at redshifts as low as z $ 0:4( D97; Fasano et al. 2000). Furthermore, over the range of densities being probed in this study, fS0 exhibits only a weak dependence on the projected density, analogous to what is seen at similar projected densities at lower redshifts (e.g., D97). The shallower growth of fEЧS0 with increasing density seen at z $ 1by S05 and by us thus appears to be due to a significant deficit of S0 galaxies and an excess of spiral galaxies relative to similar environments in the current epoch. This provides further support for observations suggesting that it is the S0 and spiral population fractions that are experiencing the most significant changes with time over the past 8 Gyr (e.g. , Moss & Whittle 2000; Fasano et al. 2000; Kodama & Smail 2001; Treu et al. 2003; S05). Figure 11 shows the MRR for the same composite cluster sample used in deriving the MDR in Figure 10. For each cluster

Fig. 10.--MDR for all clusters based on the best available data. See text for details. Error bars include the uncertainties in counting statistics and morphological classification. The previous results from low-z surveys ( D80; D97; PG84; SDSS) and from z $ 1 (S05) are shown for reference. The triangular markers along the y-axis show the low-density population fractions from the SDSS (Goto et al. 2003a).

we have computed an estimate of r200, the radius containing a mean overdensity of 200 relative to a critical universe, based on equation (8) in Carlberg et al. (1997 ). The derived r200 values are listed in Table 2. For RDCS J0910+5422 and R X J0848+ 4452, we assume ј 750 km sю1. We still need to define a cluster center for each system, and for that we use the centroid of the X-ray surface brightness distribution. X-ray imaging in which the hot intracluster medium ( ICM ) is detected with adequate S/ N levels is available for all clusters except CL 1604+ 4321. For CL 1604+4321, we use the centroid of the distribution of spectroscopically confirmed members. In the case of R X J0152ю1357, the X-ray distribution shows two wellseparated peaks ( Della Ceca et al. 2000), and we thus subdivide the data for this cluster into two separate samples, a northeast and southwest component, and measure the radial distance of cluster galaxies in each subsample relative to the nearest X-ray peak. The low-z reference for the MRR is taken from Whitmore & Gilmore (1991), with their radii converted to r200 units using our cosmology and assuming a mean cluster redshift of z ј 0:04 and a mean cluster velocity dispersion of 750 km sю1. To aid in the comparison between the MDR and the MRR, we provide the approximate projected density-radius relationship log10 (ф /635) % ю1:63(r /r200 ), which is derived from our data. This approximate relation is not particularly accurate for radii less than 0.2r200, and the cluster-to-cluster variation about this relation is substantial ( factors of 2 4 variation in the projected density

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Fig. 11.--MRR for all clusters based on the best available data. See text for details. Error bars include the uncertainties in counting statistics and morphological classification. Cluster centers are determined from the centroid of the X-ray surface brightness distribution except for CL 1604+4321, where the centroid of the distribution of confirmed spectroscopic members is used instead. The solid line is the low-z MRR from Whitmore & Gilmore (1991), converted to r200 units assuming a mean cluster redshift of z ј 0:04 and a mean cluster velocity dispersion of 750 km sю1. The triangular markers along the y-axis show the low-density population fractions from the SDSS (Goto et al. 2003a).

Fig. 12.--Distribution of ellipticities for the bulge-dominated galaxies that are likely cluster members in two different redshift ranges. The lower redshift cluster data are also based on ACS imaging and come from observations of five strongly lensing clusters in the range 0:25 z 0:55. See x 6 for details. The z > 0:8 galaxies are from our photometric redshift sample for the clusters RX J0152ю1357, MS 1054ю0321, and RDCS J1252ю2927. The E+S0 ellipticity distributions are shown by the thick histogram. The elliptical galaxy ellipticity distributions are represented by the light gray shaded histograms. The top panel shows the cumulative distribution functions for the ellipticities of the E+S0 galaxies in each cluster sample.

at a given r200-scaled radius), which is not surprising given the asymmetric galaxy distributions in many of our z > 0:8clusters (e.g., Fig. 1). The key features of the MRR at z $ 1 are that (1) the bulk of the transition from an fSpЧIrr consistent with that in the field environment to its minimum value occurs within 0.6r200 (0.6r200 corresponds to physical radii of 550 kpc 1.1 Mpc for these clusters), (2) the z $ 1 fEЧS0 value, at a given radius, is systematically less than the low-z fEЧS0 for (r /r200 ) P 1:0, and (3) the fS0-radius relation shows the most significant difference from the current-epoch relationship. All of these characteristics are consistent with those inferred from the z $ 1 MDR. Given the significant asymmetry of the galaxy distributions in some of these clusters, however, it is likely that the MRR is being diluted and is, thus, not as clean an indicator of morphological population gradients as the MDR for this particular cluster sample. 5.1. Evolution of the Morpholog y-Density Relation An additional way to assess the presence of S0 galaxies in clusters is to characterize the E+S0 ellipticity distribution, as was done by D97. As shown earlier in Figure 5, the ellipticity distributions of lenticular and elliptical galaxies differ substantially. For the full ACS galaxy sample shown in Figure 5, the hypothesis that the E and S0 ellipticity distributions are drawn

