WEAK GRAVITATIONAL LENSING BY A SAMPLE OF X-RAY LUMINOUS CLUSTERS OF GALAXIES. I. THE DATA SET 1 Håkon Dahle 2, 3 and Nick Kaiser

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1 The Astrophysical Journal Supplement Series, 139: , 2002 April # The American Astronomical Society. All rights reserved. Printed in U.S.A. WEAK GRAVITATIONAL LENSING BY A SAMPLE OF X-RAY LUMINOUS CLUSTERS OF GALAXIES. I. THE DATA SET 1 Håkon Dahle 2, 3 and Nick Kaiser Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822; dahle@nordita.dk Ragnvald J. Irgens and Per B. Lilje Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029, Blindern, N-0315 Oslo, Norway and Steve J. Maddox 4 School of Physics and Astronomy, University of Nottingham, University Park, Nottingham, NG7 2RD, UK Received 2001 April 17; accepted 2001 November 14 ABSTRACT We present weak gravitational lensing mass measurements of a sample of 38 highly X-ray luminous clusters of galaxies with well-defined selection criteria. The clusters were observed with either monolithic CCDs, the UH8K mosaic CCD camera, or both. The weak shear caused by gravitational lensing was measured using recently developed techniques to correct for the effects of realistic point-spread functions and to optimally weight the contribution of each galaxy to the final shear estimate. The results are presented in the form of maps of the reconstructed dimensionless surface density and plots of the radial cluster mass profiles. The maps are compared to mass-traces-light predictions for based on two-color, V-andI-band galaxy photometry in the observed fields. About 30% of the clusters in our sample show evidence of significant dynamical activity related to mergers of subclumps. More than half of the clusters show signs of strong lensing. Our data set more than doubles the total number of galaxy clusters with a detected weak lensing signal. The data for all the clusters have been reduced and analyzed in a consistent way, and this makes our data set uniquely suitable for statistical studies of cluster properties, which will be the subject of future papers in this series. Subject headings: cosmology: observations dark matter galaxies: clusters: general gravitational lensing 1. INTRODUCTION During the last decade the mass distributions in a number of rich galaxy clusters have been mapped using the weak gravitational lensing effect which modifies the apparent shapes of background galaxies along the line of sight. The first detections of this effect were reported by Tyson, Valdes, & Wenk (1990), Bonnet, Mellier, & Fort (1994), Dahle, Maddox, & Lilje (1994), Fahlman et al. (1994), and Smail et al. (1995a), and recent reviews of the subject have been written by Mellier (1999) and Bartelmann & Schneider (2001). So far, each of the published weak lensing studies of clusters has typically targeted one or a few clusters with particularly interesting properties, such as high redshift (e.g., Luppino & Kaiser 1997; Clowe et al. 2000; Clowe, Trentham, & Tonry 2001), unusually high X-ray luminosity (e.g., Squires et al. 1997; Fischer & Tyson 1997), unusually high velocity dispersion (e.g., Tyson & Fischer 1995), or large numbers of strongly gravitationally lensed arcs (e.g., Squires et al. 1996a). By fall 2000, the masses of about two dozen clusters with redshifts ranging from z ¼ 0:055 (Joffre et al. 2000) to 1.0 (Clowe et al. 2001) have been measured 1 Based on observations made with the Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias. 2 Present address: NORDITA, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark. 3 Visiting Observer, University of Hawaii 2.24 m Telescope at Mauna Kea Observatory, Institute for Astronomy, University of Hawaii. 4 Also at Institute of Astronomy, University of Cambridge. 313 out to radii greater than 200 h 1 kpc (see Mellier 1999 for a recent compilation of cluster mass measurements). This collection of clusters with available weak lensing mass measurements does not in any way constitute a well-defined sample. The literature presents us with a heterogeneous set of weak lensing measurements. The available studies have used a variety of techniques for measuring galaxy shapes, using different software packages. Much of the progress in developing the methods to realistically account for the effects of the point-spread function (PSF) on the measured galaxy shapes is very recent, and many of the published results are consequently based on older methods that rely on unrealistic assumptions about the properties of the PSF. Furthermore, the various groups have made different assumptions about the redshift distribution n(z) of faint galaxies (which will systematically affect the derived cluster masses), and the derived values for the mass-to-light ratio M/L are often quoted in different passbands by different groups. The signal-to-noise ratio (S/N) for measurements of weak gravitational shear is determined by the density of background sources; the intrinsic distribution of their apparent shapes, sizes, and magnitudes; and the strength of the shear signal itself. The error induced by photon shot noise will depend on the size and magnitude of the object, and only recently has an algorithm become available to optimally weight the lensed galaxies when making the shear estimate (Kaiser 2000). A large sample of clusters which have been analyzed in a consistent way using recently developed methodology will represent a valuable addition to previous weak lensing