from the same parent population is rejected at greater than the 99.999% confidence level. Thus, if the z $ 1 bulge-dominated cluster galaxy population were truly devoid of a significant population of S0 galaxies, the ellipticity distribution of the E+S0 galaxies would more closely resemble that of pure elliptical galaxies and would not include a significant component of objects with ellipticities beyond 0.5. Figure 12 shows the ellipticity distributions of the E+S0 cluster galaxy populations for three of our z > 0:8 cluster galaxies along with galaxies from five clusters with redshifts in the range 0:25 z 0:55. To make a fair comparison of these two cluster samples, we must select objects that lie in similarly dense environments. Therefore, the galaxies used in this comparison are all selected from environments where the local projected density is !100 galaxies Mpcю2. The z > 0:8 sample used here consists of the photo-z selected cluster members in R X J0152ю1357, MS 1054ю0321, and RDCS J1252ю2927. We limit the z > 0:8 cluster sample to the three clusters with good photo-z data to ensure that we are selecting probable cluster members. The z < 0:6 cluster data are from GTO ACS observations of five strongly lensing clusters in the range 0:25 z 0:55 (HST PID 9292). The five clusters are Zw 1455+2232 (z ј 0:258), MS 1008ю1224 (z ј 0:301), MS 1358+6245 (z ј 0:328), CL 0016+1654 (z ј 0:54), and MS J0454ю0300 (z ј 0:55). Visual classification of all galaxies with i775 22:5 in each z < 0:6 cluster ACS image was performed by M. P. The rest-frame wavelengths sampled by the i775 filter for 0:25 z 0:55 typically lie in the V band; thus, any ``morphological'' k-corrections between this sample and the z > 0:8 sample should be small. A total of 798 galaxies were classified in the five z < 0:6 clusters. As the low-z ACS images were all single pointings centered on the cluster core,

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the vast majority of the E and S0 galaxies identified are likely to be cluster members. For reference, the ACS WFC subtends 800 kpc at z ј 0:26 and 1.3 Mpc at z ј 0:55. A KolmogorovSmirnov ( K-S) test finds that the distribution of ellipticities of E+S0 galaxies in the z > 0:8 clusters is inconsistent with being drawn from a pure elliptical ellipticity distribution at the 97.0% confidence level. A Wilcoxon rank sum test, which is better suited to measuring differences in the mean values of two distributions than a K-S test, finds that the E+S0 and E galaxy distributions for the z > 0:8 clusters differ at the 3.1 level. We thus reject the hypothesis that there are no S0 galaxies in dense environments at z $ 1. The E+S0 and E galaxy ellipticity distributions for the 0:25 z 0:55 cluster sample are inconsistent with each other at the 99.998% confidence level. We can also apply a robust test (i.e., one that primarily relies on our ability to distinguish only between E+S0 and Sp+Irr) in an attempt to constrain the evolution of the S0 population by comparing the z > 0:8 E+S0 ellipticity distribution with that for the 0:25 z 0:55 cluster galaxy sample. The cumulative distribution functions for the E+S0 ellipticities in the two different cluster samples are shown in the top panel of Figure 12. The ellipticity distributions for the 0:25 z 0:55 and z > 0:8 cluster samples are, however, completely consistent with one another ( K-S test rejects inconsistency only at the $10% confidence level), suggesting that, at least in these particular samples, any evolution in the relative E and S0 population fractions does not manifest itself as a significant difference in the E+S0 ellipticity distribution. It is possible that with larger and more homogeneously selected cluster samples over a range of redshifts this test would provide a quite objective way to measure the evolution of the morphological population fraction in dense environments. The fEЧS0 as a function of look-back time and local density is shown in Figure 13. This figure is modeled after Figure 3 in S05. The S05 results are reproduced for reference in the bottom panel of Figure 13. The top panel of Figure 13 shows the analogous results for our ACS z > 0:8 and 0:25 z 0:55 cluster samples. The results in the top panel are based on the mean population fractions within logarithmic density bins 0.4 units wide centered at 10, 100, and 1000 h2 galaxies Mpcю2. Our 65 fEЧS0 values are in good agreement with the S05 values; any differences are comparable with the uncertainties. We corroborate the key observational result of the S05 study that the most significant differences between the MDR at low redshift and high redshift are confined to regions where the projected galaxy density is larger than $40 galaxies Mpcю2. While the agreement is reassuring given the significant overlap of the clusters used in the two programs and bolsters the concept of using visual morphological classification in comparative studies at high z, there is also significant room for reducing the existing uncertainties that will be achieved only when a much ($10 times) larger sample of z $ 1 cluster galaxy morphologies is available. Our derived population fractions as a function of projected density and radius are also provided in Tables 3 and 4 for easy reference. As noted above, our results suggest that the observed MDR evolution is primarily driven by evolution in the fractions of S0 and Sp+Irr galaxies. 5.2. A Correlation between f
EЧS0

Fig. 13.--Bottom: Evolution of the MDR reported by S05. Look-back times have been transformed to compensate for the small difference between the cosmology in S05 and that adopted in this paper, specifically our choice of a slightly larger Hubble constant (70 vs. 65). The dashed lines representing the change in fEЧS0 with time at the three different density regimes are reproduced in both panels for reference. Top: Our derived E+S0 fractions at projected densities corresponding to <10, 100, and 1000 h2 galaxies Mpcю2 (to match S05) 65 for our combined z $ 1 cluster sample and our 0:25 z 0:55 cluster sample. The latter sample is not suitable for measuring low-density population fractions.

1045 hю2 ergs sю1) is higher than that in low X-ray luminosity 70 (LX;bol 3 ; 1044 hю2 ergs sю1) clusters, even at the highest 70 projected densities. This is demonstrated in Figure 14. Here we show fEЧS0, fE, and fS0 as a function of the bolometric X-ray luminosity for the galaxies within r200 for each cluster. D80 found a modest increase in fS0, a corresponding decrease in fSpЧIrr , and no change in fE in his subsample of eight high X-ray emitting clusters relative to the full sample of 55 clusters. Least-squares, error-weighted fits to the trends in Figure 14 give fE
ЧS0

/L

0:33 ф 0:09 X;bol

;

fE / L f
S0

0:15 ф 0:09 X;bol

; :

/L

0:18 ф 0:09 X;bol

and LX ?

Our sample exhibits a potentially interesting trend between the early-type population fraction and the cluster bolometric X-ray luminosity. The bulge-dominated galaxy population fraction in clusters with high X-ray luminosity (LX;bol ! 1:5 ;

The linear correlation coefficients for the fits to the log (LX; bol ) fEЧS0 ,log (LX; bol ) fE ,and log (LX; bol ) fS0 data are 0.82 (97.6% CL), 0.84 (98.2% CL), and 0.75 (94.8% CL), respectively. The correlations are significant at the 2 3 level. A correlation between fEЧS0 and LX could, in principle, be produced as a consequence of environmental interactions subsequent to the formation of the cluster galaxies and /or as a result of the initial conditions present at the time of their formation. In a simplified example of the former scenario, the ram pressure, Pram , acting on a galaxy moving through the ICM is proportional to v 2 . If the ICM is in hydrostatic equilibrium, then the

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TABLE 3 Popu lati on Fractions as a F un ction o f Proje cted Density N (ф) 136 220 237 138 87 24 14 185 595 38 435 66 79 63 62 86 43 46 104 log10 ф (galaxies Mpcю2) 1.30 1.60 1.90 2.20 2.50 2.80 3.10 1.06 ф 0.2 2.06 ф 0.2 3.06 ф 0.2 2.06 ф 0.2 3.06 ф 0.2 !2.00 !2.00 !2.00 !2.00 !2.00 !2.00 !2.00

Vol. 623

Cluster or Sample z $ 1 composite ...............

f

EЧS0

f 0.32 0.22 0.31 0.39 0.47 0.53 0.71 0.24 0.31 0.59 0.34 0.50 0.49 0.56 0.33 0.25 0.37 0.62 0.33

E

f 0.14 0.13 0.13 0.14 0.15 0.23 0.29 0.13 0.12 0.20 0.12 0.17 0.16 0.17 0.17 0.15 0.19 0.18 0.14 0.13 0.13 0.22 0.23 0.24 0.12 0.16 0.06 0.20 0.14 0.29 0.30 0.31 0.25 0.20 0.14 0.13 0.23 0.02

S0

f 0.14 0.13 0.13 0.14 0.15 0.23 0.29 0.13 0.12 0.20 0.12 0.17 0.16 0.17 0.17 0.15 0.19 0.18 0.14

SpЧIrr

z $ 1 composite ...............

z < 0:6 composite ............ MS 1054ю0321 ............... RX J0152ю1357 .............. CL 1604+4304 ................. CL 1604+4321 ................. RDCS J0910+5422 .......... RDCS J1252ю2927 ......... RX J0849+4452 ...............

0.45 0.35 0.53 0.62 0.71 0.65 0.87 0.30 0.51 0.73 0.63 0.80 0.80 0.81 0.53 0.39 0.50 0.85 0.35

ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф

0.11 0.09 0.09 0.10 0.12 0.21 0.27 0.10 0.07 0.17 0.08 0.14 0.13 0.14 0.14 0.12 0.16 0.16 0.11

ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф

ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф

0.56 0.65 0.47 0.38 0.29 0.35 0.12 0.70 0.49 0.27 0.37 0.20 0.20 0.20 0.47 0.61 0.50 0.15 0.65

ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф

0.11 0.09 0.09 0.10 0.12 0.21 0.27 0.10 0.07 0.17 0.08 0.14 0.13 0.14 0.14 0.12 0.16 0.16 0.11

Notes.--Errors are the quadrature sum of counting statistics and classification uncertainty. See text for details.
1 bolometric X-ray luminosity, LX, is proportional to 2 T X/ 2 R3 (e.g., Ettori et al. 2004). The total mass of the system, Mtot, is 3 proportional to T X/ 2 and is also proportional to v 2 . The same family of scaling laws gives LX / T 2 , although observationally X a steeper relation is found where LX / T 2:8 (e.g., Ponman et al. X 1996; Mulchaey & Zabludoff 1998; Xue & Wu 2000). These relations can be manipulated to yield Pram / L1:0 ф 0:1 , where X the exponent value depends on the exponent in the LX-TX relation. The ram pressure is stronger within more luminous X-ray clusters. Therefore, if ram pressure stripping were the dominant mechanism responsible for the origin of S0 galaxies in clusters, fEЧS0 should exhibit a positive correlation with LX. However, many previous observations, including the relatively weak dependence of fS0 on projected density, strongly suggest that ram

pressure stripping alone cannot explain the morphological mix in clusters (e.g., D80; D97; Kodama & Smail 2001; Okamoto & Nagashima 2003). Alternatively, a positive correlation between fEЧS0 and LX could be produced as a consequence of simple dynamics: the most massive (and, hence, most X-ray luminous) clusters will collapse earlier, and any environmentally driven processes that produce bulge-dominated galaxies will therefore have been active for a longer period of time at any subsequent redshift. This simple timescale argument could result in a positive correlation between the fraction of early-type galaxies and observational proxies for cluster mass, regardless of whether or not the efficiencies of the transformation processes are correlated with the properties of the ICM. However, this would only be true if