2 314 DAHLE ET AL. Vol. 139 measurements, and the purpose of this paper is to present such a data set. In this paper we describe the techniques used for data reduction and analysis, and we present the most immediate results from our weak lensing analysis in the form of cluster masses and maps of the projected mass and luminosity density in each cluster. We also discuss briefly the clusters as individual objects. Previously, Smail et al. (1995a) have examined weak lensing in three clusters at different redshifts in a uniform way to constrain n(z) of faint galaxies. Later, Smail et al. (1997) detected weak lensing in Hubble Space Telescope (HST) WFPC2 images of 11 clusters at 0:17 < z < 0:56, for which they derived cluster masses and correlated these with the X-ray luminosities and optical properties of the clusters. Unfortunately, the small field of view of WFPC2 limits such weak lensing mass measurements to small physical radii, particularly for clusters at the low-redshift end of their sample. Hoekstra et al. (2001) argued that this may have caused Smail et al. (1995a) to underestimate the lensing masses if the clusters have significant substructure at small radii or if the cluster mass profile at small radii is shallower than the singular isothermal sphere model assumed by Smail et al. (1997). Hoekstra et al. (2001) analyzed weak lensing in four clusters in the redshift range 0:22 < z < 0:83. Three clusters were studied by making a mosaic of multiple WFPC2 pointings to cover a wider area around the cluster center. Hoekstra et al. (2001) found that virial mass estimates for these three clusters agree well with weak lensing estimates when shear measurements over a wide range of radii are being considered, but using only shear data from the central WFPC2 pointing leads to significantly lower cluster mass estimates. A comparison of X-ray mass estimates with strong and weak gravitational lensing estimates (drawn from the literature) by Allen (1998) gave the conclusion that X-ray observations and gravitational lensing yield consistent results for clusters that have massive cooling flows. A significant discrepancy between X-ray and lensing mass estimates is often seen at small radii in non cooling flow clusters, indicating that these are dynamically young systems where the central regions are not yet in a state of hydrostatic equilibrium. Clowe et al. (2000) presented a weak lensing study of six clusters at z > 0:5, which included the most X-ray luminous clusters at high redshifts known at the time their study was undertaken. Such weak lensing measurements of high-redshift cluster samples can, in combination with the data presented in this paper, be used to probe cluster evolution, although it is hard to draw firm conclusions at the current time given the limited number of known massive high-redshift clusters. The outline of this paper is as follows. In x 2 we describe how our cluster targets were selected and how our data set was obtained. We also describe the reduction process with particular emphasis on those steps which are crucial for accurate measurements of weak gravitational shear. In x 3 we detail the galaxy photometry from which a prediction of the foreground mass distribution was made. The results of the weak lensing analysis are presented in x 4, and in x 5we describe the clusters individually. The majority of the clusters studied in this work are targets for recent or planned X-ray observations with Chandra and/or XMM-Newton, which by itself makes them interesting targets for weak lensing studies. Many are also included in the samples used in ongoing efforts to measure H 0 using the Sunyaev-Zeldovich (SZ) effect (e.g., Jones et al. 2001). Since these measurements rely on the assumption of hydrostatic equilibrium of the intracluster gas (or at least sphericity, in the case of the SZ H 0 measurements), they will have large errors when considering systems which have not yet achieved equilibrium or sphericity. Information about the cluster mass distribution from weak lensing may be very useful for selecting relaxed systems that will yield the most precise value for H 0. Unless otherwise indicated, we assume an Einstein de Sitter cosmology with H 0 ¼ 100 h km s 1 Mpc 1 throughout this paper. All celestial coordinates are given in J In future papers in this series, we will focus on specific applications of this data set. One paper will be devoted to virial mass estimates of some of the clusters in our data set and comparisons with weak lensing results presented in this paper (R. J. Irgens et al. 2002, in preparation). A separate paper will present a measurement of weak gravitational lensing caused by large-scale structures along the line of sight to the clusters (often referred to as cosmic shear ). Another paper will report the detection of additional mass concentrations along the line of sight to some of the clusters. One paper will describe measurements of M/L and the relative distribution of mass and galaxy light in the cluster fields and discuss implications for m. In a different paper we will estimate the average mass profile of the clusters and compare the result to predictions from cold dark matter (CDM) N-body simulations. One of the main goals of this survey is to measure the cluster mass function at z 0:25 using our weak lensing mass measurements and use the result to constrain current models for structure formation. This will be the subject of yet another paper. Finally, a future paper will compare the weak lensing and X-ray properties of the clusters in our sample. 2. OBSERVATIONS 2.1. Sample Selection A major part of the motivation for these observations is to constrain the high-mass end of the cluster mass function (H. Dahle et al. 2002a, in preparation). Clusters with virial masses above M are extremely rare, and here we target a well-defined, representative sample of massive clusters selected from surveys covering a volume of at least 10 8 (h 1 Mpc) 3. Given the current observational capabilities, X-ray luminosity is probably the most suitable parameter for selecting very massive clusters (see, e.g., Reiprich & Böhringer 1999). We have targeted clusters in the redshift range 0:15 < z < 0:35, selected from three samples of X-ray luminous clusters based on ROSAT data (Briel & Henry 1993; Ebeling et al. 1996, 1998) as detailed below: 1. The X-Ray Brightest Abell Cluster (XBAC) sample of Ebeling et al. (1996) was derived by comparing a flux-limited X-ray source catalog based on the ROSAT All-Sky Survey (RASS) with the Abell and ACO catalogs (Abell 1958; Abell, Corwin, & Olowin 1989). For our target list, we selected clusters from the XBAC sample above a lower limit in X-ray luminosity (L X;0:1 2:4 kev ergs s 1 ), in the redshift range 0:15 < z < 0:35 (the values for L X given here are all based on h ¼ 0:5). Further selection constraints were made to ensure that the clusters were readily observable from the latitudes of Hawaii and La Palma ( > 25 )and

3 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 315 that the target clusters were not heavily obscured by Milky Way extinction ( jbj > 20 ). All XBACs subject to the stated selection criteria were observed, except A1300 (missed because of poor weather), as well as A2390 and A2163, which have both been studied already by Squires et al. (1996b, 1997). The observations of A1689 will be analyzed in a separate paper together with HST WFPC2 data for this cluster (H. Dahle et al. 2002b, in preparation). 2. The ROSAT Brightest Cluster Sample (BCS) of Ebeling et al. (1998) was derived in a similar manner as the XBAC sample, and the two samples have significant overlap. However, the BCS differs from the XBAC sample in two important respects: (1) it covers only the northern half of the sky and (2) it includes non-abell clusters. The completeness of the BCS within the given X-ray flux limit of 5: ergs cm 1 s 1 is estimated to be 90%. We include in our sample all BCS clusters passing the same selection criteria that were applied to the XBAC sample, except six clusters. A689 and Zw 2701 are both marked with a c flag in the sample list, meaning that a significant fraction of the X-ray flux comes from embedded point sources. RX J was observed in FWHM ¼ 2 00 seeing, which is useless for weak lensing measurements. A781 and Zw 3146 were not observed because of telescope scheduling constraints, and A2390 was not targeted, since there is an existing weak lensing study of this cluster in the literature (Squires et al. 1996b). 3. Briel & Henry (1993) list ROSAT X-ray luminosities for a complete sample of Abell clusters with known redshifts measured by Huchra et al. (1990) in a 561 deg 2 region at high Galactic latitude and high northern declination. We subjected this sample to the selection criteria L X;0:5 2:5 kev ergs s 1 (for h ¼ 0:5) and 0:28 < z < 0:36, which gave six additional targets. In addition to the main samples, three cluster fields that fall below the X-ray luminosity cutoff were also observed for various reasons. A914 and A922 form a pair of clusters at very similar redshifts (0.193 and 0.189, respectively), separated by only 11 0 on the sky, and hence they both simultaneously fit into the field of view of the UH8K camera. Both of these clusters are listed by Briel & Henry (1993). Two more XBACs were also targeted for observations. A2104 was observed on a night with very strong wind, which led to azimuthal constraints on the pointing of the UH 2.24 m telescope. A2345 falls below the quoted luminosity limit by a very small margin. The complete list of observed clusters is given in Table The Data The optical imaging data presented here were obtained over 16 nights at the 2.56 m Nordic Optical Telescope (NOT) on La Palma (UT dates 1997 March 7 10, 1998 April 22 25, 1998 July 20 24, and 1999 May 7 13) and 21 nights at the 2.24 m University of Hawaii telescope at Mauna Kea Observatory (UT dates 1997 April 29 May 1, 1998 February 19 23, 1998 October 20 23, 1999 January 20, 1999 March 5, 1999 May 14 16, and 2000 March 8 11). The suitability of the NOT and the UH 2.24 m telescope for weak lensing observations has already been demonstrated by Dahle et al. (1994) and Luppino & Kaiser (1997). The detector at the NOT was the ALFOSC camera equipped with a thinned Loral CCD, with a pixel size of 0>189 at the f/11 Cassegrain focus. The detectors on the UH 2.24 m telescope were a thinned Tektronix CCD, yielding a pixel size of 0>22 at the f/10 Cassegrain focus, and the 8 chip UH8K CCD mosaic (rebinned during these observations to effectively become a detector with a pixel scale of 0>275). The exposure time for each individual frame was usually 900 s for the 2k CCDs and 1800 s for the UH8K. More details about the total exposure times and the detector(s) used for each cluster can be found in Table 1. Histograms showing the distribution of FWHM values of stellar objects in the final combined I- and V-band frames are shown in Figure 1. In our following description of the data reduction methods we have used, we first describe how the UH8K mosaic CCD data were reduced. They required separate reduction steps to ensure accurate registration of the different mosaic chips and allow for the discontinuous variation of the PSF across chip borders in the mosaic. Following that description, we describe our reduction methods for the monolithic CCDs, which in general are simplified versions of the methods used for the mosaic data Reduction of Mosaic CCD Data Here we describe the main reduction steps for the UH8K mosaic CCD data, with particular emphasis on the process of obtaining a precise astrometric solution while performing the image registration. We generally follow the methods of Kaiser et al. (1999, hereafter K99), and we have used the IMCAT software package (Kaiser, Squires, & Broadhurst 1995, hereafter KSB95) for the data reduction and analysis described in this paper Basic Reduction There is a highly significant dark current signal in long exposures taken with the UH8K camera. Dark frames (typically generated from five to s exposures) were subtracted from the science frames. The frames for each chip were then cropped down to a format of (in rebinned pixels) to remove the overscan region. For each chip in the mosaic, the set of normalized 1800 s science exposures taken during a given run with a given filter were median combined to yield superflats (this was done in two iterations; objects and transient artifacts were masked Fig. 1. Distribution of FWHM seeing values in the combined V- and I-band frames.

4 316 DAHLE ET AL. Vol. 139 TABLE 1 Observed Cluster Sample Cluster Designation (J2000.0) (J2000.0) Redshift z L X (10 44 ergs s 1 ) t exp (V ) t exp (I ) Detector Name(s) FWHM (V ) (arcsec) FWHM (I ) (arcsec) A a Tek A a ALFOSC A b Tek, UH8K A b Tek, UH8K A a Tek, UH8K A a Tek, UH8K A a ALFOSC A a ALFOSC A a ALFOSC, Tek Zw a ALFOSC A a ALFOSC A914/ c UH8K A c UH8K ALFOSC A a UH8K A c UH8K A a ALFOSC Zw a ALFOSC A c UH8K A a ALFOSC A b UH8K A c UH8K A c UH8K A a ALFOSC A a ALFOSC A a Tek A a ALFOSC A c UH8K Zw a ALFOSC RX J a ALFOSC A a ALFOSC A b ALFOSC, Tek A a ALFOSC A a ALFOSC RX J a ALFOSC A a ALFOSC A b ALFOSC RX J a ALFOSC A b ALFOSC, UH8K Note. Units of right ascension are hours, minutes, and seconds, and units of declination are degrees, arcminutes, and arcseconds. The L X values are given for an Einstein de Sitter universe with h ¼ q 0 ¼ 0:5. When two detector names are given for a particular cluster, the first and second detector names indicate the telescope/instrument used for the V-band and I-band observation, respectively. Tek indicates the Tektronix CCD at the UH 2.24 m Telescope. ALFOSC indicates the Andalucia Faint Object Spectrograph and Camera at the NOT. UH8K indicates the University of Hawaii CCD mosaic at the UH 2.24 m Telescope. The redshift value for A2537 was obtained by H. Ebeling, C. Mullis, & J. P. Henry 2002, in preparation. References for the other cluster redshifts are given by Briel & Henry 1993 and Ebeling et al. 1996, a Luminosity in the kev (cluster rest-frame) energy band, measured by Ebeling et al b Luminosity in the kev (cluster rest-frame) energy band, measured by Ebeling et al c Luminosity in the kev (cluster rest-frame) energy band, measured by Briel & Henry in the second iteration). Each superflat was typically generated from individual exposures of five to seven different cluster fields. They had a slight positive bias near the center of the mosaic caused by the presence of extended galaxy halos and faint intracluster light in the central regions of the clusters. After flat-fielding the individual science frames, this bias was removed along with other low-level gradients in the sky background by subtracting a smoothed estimate of the local sky variations (see K99 for details). This procedure will tend to suppress very diffuse outer envelopes of galaxies (e.g., cd halos), and hence it is not optimal for precise photometry, but the main purpose of this data set is to accurately measure galaxy shapes, which could be slightly biased by any gradients in the background level. A constant count was subtracted from each image to set the background sky level to zero. From the images we generated mask files that define bad areas intrinsic to each chip. These were then applied to the images. Each individual exposure was visually inspected, and additional masks were applied to cover transient events such as satellite and meteor trails and reflections from bright stars outside the field. Chip 4 in the UH8K mosaic, which is situated at the northeast corner of the mosaic when it is mounted at the Cassegrain focus of the UH 2.24 m, had very poor cosmetic quality, and the data from it were therefore not used in the further reduction and analysis.

5 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 317 To cover the gaps between the chips, the UH8K exposures of each field were dithered along a diagonal direction in steps of D ¼ D ¼ We used unsaturated stellar objects in the frames to reregister the exposures Registration and Astrometric Solution It is crucial to accurately align the individual exposures before the images are combined, so that we avoid introducing artificial galaxy shape distortions that may resemble a weak shear signal. In this section we describe our relatively complicated methods for performing this alignment (for a more detailed description see K99). Figure 2 shows the offsets between object positions in the Digitized Sky Survey (DSS) and the positions derived by translating the chip coordinates according to the nominal chip layout in the UH8K mosaic. The rms offset is about 0>8 in both x and y. The main contribution to this offset is the nonperfect layout of the chips, which are translated and slightly rotated with respect to a uniform grid. Additional scatter is caused by uncertainties in the positions of faint objects in the DSS data and by the proper motion of stars during the four decades between our observations and the original POSS I observations. As indicated by Figure 2, the field distortions at the Cassegrain focus of the UH 2.24 m telescope are small, and they can only give rise to an artificial shear of 1: or less, which is negligible for cluster mass reconstructions. To model these distortions, we used the Jello detector model of K99, in which the telescope+detector system is assumed to be rigid during a single exposure but is allowed to deform in a restricted way between exposures. The restriction on the deformations is that the mapping from chip coordinates to rectilinear sky coordinates for each chip image is required to always be well represented by a low-order polynomial. This model yields an accurate solution for the chip layout and accounts for various sources of image deformations such as atmospheric refraction, distortions caused by the telescope optics and filters, and thermal expansion and mechanical strain in the instrument. As our reference system, we chose the shape-preserving stereographic projection of Greisen & Calabretta (1995). When mounted on the UH 2.24 m telescope, the UH8K camera is bolted in a fixed position, and the orientation of the mosaic is aligned with the principal sky directions to better than a tenth of a degree. Hence, it is convenient to set the rotation angle of the reference system to zero, such that north is up at the field center. If we from our data alone try to get internal solutions for the mapping from chip pixel coordinates of a given star in a given exposure x pi ¼ðx pi ; y pi Þ (where p denotes star number and i image number; a description of how they are assigned is given later) to stereographic sky coordinates r ¼ðr 0 ; r 1 Þ (where r 0 denotes the x-component and r 1 the y-component), we find that they tend to have strong large-scale field distortions when the offsets between exposures are small. The small number of registration objects that are located in the narrow areas that appear on different chips in different exposures can be adequately aligned without accurately constraining the overall geometry of the field. Hence, to get good solutions for the alignment of separate exposures of the same field, it is necessary to utilize external astrometry. To facilitate the registration of our exposures on the common stereographic sky coordinate system, we used external astrometry from the USNO-A2.0 catalog (Monet et al. 1998) in combination with astrometry extracted from the DSS (which gives us a higher density of reference objects than we can obtain from the USNO-A2.0 catalog alone). To combine the astrometry of DSS with the USNO-A2.0 astrometry, we transformed the DSS positions r DSS into the USNO-A2.0 system. This was done by modeling the transformation as a low-order polynomial for each of the two components of the position vector, r j;usnoa ¼ r j;dss þ Xl max X l l¼0 m¼0 a lmj f lm ðr DSS Þ ; ð1þ in which the mode functions f lm are given in Cartesian coordinates (r 0, r 1 )as f lm ðrþ ¼r l m 0 r m 1 : ð2þ Fig. 2. Circles indicate object positions derived from DSS data in the field of A520. The axis values are given in arcseconds, and the vectors (their lengths having been multiplied by a factor of 50 for clarity) show the offset between the DSS position and the corresponding object position derived from a pure translation of the chip coordinates according to the nominal chip layout of the UH8K mosaic. The borders between the chips are delineated by solid lines. The nominal gaps between the chips in each row are 17 pixels (4>7) wide, and the gap between the rows is 13 pixels (3>6) wide. Modes up to l ¼ 2 were used to generate a reference catalog (in the following referred to as the DSS catalog ) in the USNO-A2.0 system containing the 500 brightest DSS objects in the cluster field. This was used as a reference catalog for the registration of the UH8K data, which were performed in several steps. First, the object finder and aperture photometry algorithms in IMCAT were applied to each image, and stellar objects were selected in a magnitude range where stars would be nonsaturated and clearly distinguishable from galaxies (17 I 20, 18 V 22). This left registration stars per chip, depending on the Galactic latitude of the field. The centroid position x pi of a star p on an image i was measured using a linear interpola-