TABLE 4 Population Fractions as a F un ction o f r Cluster or Sample z $ 1 composite ............... N(r/r200) 63 80 90 83 94 99 114 129 96 74 23 11 130 125 124 150 146 67 214 r/r200 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05 1.15 1.0 1.0 1.0 1.0 1.0 1.0 1.0 f
EЧS0

20 0

Radius f
E

f 0.17 0.16 0.15 0.16 0.15 0.15 0.15 0.14 0.15 0.16 0.24 0.32 0.14 0.14 0.14 0.14 0.14 0.16 0.13 0.23 0.15 0.21 0.21 0.17 0.06 0.12 0.15 0.24 0.10 0.00 0.19 0.32 0.26 0.17 0.12 0.06 0.21 0.01

S0

f 0.17 0.16 0.15 0.16 0.15 0.15 0.15 0.14 0.15 0.16 0.24 0.32 0.14 0.14 0.14 0.14 0.14 0.16 0.13

SpЧIrr

MS 1054ю0321 ............... RX J0152ю1357 .............. CL 1604+4304 ................. CL 1604+4321 ................. RDCS J0910+5422 .......... RDCS J1252ю2927 ......... RX J0848+4452 ...............

0.75 0.52 0.56 0.45 0.42 0.27 0.32 0.30 0.35 0.25 0.32 0.19 0.78 0.72 0.57 0.39 0.38 0.68 0.30

ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф

0.14 0.13 0.12 0.13 0.12 0.12 0.11 0.11 0.12 0.13 0.22 0.31 0.11 0.11 0.11 0.10 0.10 0.14 0.09

0.52 0.37 0.35 0.24 0.25 0.21 0.20 0.15 0.11 0.15 0.32 0.00 0.46 0.46 0.40 0.27 0.32 0.47 0.29

ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф

ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф

0.26 0.48 0.44 0.55 0.58 0.73 0.69 0.70 0.64 0.75 0.68 0.81 0.22 0.27 0.42 0.60 0.61 0.32 0.70

ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф ф

0.14 0.13 0.12 0.13 0.12 0.12 0.11 0.11 0.12 0.13 0.22 0.31 0.11 0.11 0.11 0.10 0.10 0.14 0.09

Notes.--Errors are the quadrature sum of counting statistics and classification uncertainty. See text for details.

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Fig. 14.--Dependence of the bulge-dominated galaxy population fractions, fEЧS0 , fE, and fS0, on the bolometric cluster X-ray luminosity within a radius corresponding to r200. Names of the individual clusters are shown in the top panel. The solid line is the best-fit relation when the data are weighted by the inverse square of their uncertainties. The dashed line is the best fit when each data point is given equal weight. The dotted line is the best error-weighted fit with CL 1604+4321 excluded. The data for RX J0152ю1357 in this figure include both the northeast and southwest components of the cluster. Error bars include the uncertainties in counting statistics and morphological classification.

Fig. 15.--Bulge-dominated galaxy population fraction, fEЧS0 , within a radius corresponding to r200 as a function of the X-ray gas temperature and cluster velocity dispersion. Names of the individual clusters are shown. Error bars include the uncertainties in counting statistics and morphological classification.

the timescales required to establish a significant population of early-type galaxies were long compared to the collapse time. If the timescale for establishing the early-type population were comparable to the collapse time (i.e., if deeper potential wells are ``born'' with a higher early-type population fraction), then the fEЧS0 -LX relation may be telling us more about cluster and galaxy formation processes than about the cluster evolution process. As the results in Figure 14 are based on only seven clusters and as the significance of the correlations are only significant at the P3 level, we refrain from overinterpretation. Indeed, the correlations between fEЧS0 and TX and between fEЧS0 and cluster velocity dispersion, ,are not significant(seeFig.15).Inthe literature, the mass dependence of cluster galaxy evolution has been a subject of debate. For example, Fairley et al. (2002) studied eight X-ray selected clusters and did not find any dependence of the blue galaxy fraction on LX, a trend that might be expected if fEЧS0 correlated with LX. De Propris et al. (2004), using a larger sample of 60 clusters from the 2dF Galaxy Redshift Survey, find that the blue galaxy fraction does not depend on the velocity dispersion of the cluster galaxies. However, there is tentative evidence that cluster-integrated star formation rates (e.g., Finn et al. 2004) correlate with TX and LX (Homeier et al. 2005), which is presumably a dependence on cluster mass. Furthermore, Zabludoff & Mulchaey (1998) found that groups of galaxies exhibit a strong correlation between the bulgedominated galaxy fraction, fEЧS0 , and the group velocity dispersion. While the specific relation they found cannot be extended to very massive clusters (their predicted fEЧS0 reaches a value of unity at a velocity dispersion of $700 km sю1), it does suggest that groups of galaxies have a positive correlation between fEЧS0 and LX through the observational relation LX / 4:3