6 318 DAHLE ET AL. Vol. 139 tion scheme (see Appendix B of K99 for details). The mapping from x pi to the corresponding position r p in r-coordinates was modeled as a polynomial 2, an artificial shear of order = obj where hobj is the size of an object, and these errors should be negligible for the purposes of this paper. r p ¼ x pi þ Xl max X l l¼0 m¼0 b ilm f lm ðx pi Þþe pi ; where f lm is given by equation (2) and e pi is the positional error, which is assumed to have a probability distribution function which is well represented by an isotropic twodimensional Gaussian of scale length p. The index i ¼ 0is here taken to represent the DSS catalog which has an error e p0 (with an rms precision of 0 0>25, compared to p 0>01 for the UH8K images) and transformation parameters a 0lm ¼ 0. The set of equations in equation (3) was solved by a least-squares minimization technique in the following series of steps: 1. For each exposure, the nominal chip layout was used to translate the x pi coordinates in the individual chip catalogs and combine these into a larger catalog covering the entire UH8K field. This catalog was then matched with the DSS catalog using a cross-correlation registration technique (see K99, Appendix A). Figure 2 illustrates the typical size of the residuals associated with this rough initial registration. A subcatalog containing only the DSS objects in the area covered by a given chip could be extracted from the larger DSS catalog and used for a second cross-correlation matching with the individual chip catalog, such that an l ¼ 1 solution was generated for the transformation of x-coordinates into r-coordinates for each exposure and chip. 2. To apply a unique identifier to each star, we used the l ¼ 1 solution to generate a pixel image, covering the whole field in r-coordinates. In this picture, we assigned a value to each pixel equal to the number of star detections falling on that pixel, and from this we generated a filtered catalog containing positions of objects detected in at least half of the exposures of each field. These objects were randomly assigned a unique index number p. Each of the individual chip/exposure catalogs was then compared to this master catalog so that every catalog star which coincided with a master catalog star within a tolerance of 10 pixels would inherit the relevant p-number of that star. To avoid ambiguities, any star within a distance of 20 pixels from a brighter neighbor had already been excluded. 3. After appending the p-indices to the catalogs, equation (3) was solved, using modes up to l ¼ 2. Using this solution, steps 2 and 3 were repeated to yield final values for the transformation parameters b ilm.asa check on the accuracy, the positions of a random subset of 50 control stars (which had not been used for the registration) were transformed according to the solution, and this resulted in an rms displacement of control star positions between two different exposures of typically pixels (corresponding to 0>011) per component or 0>008 for the positional inaccuracy of a given star. This was similar to the displacements of stars which had been used in the solution (see Fig. 3). The rms displacements of stellar positions between I-band and V-band images of the same field were larger by 50% 100%, which is probably caused by the difference in atmospheric dispersion for stars of various spectral types. Inaccuracies in the image mapping will create ð3þ Correction for Extinction and Gain Variations Before combining the individual UH8K images, it was also necessary to correct for variation in atmospheric extinction from exposure to exposure and for offsets in the photometric zero points caused by gain variations between the different chips. The latter were assumed to be constant during a particular observing run, and we used the uncalibrated instrumental magnitudes of stars to calculate a leastsquares solution for extinction and chip gain variation. The extinction variations between exposures in the I band were mostly less than 0.01 mag during the 1998 February and 1999 May runs (the maximum was 0.06 mag). For the 2000 March run, the extinction variations between exposures in the V band were typically around 0.02 mag. During the 1998 October run, which had less stable photometric conditions, the I-band extinction corrections were found to be less than 0.1 mag for A209 and A520, typically 0.2 mag for A267 and A2537, but up to 1 mag for A141, which was observed in rather poor conditions. The weak lensing measurements do not depend on photometric conditions, but photometric uncertainties of several tens of percent would contribute significantly to the uncertainty in the calculated mass-to-light ratios (H. Dahle et al. 2002c, in preparation). Fortunately, the clusters observed in the I band in nonphotometric conditions during the 1998 October run all have V- band data obtained in photometric conditions, so errors in the photometric zero-point calibration do not contribute significantly to errors in M/L Recircularization of the PSF An elongated PSF will artificially distort the observed galaxies and may thus introduce a false shear signal to the data. As described below, a model PSF was generated for each chip/exposure and used to recircularize the PSF in the individual exposures. Later, in x 2.3.7, a similar approach is used to generate a PSF model for the combined images, which is used for the shear estimation. Because of optical aberrations in the UH 2.24 m telescope, the PSF will change its shape as the detector is moved from one side of the focus to the other. The chips in the UH8K mosaic are slightly tilted with respect to the focal plane, and this will cause the PSF [denoted as gðrþ] to vary discontinuously across chip boundaries. Hence, the PSF anisotropy was modeled and corrected for each chip image separately before combining the various exposures into a final image. When calculating this correction, the PSF was to vary smoothly as a function of position within each chip, as well as discontinuously across the chip boundaries. By reconvolving each source image with a kernel given by a 90 rotated version of the PSF, g y ¼ R =2 ðgþ, images with almost circular PSFs were generated. The PSF model was generated as follows. Stars were selected by comparing a 32 2 pixel, flux-normalized image of each star with a median star image, automatically rejecting stars with unusually large pixel value discrepancies with respect to the median star. The PSF was then derived from the 20 good stars per chip by taking a least-squares solution for a model on the form given by K99, using modes up to l ¼ 1.

7 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 319 Fig. 3. Residuals in the image mapping for all stars (left) and residuals after holding back a random subset of control stars which were not used for calculating the astrometric solution (right). The lower panels show the differences between model r-values for exposures 4 and 8 of A1576 in units of the original pixel scale of 0>275, and the upper panels show the same, multiplied by a factor of 1000, plotted as a function of position in the field. It is evident from these plots that the mapping is very accurate, with no significant systematic effect, and both the registration stars and the control sample have residuals that appear to follow an isotropic distribution of similar width Image Combination To retrieve some of the spatial information lost by rebinning the pixels during the observations, we set the final pixel size in stereographic r-coordinates to 0>15. Instead of combining the source images into a single FITS file, we chose to make a quilt consisting of 4 4 patches of size that cover the entire field (to allow for accurate measurements of objects close to the border between images, each patch image was given a margin of 24 pixels that overlapped with the adjacent images on each side). All images contributing to a given patch were transformed into the stereographic sky coordinate system, scaled according to the gain and extinction variation correction described in x and median combined. This procedure was used to create two quilts for each field and filter, one from the images after the recircularization procedure of x had been applied (hereafter called the recircularized images ) and one from the raw images before the recircularization procedure had been applied. As described below in x 2.3.7, both the raw and the recircularized images are necessary for estimating the shear. Astrometric information (with positional accuracy good to approximately 0>25) was incorporated in the FITS header for each patch image. The combined images were visually inspected to define masks to exclude areas covered

8 320 DAHLE ET AL. Vol. 139 by bright stars, bleeding pixel trails, diffraction spikes, ghost images, and areas with high sky noise (because of fewer contributing exposures) near the edges of the observed field. The warping, resampling, and interpolation of 0>275 source pixels into 0>15 pixels in the combined images resulted in short-range noise correlations, which had to be accounted for when estimating the detection significance of faint objects. To model this effect, we generated a set of random white-noise images which were dithered with random subpixel offsets, then rebinned and combined. The resulting image was autocorrelated to produce a 32 2 pixel image of the noise autocorrelation function, which was used by the object detection algorithm (see x 2.3.7) The Shear Estimator In x we describe how we detected the objects in the images and from them determined the shear. As a background for this shear determination, we here describe in more detail our shear estimator which is closely based upon the estimator of Kaiser (2000). We measured galaxy shapes using the weighted second moments q lm of the flux distribution f s ðrþ in the recircularized images, Z q lm ¼ d 2 rwðrþr l r m f s ðrþ ; ð4þ where wðrþ is a two-dimensional Gaussian weighting function. We also define a weighted flux F ¼ R d 2 rwðrþf s ðrþ. From equation (4), three components (denoted by subscripts 0, 1, and 2; here the subscript A denotes all three components while the subscript denotes the two last components) are formed, 0 q A ¼ q xx þ q yy 2 q xx q yy 2 q xy 1 C A ; where the first component q 0 is a measure of the sky area of an object. The latter two components, q, which can be written as q ¼ q^q, measure the elongation of an object and will hereafter be referred to as the polarization. Here ^q ¼ ðcos ; sin Þ is the unit polarization vector. The response of the measured properties F, q 0, and q of an individual galaxy to a shear is given by the polarizabilities R, P 0,andP, F 0 ¼ F þ R ; q 0 0 ¼ q 0 þ P 0 ; q 0 ¼ q þ P ; ð5þ ð6þ where primed and unprimed symbols denote lensed and unlensed quantities, respectively. The polarizabilities are calculated from the raw images and the model PSF (for full expressions and derivations see Kaiser 2000). In weak lensing analysis, the shear measurement is based on a large ensemble of galaxies ( galaxies, depending on field size, for the data presented here). Hence, we needed to determine how the ensemble average polarization responds to shear. This is quantified by the effective polarizability P, such that hq i ¼ P. However, this effective polarizability is not equal to the average of the polarizabilities of individual objects. This difference between the effective polarizability and the average polarizability is caused by the fact that in the presence of a shear, the galaxies will systematically scatter in the three-dimensional F-q 0 -q space. This will bias the net polarization in a way which depends on the local gradients of the distribution function nðf; q 0 ; qþ. We used the effective polarizability, calculated by Kaiser (2000) for the case in which q 0, q, R, P 0,and P are all normalized by the flux F, q P ^q P ¼ P P 0 q 0 þ q ln F nr ^q : ln q ln q For an isotropic PSF, P ¼ P, where P P =2, and the shear estimator for a cell in F-q 0 -q 2 space (the reason for using q 2 instead of q is given by Kaiser 2000) with occupation number N is given by ^ ¼ 1 X q : ð8þ N P The expectation value for the variance in ^ is q 2 =N P 2, and the optimized total shear estimate when averaging over all cells is given by X ^ total ¼ Q^q galaxies ; ð9þ Q2 Xgalaxies where Q P=q (Kaiser 2000). The variance of the total shear estimator is ð P Q 2 Þ 1, and this provides a useful figure of merit P Q 2 =d (where d is the solid angle covered by the observed field), by which the quality of different weak lensing data sets can be compared Object Detection and Shear Determination To be able to measure the shear, we had to first detect the galaxies from which the shear was determined and the stars from which the PSF was constructed. For this we used the hfindpeaks object detection algorithm of IMCAT (see KSB95 for details). This was applied to the raw combined images, generating catalogs of objects above a significance cutoff min ¼ 4, after allowing for noise correlations introduced by pixel interpolation and resampling. The next step was to generate an accurate model PSF, g, to be used in the calculation of the effective polarizability. This was done by generating a catalog of nonsaturated, isolated stars which were clearly separated from galaxies in a size-magnitude diagram (see Fig. 4). This star catalog was filtered in a similar way to that described previously in x to reject stars with discrepant pixels (above a certain tolerance) with respect to a median star. This left about 300 stars in each UH8K field (the higher density of good stars in these combined images than in the individual exposures is because of the greater depth and the absence of cosmic rays and cosmetic defects in the combined images). The stars were used to generate an l ¼ 3 model (see K99) for the PSF variation in the field (see Figs. 5 and 6 for illustrations of typical PSFs in the raw and recircularized images). This PSF model was then used to generate a synthetic PSF for the center of each image patch in the quilt. This PSF was used by the getshapes3 program of IMCAT, along

9 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 321 P Q2 =d 0:5 1: deg 2 for the V-band data obtained with the UH8K camera. The quality of the shear measurements from the I-band data is thus comparable, e.g., to that of a recent Canada-France-Hawaii Telescope (CFHT) UH8K weak lensing study of the mass distribution in blank fields (Wilson, Kaiser, & Luppino 2001). Fig. 4. Size-magnitude diagram for 8824 objects detected in both the I band and the V band in the field of A1722. Stars in the magnitude range 16 < I < 21 form a clearly defined locus at a constant half-light radius of 0>45. Brighter stars get saturated and have larger apparent sizes, and fainter stars cannot be clearly separated from small, faint galaxies. with the raw and recircularized FITS files for the relevant patch. This program computes from the galaxy images (there were typically 15,000 objects in each field) the values for F, q 0,andq (the latter two being normalized by the flux) along with their flux-normalized polarizabilities, using the raw image to calculate the polarizabilities and the recircularized image to calculate F, q 0, and q. To calculate the effective polarizability of equation (7), the objects were binned in a cube in F-q 0 -q space with cells, and P was determined for each cell using the IMCAT program makepeff. After excluding cells with occupancy n < 3, the value for Q was determined for each object and entered into the object catalogs. We find typical figure-of-merit values of P Q2 =d 1:5 2: deg 2 for the I-band data and Fig. 5. Ellipticities of stellar objects in the combined raw image of A520. The ellipticities are exaggerated by a factor of Monolithic CCD Data Reduction Throughout the rest of the paper, we will refer to the data obtained with the Tek2048 CCD at the UH 2.24 m Telescope and the data obtained with the ALFOSC camera at the NOT (see Table 1) as monolithic CCD data or simply 2k data. The reduction steps for the monolithic CCD data were generally similar to the procedure for UH8K which is described in relative detail in x 2.3, but with a few significant differences. Here we mainly point out these differences and refer to x 2.3 for the details. The raw images were bias subtracted (the dark current was negligible for the 2k detectors used here) and cropped down to a format. Superflats were generated from the median of a set of normalized science exposures, and low-frequency variations in the sky background of the flat-fielded images were taken out in the same way as for the UH8K data. A set of masks covering cosmetic defects intrinsic to a particular CCD chip were applied to the images. The individual exposures of a particular cluster were registered using the positions of more than 20 bright, unsaturated stars in the field. A fiducial frame was chosen for each of the passbands, and the transformation of each of the other catalogs into this reference frame was calculated using an iterative process in which the astrometric transformation was modeled as a second-order polynomial. In each iteration, outliers to the best least-squares fit were rejected until a good fit was found with rms residuals typically less than 0.05 pixels in x and y. To ensure accurate photometry when combining imaging data taken over several nights (some of which were nonphotometric), we computed for each exposure the average magnitude offset of the registration stars with respect to the reference exposure. A multiplicative factor was then calculated to rescale the individual exposures to the reference exposure, which was generally chosen to be the exposure with the lowest extinction. This procedure removed the effects of variable extinction, e.g., because of variations in zenith angle, cirrus clouds (if present), or increased atmospheric extinction caused by Saharan dust storms (this occurred on La Palma during the observing run in 1998 July). The combined images were generated by first taking a straight median of the individual exposures and then masking out pixels in these exposures that differed by more than a certain tolerance from the pixel value in the median images. The masked images were then combined into a final image by taking a simple average. Object detection and aperture photometry were performed on the combined images using the IMCAT programs hfindpeaks and apphot. A catalog of bright stars in the combined frame was generated and filtered by comparison with a median star in the same way as for the UH8K data. After this procedure, about objects were left in the star catalogs from the 2k images.