( Mulchaey & Zabludoff 1998). Margoniner et al. (2001) and Goto et al. (2003b) find that blue fractions of cluster galaxies are lower for richer clusters, a result that is consistent with a positive fEЧS0 -LX relationship. The significance of the fEЧS0 -LX relation clearly needs to be studied using a larger sample so that subdivision by mass (or a suitable observational proxy for mass) can be conducted for a far greater number of clusters. The HST ACS snapshot program of 73 homogeneously selected X-ray clusters ( ID 10152; PI M. Donahue) should provide the sample needed to assess this relation in the range 0:3 < z < 0:7. If a significant fEЧS0 -LX relation is ultimately found, one implication is that the MDR and its evolution may be dependent on the total cluster mass. Certainly on galaxy-mass scales, there is evidence that the star formation process occurs more rapidly in systems with higher stellar mass (e.g. , Heavens et al. 2004). For the present sample, correlations between the fraction of early-type galaxies and the X-ray properties of the clusters provide, at best, a strong inspiration to study the trends with samples explicitly geared to investigate this relationship. 6. DISCUSSION As originally discussed by Tully & Shaya (1984), the measurement of the evolution in the MDR is a significant step in understanding the relative roles of environment and initial conditions in establishing morphological population gradients. The less rapid growth in the bulge-dominated galaxy population with increasing density (or decreasing radius) that is seen at z $ 1 implies that environment must play an important role in the establishment of the current-epoch MDR. S05 explore a range of morphological transformation scenarios based on the expression f јf юf Nzј0:5 а NE Ч ; Nzј1 Nzј1 П 3ч

S0; zј1

EЧS0; zј1

E; zј0:5

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where fS0; z ј1 is the S0 population fraction in clusters at z ј 1, f EЧS0; z ј1 is the E+S0 fraction in clusters at z ј 1, f E; zј0:5 is the elliptical fraction in clusters at z ј 0:5, Nzј0:5 /Nzј1 is the ratio of the number of galaxies in clusters at z ј 0:5to that at z ј 1, and а NE is the change in the number of cluster elliptical galaxies between z ј 1 and 0.5. By combining varying amounts of infall (including infall of early-type galaxies), mergers, and cannibalism, S05 find that for reasonable levels of each process the fS0 at z ј 1 is typically less than 0.1. The exception is for the case in which there is no infall and 10% of the spiral galaxies merge in pairwise manner to form elliptical galaxies. In this case, the model predicts fS0 ј 0:18 at z ј 1. The degree to which our observations conflict with the predictions for very low S0 population fractions in z ј 1 clusters is, of course, directly tied to the uncertainty in our fS0 measurements. Our mean S0 population fraction is inconsistent with being zero at about the 90% confidence level, which is not strongly in conflict with the S05 predictions for fS0; zј1. However, given that the ellipticity distribution of the E+S0 galaxies in the z $ 1 clusters is inconsistent with being drawn from a population dominated largely by pure elliptical morphologies and given that we do get a mean fS0 of 0:20 ф 0:12 for ф ! 30 galaxies Mpcю2, we investigate minor variations to the S05 scenario that can increase in the predicted S0 population fraction at z $ 1. An obvious choice is to explore reasonable modifications of the value of fE; zј0:5 . S05 adopted fE; z ј0:5 ј 0:6. However, we find that for ф ! 100 galaxies Mpcю2 a value in the range 0.4 0.5 appears to be closer to what the data suggest. Decreasing fE; zј0:5 to 0.5 increases the range of the S05 predictions to 0:09 fS0; zј1 0:28 for the models considered. This would make their predictions and our mean fS0 values consistent within 1 . However, doing so does change the conclusions of S05 a bit, namely, that $50% of the lenticular galaxies in clusters could already be in place at z ј 1 and that the remaining half form largely between z $ 0:5 and the current epoch. Different morphological transformation mechanisms operate in different environments; thus, by identifying the radius or density where the morphology of cluster galaxies starts to change, we can hope to identify the underlying physical mechanisms. The breaks in the MDR , first characterized by PG84 and more recently by Goto et al. (2003a), suggest that different processes are probably responsible for the origin of elliptical and S0 galaxies. For example, ram pressure stripping (Gunn & Gott 1972) is only efficient within the cluster core (typically P250 kpc) where the ICM density is high enough to allow the dynamic pressure to overpower the gravitational restoring force of interstellar gas in a galaxy's disk. Figure 11 indicates that the fraction of elliptical galaxies starts to increase inward of 0.6r200, or in terms of local galaxy density, at around 70 galaxies Mpcю2 ( Fig. 10). This environment matches that where the population fraction of Sp+Irr galaxies starts to decline. The scale of 0.6r200 for the onset of the transition between the low-density field population and that in high-density regions is in agreement with previous low-redshift observations (e.g., Kodama et al. 2001; Treu et al. 2003; Goto et al. 2003b). At distances beyond 250 kpc or so, ram pressure becomes much less effective as a morphological transformation process; thus, other environmental processes must play a significant role in the establishment of the MDR and MRR (e.g., Treu et al. 2003). Galaxy-galaxy merging, for example, is most effective when relative velocities of galaxies are comparable to the rotation of the galaxy itself ($200 km sю1) and is thus likely to be most effective in regions far from the cluster core. Galaxies beyond 5 Mpc from the cluster center will, at z $ 1,