10 322 DAHLE ET AL. Vol. 139 Fig. 6. Typical raw (left) and recircularized (right) PSF models, here shown for a particular position in the field of A914 (x ¼ 2000, y ¼ 4000). The two PSFs are normalized to have the same total flux, and the contour levels are the same for both PSFs. Since the PSF variation across a monolithic CCD field can be assumed to be smooth without any discontinuities, we did not need to perform any PSF corrections on the individual exposures prior to making averaged frames. Instead, we performed all corrections for PSF effects based on the final combined images. As for the UH8K data, these corrections consisted of a procedure to remove PSF anisotropies (as described in x 2.3.4) and a procedure to calculate the effective polarizability defined in x The same star catalog was used to model the properties of the PSF for both of these purposes. The star catalog and corresponding stellar images were used by the IMCAT routine modelpsf which generated a best-fit model PSF for modes up to l ¼ 1 (see K99 for details). The images were convolved with this model PSF, rotated by 90 to produce the recircularized images. The values for F, q 0, q, R, P 0, and P were calculated based on the PSF model and on the raw and recircularized images using the IMCAT routine getshapes3. The polarizabilities as well as the size and shape were normalized by F. The effective polarizability P was determined for each cell in a cube in F-q 0 -q space using the IMCAT program makepeff. Because of the smaller number of available objects (2000 objects for typical 2k fields, compared to 15,000 objects for the UH8K data), the effective polarization in equation (7) had to be calculated with a coarser binning of the F-q 0 -q cube. To improve the statistical accuracy of the P calculation, we included galaxies from several cluster fields with similar seeing quality. After excluding objects in cells with occupancy n < 3, the Q value was determined for each object and entered into the object catalogs Consistency between UH 2.24 m and NOT Data As shown in Table 1, one cluster (A959) was observed with the same image quality and depth (taking into account the differences in detector sensitivity) in the same passband with two different telescope/instrument combinations. These data were therefore used to check the homogeneity in the shear measurements across the two telescopes. Our shear estimator, given in equation (9), incorporates weights defined such as to provide an optimized total shear estimate when the shear measurements are averaged over an ensemble of objects with different sizes, fluxes, and shapes. The weight given to an individual galaxy will thus depend on these intrinsic properties of the galaxy as well as the characteristics of the given observation (e.g., seeing, depth, and pixel size). Thus, when comparing shear measurements from different data sets, it is more meaningful to compare net shear values obtained from an average of a large number of galaxies, rather than to compare the shear estimates for each galaxy individually. To make a comparison of our UH 2.24 m and NOT data, we measured the net tangential distortion hg T i (see x 4.2) in radial bins around the center of A959, out to the largest radius covered by both telescopes. A comparison of the shear measurements from the V-band data from the two telescopes showed that the shear measurements were consistent at the.1 level in each of six radial bins. The estimated 1 errors in the tangential distortion differed by.10% for each bin. 3. PHOTOMETRIC ANALYSIS 3.1. Photometric Calibration Object catalogs containing instrumental magnitudes were generated using two different software packages: 1. As described in xx and 2.4, we used the IMCAT routines hfindpeaks and apphot for object detection and photometry. The hfindpeaks routine smooths an image with a set of progressively larger Mexican hat type filters, and for each object it determines a characteristic radius r g,