not yet have had sufficient time to traverse the cluster core and should, therefore, not experience tidal stripping or tidal triggering of the star formation due to the cluster gravitational potential. The lack of any significant redshift dependence in the fEdensity relation, coupled with the significant changes with redshift seen in the fS0-density relation, suggests that the origin of the MDR and MRR in high-density regions is most likely determined by two distinct processes: (1) the formation of elliptical galaxies at the cluster core, which occurred at redshifts significantly greater than unity; and (2) the formation of S0 galaxies, which appears, for at least half of the lenticular galaxies, to be a process that is still underway even at redshifts as low as z $ 0:5. Evidence for different formation timescales for elliptical and S0 galaxies comes from other types of studies as well. For example, the analysis of the CMR in RDCS J1252ю 2927 by Blakeslee et al. (2003b) finds that the observed scatter in the CMR for S0 galaxies in that system is consistent with relatively recent or even ongoing star formation activity, whereas the CMR for elliptical galaxies in this z ј 1:24 cluster is compatible with no significant star formation activity for more than 1 Gyr. In addition, Poggianti et al. (1999) and Goto et al. (2004) derive shorter evolutionary timescales for blue to red spiral transformation than for red spiral to red elliptical transformation, consistent with the hypothesis that transformation of a galaxy's spectral energy distribution typically occurs more rapidly than morphological transformation. A fundamental question that remains is whether or not the MDR and MRR depend on luminosity. It is well established that intrinsically luminous, red galaxies are almost always elliptical and, hence, at some level limiting the analyses of the MDR to intrinsically luminous galaxies may produce a different relationship between morphology and projected density than found in a sample containing a broader range of luminosities. Tanaka et al. (2004) demonstrate that there is indeed a change in the MDR at z < 0:07 as a function of luminosity based on an analysis of $20,000 SDSS galaxies. They find that galaxies fainter than Mrц Ч 1 do appear to have a different MDR at low densities than brighter galaxies. We have divided our spectroscopic samples for MS 1054ю0321 and R X J0152ю1357 into four apparent magnitude ranges i775 22, i775 22:5, i775 23, and i775 ц ц 23:5 corresponding to M ц M775 ю 0:3, M ц M775 Ч 0:2, ц ц ц ц M775 Ч 0:7, and M M775 Ч 1:2. We find no signifiM cant difference between the MDR derived for these four samples. If the luminosity dependence of the MDR does not exhibit strong evolution, then our current sample does not go deep enough at z ј 0:83 to accurately measure the dependence. Our failure to detect any luminosity dependence in the MDR in our z ј 0:83 spectroscopic sample is thus not inconsistent with the work done at low redshifts. Furthermore, our survey is not well suited to studying densities below 30 galaxies Mpcю2, well above the density where Tanaka et al. (2004) find the strongest luminosity-dependent effects. All we can conclude for now is ц that for ф > 30 galaxies Mpcю2 and for M ц P M775 Ч 1:2 the z ј 0:83 MDR is not sensitive to luminosity. The caveat to this conclusion is that our i775 data at z ј 0:83 sample the rest-frame B band. It may be that galaxies selected according to a redder rest-frame luminosity will show a different trend. The underlying goal of studying the MDR as a function of luminosity is, of course, to assess the dependence of the MDR on galaxy mass. We are assembling near-IR photometry for our cluster galaxies to provide more accurate stellar mass estimates, and we will explore trends between morphology, density, r200, and galaxy mass in a future paper.

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We have performed deep, multiband observations with the ACS WFC of seven clusters with 0:83 z 1:27 to study the morphological composition of the galaxy population over three decades of local density and out to radii of up to 2 Mpc from the peak of the X-ray emission from the ICM. The key results are as follows: 1. The high sensitivity and angular sampling of the ACS WFC enable reliable visual distinctions to be made between the major morphological galaxy classes ( E, S0, Sp+Irr) down to $0:25L /Lц in the range 0:8 < z < 1:3. 2. We confirm the results of S05 that an MDR exists at z $ 1. We also explicitly confirm the less rapid growth in fEЧS0 with increasing density and that the change in the slope of the MDR is due primarily to changes in the high-density population fraction. A flattening of the fEЧS0 -density relation with increasing redshift can be a consequence of environmentally driven transformation of galaxies from late to early types. Our new results provide direct measurements of the lenticular population fraction at z $ 1, and we conclude that the observed differences in the MDR at z $ 1 are due primarily to a deficit of S0 galaxies and an excess of Sp+Irr galaxies relative to the local galaxy population. The fE-density relation does not appear to evolve over the range 0 < z < 1:3. A deeper understanding of the implications of these results for models of galaxy and cluster formation will require further exploration of the dependence of morphological population fractions on galaxy mass and an assessment of the frequency of cluster galaxy merger activity. 3. The MDR at z ј 0:83 is not sensitive to the rest-frame B-band luminosity for galaxies with luminosities brighter than M ц Ч 1:2 and in regions with ф > 30 galaxies Mpcю2. Work done at low redshift suggests, however, that luminosity effects may be more pronounced at fainter luminosities and in regions of lower density. Our present survey is not well suited to studying these regimes. 4. We directly measure the lenticular population fraction and find fS0 ј 0:20 ф 0:12 when we average over densities with ф ! 30 galaxies Mpcю2. The error in fS0 includes contributions from both counting statistics (ф0.035) and errors in our ability to visually classify lenticular galaxies (ф0.11). Our z $ 1 fS0 value is about a factor of 2 less than the fS0 seen in similarly dense environments in the local universe but is comparable to what is seen at 0:4 P z P 0:5. Our 20% population fraction of S0 galaxies is higher than almost all of the scenarios proposed by S05 to explain the shallower fEЧS0 -density relation; they predict fS0 < 0:1. However, a small reduction in the elliptical population fraction at z ј 0:5 adopted by S05 from fE ј 0:6 to 0.5, a value that appears to be in better agreement with the observa-