11 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 323 which is the smoothing filter scale which gives the highest S/N detection of the relevant object (see KSB95 for details). The apphot routine was used to measure the instrumental magnitude of each object within an aperture of size 3r g. This choice of aperture radius is large enough to include the bulk of the flux from an object but still small enough to avoid heavy contamination by neighbor objects. 2. We also generated object catalogs using Version of the SExtractor package, which is optimized for accurate photometry. We used the MAG_BEST estimate of the total magnitude that is derived from either an adaptive aperture algorithm or, in the presence of neighbors that may significantly bias the aperture photometry, corrected isophotal magnitudes (see Bertin & Arnouts 1996 for details). A comparison of the photometry from IMCAT and SExtractor showed that the SExtractor magnitudes were on average brighter by about 0.2 mag, with somewhat larger magnitude offsets for bright objects. The offset probably corresponds to galaxy flux beyond 3r g, which was not measured by IMCAT. In a few very crowded cluster cores, IMCAT occasionally failed to split overlapping galaxies into individual objects. When subsequently matching the V- and I-band catalogs by selecting objects that spatially coincide within a tolerance of 3 pixels, such composite detections were sometimes excluded, which might have led us to underestimate the cluster luminosities. The results in the remainder of x 3 are hence derived using SExtractor photometry. The V- and I-band magnitudes were calibrated using the standard-star fields of Landolt (1992), which were generally observed at a range of air masses that bracket the air-mass values of the science exposures. As noted above in x 2.3.3, the extinction variations between exposures and gain variations between the chips in the UH8K mosaic were taken out before the combination of individual exposures. If the reference exposure had been obtained in photometric weather (this was the case for all but a few clusters; see xx and 2.4), standard Mauna Kea and La Palma extinction corrections were applied for the air-mass value of the reference exposure. The I-band filter for the UH8K camera is somewhat wider than standard Cousins I, and a color term of 0.05(V I ) had to be applied to transform the UH8K I magnitudes to the standard system. The object flux is not conserved when images are transformed into a different pixel scale, so an additional photometric correction term was calculated from the ratio of the area of the source pixel to that of the final pixel. Finally, Galactic extinction values E(B V ) were estimated for the center coordinates of each field (see Table 1) using the dust maps of Schlegel, Finkbeiner, & Davis (1998), and the magnitudes were corrected by DI ¼ 1:940EðB V ), DV ¼ 3:315EðB V ) (the given values assume an R V ¼ 3:1 extinction curve). As a check on the photometric accuracy, we compared photometry of A959 obtained with two different telescope/ instrument combinations (see Table 1). For objects detected in both the NOT and UH 2.24 m I-band catalogs, the average magnitude difference was DI ¼ 0:03. The galaxy photometry was used to generate the plots in the upper left panel of Figures In these plots, bright galaxies in each cluster field are represented as circles with area proportional to their I-band flux, and with shading representing the V I color, if available. The three columns of circles (shown in the upper left corner in the upper left panel of the UH8K data plots in Figs. 7 18; shown above the upper left panel in the 2k data plots in Figs ) indicate the predicted fluxes and colors corresponding to an L * galaxy (M B ¼ 19:68) at a given redshift for E0-, Sbc-, and Scd-type galaxies, assuming no evolution compared with z ¼ 0 spectral energy distributions (SEDs) of the given galaxy types (see x 3.2) Photometric Prediction of Surface Mass Density One of the goals of our study is to compare the distributions of galaxy light and dark matter in the clusters. Here we provide a description of our procedure(s) for using galaxy photometry to generate two-dimensional maps of the predicted mass density, assuming that mass traces light with a constant M/L. A similar procedure was used by Kaiser et al. (1998) to study the early-type galaxy light distribution in the MS supercluster and by Wilson et al. (2001) to study the early-type galaxy light distribution in six blank fields. We will describe our measurements of cluster M/L ratios and the radial mass and light profiles in subsequent papers in this series. Our aim is to predict the dimensionless surface mass density ¼ = crit [ crit ¼ ðc 2 =4GÞðD s =D ls D l Þ, where D l, D s, and D ls are the angular diameter distances to the lens, to the source and between the lens and source, respectively]. If all galaxies in the field were situated at the cluster redshift, it would be simple to predict by calculating the rest-frame surface luminosity density lum from the galaxy fluxes and scaling it with a given M/L. In reality, foreground and background galaxies contribute significantly to the total flux, the former being particularly troublesome, since foreground galaxies will contribute a disproportionate amount to the surface luminosity density in the field. However, even in the absence of spectroscopically measured galaxy redshifts in the observed fields, the galaxy redshifts may be constrained using photometric information. The effect of the morphology-density relation (Dressler, Gunn, & Schneider 1985; Whitmore, Gilmore, & Jones 1993) is very strong in the central regions of rich clusters, where the early-type galaxy fraction is strongly enhanced. Both observations and theoretical models of hierarchical structure formation indicate that the process of galaxy formation is accelerated in dense environments, implying an early formation epoch (z f > 2 4) for the stellar populations of early-type cluster galaxies (Lubin 1996; Kodama et al. 1998). Hence, the SED of early-type cluster galaxies is evolving very slowly at the current epoch, and early-type galaxy colors are well represented by a no-evolution model at redshifts z < 0:4 (Lubin 1996). The deviation in V I color from the no-evolution model is increasingly sensitive to z f with increasing redshift (Kodama et al. 1998). The early-type galaxies in rich clusters at moderate redshifts form a remarkably tight, almost horizontal sequence in a V I color-magnitude diagram (see Fig. 46) and can thus be fairly cleanly separated from foreground and background objects (e.g., Garilli et al. 1996; Olsen 2000). The tightness of the observed early-type sequence gets even more pronounced if the V I colors are measured within a fixed aperture with diameter a few times the seeing FWHM. In the following we use total V and I magnitudes but use V I colors measured within a fixed aperture of 2>7, corresponding to 4.6 h 1 kpc at z ¼ 0:15 and 8.1 h 1 kpc at z ¼ 0:35.

12 324 DAHLE ET AL. Vol. 139 Fig. 7. Mass, light, and galaxy number density distributions in the field of A141. In the upper left plot, all I < 20:5 galaxies are plotted as circles, with areas proportional to the flux. The upper right plot shows the projected mass density in the field, inferred using the algorithm of KS93. The scale bar on the right runs from zero to the peak value of. The lower left plot shows a prediction of the surface mass density in the field, assuming that all galaxies are at the cluster redshift and have a mass-to-light ratio M=L B ¼ 400hM=L B. The contour levels are the same as in the upper right plot. The lower right plot shows the number density of galaxies in the field. The three surface density plots have all been smoothed with a Gaussian filter with scale See xx and 4.1 for further details. The plots in Figs contain the same information as this figure for other clusters. Given that the clusters studied here are situated at moderate redshifts, the V I colors of early-type cluster galaxies can be predicted by redshifting locally measured SEDs. Figure 47 shows the predicted standard Johnson-Cousins V I colors of various galaxy types as a function of redshift, given no evolution. In the redshift range of our clusters (0:15 < z < 0:35), there is a gap between the early-type galaxies (represented by the E0 SED) and spirals and irregulars. Thus, when filtering the galaxy catalogs to only include objects above a certain V I threshold, the contamination by spirals and irregulars will be minimal (such galaxies must lie at significantly higher redshifts to survive the colors cuts, with correspondingly lower fluxes; see Kaiser et al. 1998). In a predicted image with a pixel size corresponding to a solid angle d, the contribution of a galaxy of apparent magnitude m within a pixel to the value for that pixel is given by d ¼ M 4GM a 0 L B c 2 ð10 pcþ 2 ð1 þ w l w ls zþ3 w s 10 0:4 ½ M B m k mb ðzþ Š ; ð10þ where M/L B is the rest-frame B-band mass-to-light ratio (in solar units) used for the prediction, w ¼ 1 ð1 þ zþ 1=2 for m ¼ 1, ¼ 0, and we have assumed M B ¼ 5:48 and a 0 ¼ 6000 h 1 Mpc. The effect of the source galaxy redshift distribution is estimated in x 4.2. The k-correction k mb (z),

13 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 325 Fig. 8. A209 which converts the observed magnitudes in a given passband into rest-frame B-band magnitudes, is estimated by redshifting Coleman, Wu, & Weedman (1980) SEDs and convolving them with transmission curves for the Johnson- Cousins filter system. We adopt M=L B ¼ 400 h for our predictions, typical of mass-to-light values determined for rich galaxy clusters (H. Dahle et al. 2002c, in preparation). To predict we use three different methods, as detailed below, each of which was tailored to suit a particular subset of our data. The primary purpose of presenting the predicted images in this paper is to make a qualitative comparison of the morphologies of the mass and light distributions in the clusters. A later paper in this series will focus on determinations of the mass-to-light ratios of these clusters and will discuss issues such as field galaxy subtraction and comparisons of results from the three different methods described in xx 3.2.1, 3.2.2, and UH8K Data with Color Information The following method was applied to the clusters for which we have UH8K data obtained in both the I and V band (see Table 1). Plotted in Figure 47 is the median color of bright (I < 21) galaxies in the observed cluster fields. Our galaxies appear to be slightly bluer than the E0 prediction, and after applying an empirical correction factor of DV I ¼ 0:10, the predicted colors match the observed ones fairly well. The difference between the observations and the prediction is most likely caused by a combination of several small effects such as slight galaxy evolution with respect to the z ¼ 0 SED, a nonzero slope of the early-type galaxy sequence in the color-magnitude diagram, color gradients in early-type cluster galaxies, and contamination from spiral galaxies and foreground ellipticals when estimating cluster galaxy colors. The redshift-color relation and

14 326 DAHLE ET AL. Vol. 139 Fig. 9. A267 the k IB -correction for E0 galaxies were approximated as linear relations in the redshift range of our clusters. For each galaxy in the color range 1:0 < V I < 2:5 (which eliminates most spirals and irregular galaxies in the redshift range of the clusters), a color redshift estimate was used in equation (10) to generate a pixel predicted image, which is shown in the lower left panel of Figures In the lower right panel of these figures we plot the number density distribution of galaxies that were detected in both passbands above a threshold significance ¼ 4. To match the resolution of our weak lensing mass reconstructions, these images were smoothed with a Gaussian kernel of scale length 3 pixels, corresponding to The average pixel value in the images was subtracted to mimic the finite-field bias in the mass reconstructions (see x 4.1) UH8K Data without Color Information Some of the clusters were observed in the I band with the UH8K detector and in the V band with a 2k camera (see Table 1). A prediction covering the larger UH8K field was thus generated from I-band data only. First, a few large bright galaxies that are unambiguous foreground objects were filtered out of the photometric catalog. A prediction was then generated from equation (10), assuming that all galaxies have z ¼ z cluster and have k IB corresponding to E0- type galaxies. The resulting images are plotted in the lower