tions, is sufficient to increase their predicted z ј 1 S0 population fractions to 0:2 ф 0:1, overlapping our measurement. The distribution of ellipticities in z > 0:8 bulge-dominated ( E+S0) cluster galaxies is inconsistent with an ellipticity distribution that would arise from a sample consisting solely of elliptical galaxies. In other words, our results suggest that rich clusters at z $ 1 most likely have a significant population of lenticular galaxies and, therefore, a significant percentage of lenticular galaxies could have formed at redshifts z > 1:3. 5. We measure the MRR and find that its evolution is consistent with that seen in the MDR: a) The bulk of the transition from an fSpЧIrr consistent with that in the field environment to its minimum value occurs within a radius of 0.6r200 (which corresponds, on average, to densities >70 galaxies Mpcю2 and to physical scales less than $750 kpc). b) The z $ 1 fEЧS0 value, at a given radius, is systematically less than the low-z fEЧS0 value for radii less than $r200. c) The fS0-radius relation shows the most significant difference from the current-epoch relationship. However, elongation of and clumpiness in the galaxy distributions for many of our z > 0:8 clusters makes interpretation of the azimuthally averaged MRR more difficult (and perhaps less meaningful) than trends between morphology and local density. 6. We find that the bulge-dominated galaxy population fraction, fEЧS0 , is mildly correlated with the bolometric X-ray luminosity of the cluster. Clusters with high X-ray luminosities have higher fEЧS0 values within r200 than clusters with lower X-ray luminosities. In the present sample, the trend is significant at the P3 level. A correlation between fEЧS0 and bolometric X-ray luminosity can arise as a consequence of either environmentally driven transformation processes or initial conditions. However, we do not find significant correlations between fEЧS0 and the X-ray temperature or cluster velocity dispersion. A definitive study of the relation between galaxy population fraction and cluster X-ray properties will require the analysis of large homogeneously selected cluster samples.

ACS was developed under NASA contract NAS5-32865, and this research has been supported by NASA grant NAG57697. The STScI is operated by AURA, Inc., under NASA contract NAS5-26555. We are grateful to Ken Anderson, Jon McCann, Sharon Busching, Alex Framarini, Sharon Barkhouser, and Terry Allen for their invaluable contributions to the ACS project at JHU. We wish to thank the referee, Alan Dressler, for his insightful comments.

APPENDIX A COMPARING PROJECTED DENSITY ESTIMATION TECHNIQUES We demonstrate here that the nearest neighbor ( NN ) and FoF algorithms for estimating local projected density yield consistent results. We also show that it is possible to construct a composite MDR or MRR using a combination of galaxy samples selected using spectroscopic redshifts, photometric redshifts, and samples with only statistically subtracted background corrections providing that each of the samples is confined to specific density ranges. The FoF algorithm provides an alternative to the NN algorithm as a means to measure the morphological composition as a function of density. The FoF algorithm, first developed by Huchra & Geller (1982), has been used widely thereafter for automated detection of overdensities in galaxy catalogs. This approach has the advantage that it is not tied to a specific choice of N nearest neighbors although it is not the method typically used by other workers in the analysis of the MDR. The FoF algorithm locates groups of galaxies by identifying all the neighboring systems that lie within a given ``percolation'' length of a given galaxy. Each neighbor is then searched for galaxies within the same percolation length. This linking process is continued until no additional members can be identified. The

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Fig. 16.--Composite MDR for the clusters MS 1054ю0321, RX J0152ю1357, and RDCS J1252ю2927. These results are based on the photo-z selected samples that include galaxies with zph values in the range jzcl ю zph j /(1 Ч zcl ) 2ph . Results from the Nth nearest neighbor ( NN ) and friends-of-friends ( FoF ) density estimators are both shown here. The density values have been offset by a small amount from one another for clarity. The total number of galaxies in each density bin is shown in the top panel of the plot. The low-density population fractions from the SDSS (Goto et al. 2003a) are denoted by the triangles along the y-axis.

percolation length and the local projected density are related as lperc / 1/ ф1=2 . For our comparison, we use percolation lengths that correspond to overdensities in the range 15 galaxies Mpcю2 < ф < 1500 galaxies Mpcю2 . At each overdensity, the morphological populations within all identified groups are tallied, weighted by the inverse of the selection function. The difference between the cumulative E, S0, and Sp+Irr population at two overdensities ф and ф ю ф then defines the morphological populations at projected density ф. As with the NN algorithm, we correct the FoF densities to correspond to our fiducial luminosity limit using equation (2). Figure 16 shows a comparison between the NN and FoF density estimators for the clusters for which we have reliable photometric redshifts ( MS 1054ю0321, R X J0152ю1357, and RDCS J1252ю2927). The error bars in all these figures include the uncertainties from counting statistics and from the intrinsic classification uncertainties quantified in x 3(e.g., ф0.06 in fEЧS0 and fSpЧIrr ; ф0.11 in fS0 and fE ). The two density estimators produce consistent results over the full range of densities analyzed. A1. USING COMPOSITE CLUSTER SAMPLES Because not all clusters in our sample have sufficient data to compute the local density based on either spectroscopic or photometric redshift values, it is also important to establish that our results are not very sensitive to the details used to derive the MDR (e.g., whether the sample is selected based on photometric redshift value, spectroscopic redshift value, or a flux-limited sample with statistical background subtraction). If we can demonstrate this, then we can construct a composite MDR by combining for each individual cluster the sample that yields the most reliable available estimate ( e.g., the samples with the least contamination from foreground / background objects). The clusters R X J0152ю1357 and MS 1054ю0321 allow us to perform this test as they have sufficient information to independently generate the MDR from spectroscopic data, from photometric redshift data, and from flux-limited samples with a statistically subtracted background correction applied. The results are shown in Figure 17. For densities greater than 80 galaxies Mpcю2 there are no significant systematic differences in any of the derived population fractions as a function of density. Below 80 galaxies Mpcю2, the statistically subtracted background-corrected density and population fraction estimates become less reliable as fluctuations in the background galaxy surface density become comparable with the projected density (see discussion in x 4). The spectroscopic samples exhibit a lower elliptical galaxy fraction at densities below about 50 galaxies Mpcю2, but the differences lie within the 1 uncertainties. The spectroscopic data do not provide good sampling of the very highest densities (ф > 1000 galaxies Mpcю2) because of the number of slit masks used. However, in this regime, the photo-z and /or statistically subtracted background results are very reliable. We conclude that the MDR and MRR derived from a composite sample will be reliable if spectroscopically selected samples are limited to regions with ф 1000 galaxies Mpcю2 and samples with statistically subtracted background corrections are limited to regions with ф > 80 galaxies Mpcю2.

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Fig. 17.--Dependence of MDR on sample selection, demonstrated for MS 1054ю0321 and RX J0152ю1357. We show the population fractions as a function of projected density based on the samples of confirmed spectroscopic members (Spec), the samples of photo-z selected members ( BPZ ), and the full flux-limited samples with statistically subtracted background corrections applied (SSub). The latter results are only shown when ф > 40 galaxies Mpcю2. Error bars include the uncertainties in counting statistics and morphological classification.

APPENDIX B COMPUTING MORPHOLOGICAL POPULATION FRACTIONS Our morphological population fractions are corrected for both contamination and incompleteness in a manner that depends on the sample being analyzed. For samples using only confirmed spectroscopic redshifts, the only correction applied is the weighting by the inverse of the redshift selection function (see eq. [1]). The redshift selection function is computed empirically by measuring the ratio of the number of redshifts acquired to the total number of galaxies in magnitude bins 0.5 mag wide. The redshift selection function is dependent on the galaxy magnitude and to a lesser degree on the galaxy color. The latter dependence translates to a dependence on morphology for those galaxies in the cluster. By measuring the redshift completeness as a function of color and magnitude, we can make reasonable corrections for the observational selection effects. The clusters for which we have a sufficient number of redshifts to compute the MDR solely from a spectroscopic sample are MS 1054ю0321 (with 143 confirmed members, all within the boundaries of our ACS mosaic) and R X J0152ю1357 (with 102 confirmed members, 93 of which lie within the boundaries of our ACS mosaic). The redshift selection functions for these two clusters are shown as a function of i775 magnitude and morphological type in Figure 18. For photometric redshift selected samples ( MS 1054ю0321, R X J0152ю1357, and RDCS J1252ю2927), we correct the population fractions as follows: N
corr T uncor ј NT ЧN missed T cont ю NT am ;

ПB1ч

un mi where NT cor is the observed number of galaxies of morphological type T, NT ssed is an estimate of the number of cluster members contam is an estimate of the number of noncluster members of type T that have been excluded by our photo-z selection criteria, and NT of type T that have been included in the observed count. The number of missed members is computed as follows:

N

missed T

јN

total ftot; miss fmiss; T

;

ПB2ч

where Ntotal is the total number of galaxies counted at a given density, ftot; miss is the fraction of cluster members excluded by our photoz selection limits, and fmiss; T is the fraction of those excluded galaxies that have morphological type T. The value of ftot; miss is estimated by counting the number of spectroscopically confirmed members that have photo-z's outside our photo-z selection limits. For MS 1054ю0321 and R X J0152ю1357, ftot; miss ј 0:38 and 0.20, respectively. For RDCS J1252ю2927, ftot; miss ј 0:04. The morphological dependence of the number of true cluster galaxies missed by our photo-z selection is weak for MS 1054ю0321 and RDCS J1252ю2927 but is more significant for R X J0152ю1357 (see Fig. 18). For MS 1054ю0321 and RDCS J1252ю2927, we set fmiss; T equal to the initial uncorrected population fraction for galaxies of type T at the given density. For R X J0152ю1357 we assign fmiss; T using a morphological distribution that is slightly more heavily weighted to late-type galaxies at a given density to compensate for the

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Fig. 18.--Redshift selection functions for E+S0 and Sp+Irr galaxies vs. i775 magnitude for MS 1054ю0321 and RX J0152ю1357. The larger difference between E+S0 and Sp+Irr selection efficiency in RX J0152ю1357 is caused by the color selection criterion used in target selection for that cluster.

spectroscopic selection bias in this cluster. Fortunately, the results are not strongly dependent on the precise prescriptions for setting the fmiss; T values. The number of noncluster members contaminating our photo-z selected counts is computed as follows:
con NT t am

јN

total ftot; contam fcontam; T

;

ПB3ч

where ftot; contam is the fraction of noncluster members included by our photo-z selection limits and fcontam; T is the fraction of these that have morphological type T. The value of ftot; contam is estimated by counting the number of spectroscopically confirmed noncluster members that have photo-z's lying within our photo-z selection limits. For MS 1054ю0321 and R X J0152ю1357, ftot; contam ј 0:09 and 0.12, respectively. For RDCS J1252ю2927, ftot; contam ј 0:33. These noncluster galaxies have a morphological distribution that is representative of the field galaxy population, and we thus set fcontam ; E ј 0:10, fcontam; S0 ј 0:25, and fcontam; SpЧIrr ј 0:65. Note that because we only have $35 spectroscopic redshifts for RDCS J1252ю2927, the incompleteness and contamination estimates have larger uncertainties than those in MS 1054ю0321 or R X J0152ю1357. For population fractions derived from magnitude-limited samples using only statistically subtracted background counts (e.g., as in RDCS J0910+5422), the morphological distribution of the background is assumed to be representative of the field galaxy population, and we thus divide the expected background counts into E, S0, and Sp+Irr components assuming the same fractions given above: fE ј 0:10, fS0 ј 0:25, and fSpЧIrr ј 0:65.
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