15 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 327 Fig. 10. A520 left panels of Figures 7 10 and have the same size and resolution as the other UH8K images (see above) k Data The following method was applied to all clusters for which we have 2k data, including the ones in x Some bright central galaxies in X-ray luminous clusters display an excess blue continuum over that expected from regular cd galaxies, the blue light being consistent with starbursts of O stars near the galaxy centers (e.g., Crawford et al. 1999). The starburst activity may be related to gas deposition by a cooling flow. As a result of this effect, some bright central galaxies may be excluded by applying the color cuts in x 3.2.1, and even if they are included, their rest-frame B- band luminosities would be strongly underestimated by the method described in x (we note however that none of the central galaxies in the clusters observed with the UH8K camera were unusually blue, so the method of x was found to be adequate for those clusters). Some of these galaxies contribute significantly to the total flux within the 2k fields, and we want to include them (with the correct redshift) when predicting. We also note that the 2k fields are small enough and the clusters at low enough redshift to limit severe contamination by foreground/background galaxies within the observed field (the wider UH8K fields are more likely to show significant foreground/background structure somewhere inside the field). Hence, we assumed z ¼ z cluster for all galaxies in the field and made the estimate of in equation (10) using V-band data instead of I-band data. We note that the restframe B band is approximately redshifted into the V band at the average redshift of our clusters, and k VB is essentially independent of galaxy type at this redshift. The resulting images (of size 32 2 pixels) are plotted in the lower left panels

16 328 DAHLE ET AL. Vol. 139 Fig. 11. Mass, light, and galaxy number density distributions in the field of A914. In the upper left plot, all I < 20:5 galaxies are plotted as circles, with areas proportional to the flux. The circles are shaded according to the V I colors of the galaxies, with darker shades indicating redder galaxies. The legend in the upper left part of the upper left plot indicates the predicted fluxes and colors of E0-, Sbc-, and Scd-type galaxies with M B ¼ 19:68 þ 5logh as a function of redshift. The upper right plot shows the projected mass density in the field, inferred using the algorithm of KS93. The scale bar on the right runs from zero to the peak value of. The lower left plot shows a prediction of the surface mass density, based on photometry of early-type galaxies in the field. The contour levels are the same as in the upper right plot. The lower right plot shows the number density of galaxies in the field. The three surface density plots have all been smoothed with a Gaussian filter with scale See xx and 4.1 for further details. The plots in Figs contain the same information as this figure for other clusters. of Figures The images were smoothed with a Gaussian kernel of scale length 3 pixels, corresponding to for ALFOSC data and for Tek2048 data. 4. WEAK LENSING ANALYSIS 4.1. Shear-based Reconstruction of Surface Mass Density A variety of techniques have been invented for inverting a set of discrete shear measurements in a field into an image of the projected mass density. For our UH8K data, we chose to use the original inversion algorithm developed by Kaiser & Squires (1993, hereafter KS93), which is fast, is easy to implement, and has well-understood noise properties (essentially white noise). The latter is the main reason for choosing this algorithm, since the reconstructed images were to be correlated with the predicted images to derive M/L in the cluster fields, as a function of physical scale (H. Dahle et al. 2002c, in preparation; see also Kaiser et al and Wilson et al for descriptions of this technique). The estimator of KS93 can be expressed as a sum ^ðrþ ¼ 1 X 2n galaxies Wðr 0 rþ ðr 0 rþ ðr 0 Þ ; ð11þ

17 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 329 Fig. 12. A959 where WðrÞ is a smoothing window, n is the number density of objects in the faint galaxy catalog (see below), and the geometric kernel v is defined by ðrþ 1 r 2 0 r2 1 r 2 : ð12þ 2r 0 r 1 The two-dimensional reconstructions were generated by calculating ^ for a grid of test centers r to produce a map of the projected mass density across each field. It is convenient to specify the smoothing window by using a transfer function in Fourier space, so Z d WðrÞ ¼ 2 x ð2þ 2 TðxÞJ 2ðxrÞ ; ð13þ where T(x) is the transfer function and J 2 is the Bessel function of second order (KS93). The use of a Gaussian transfer function, TðxÞ ¼e x2 2 =2 ; ð14þ is then roughly equivalent to smoothing the mass density field with a Gaussian filter proportional to exp½ r 2 = ð2 2 ÞŠ. The method is strictly valid only in the limit of weak shear, 5 1, which is a good approximation everywhere except within 50 h 1 kpc from the center of a typical rich cluster at these redshifts. The distortion of background galaxies really measures the quantity =ð1 Þ, sometimes referred to as the reduced shear. We note that we have already adopted the weak shear approximation by expressing our observable as rather than =ð1 Þ in x The KS93 inversion method has some disadvantages. The lack of observed shear outside the field introduces an inte-

18 330 DAHLE ET AL. Vol. 139 Fig. 13. A963 gral constraint which forces the net mass inside the observed field to be zero. In addition, shear measurements are always subject to the mass-sheet degeneracy, i.e., the shear is insensitive to any uniform sheet of matter covering the observed field. It is, however, reasonable to assume that the projected mass density approaches zero near the edges of a large field. The missing shear information beyond the field edges will bias the measurement close to the edges, particularly in the corners. For our wide-field UH8K images, in which the target clusters are placed far from the edges, these effects will manifest themselves in a benign way by preserving the morphology of massive structures while subtracting a small constant from their real values. Edge effects related to the KS93 reconstruction technique are somewhat more troublesome for the smaller 2k fields, particularly in the case of clusters that do not have a simple morphology with a single, well-defined cluster center situated in the middle of the field. For our 2k data, we have used the Squires & Kaiser (1996) maximum probability extension to the KS93 algorithm, which is more computationally expensive but has virtually no bias in the recovered signal. We used a regularization parameter ¼ 0:05 and wave modes up to k ¼ 6 (see Squires & Kaiser 1996 for details). Faint galaxy catalogs were generated by selecting galaxies in the significance range 6 <<100, and each galaxy was assigned a weight according to equation (9). The weak lensing measurements were insensitive to the exact lower significance cutoff, since galaxies at low receive very low weights. The mass maps (i.e., the reconstructed images) of the cluster fields were generated from the faint galaxy catalogs with the same pixel size and smoothing scale as for the predictions described in xx Mass maps were generated from both I-band and V-band object catalogs, plus a combined V þ I catalog which was made from a combination of the two (by selecting the catalog entry from the passband in which the object was detected with the highest

19 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 331 Fig. 14. A1351 significance ). The combined catalogs were used to generate the mass maps shown in Figures 11 45, except for the clusters A68 and A2104 (Figs. 19 and 33, respectively) where the image quality differed strongly between the V- and I-band images (see Table 1). For these two clusters, the catalog generated from the poorest image was not used in the weak lensing analysis. An I-band catalog was used to generate the mass maps shown in Figures To evaluate the uncertainty in the mass maps, we generated a set of 32 catalogs with randomized shear values for each V, I, and V þ I faint galaxy catalog. The 32 catalogs were generated by keeping the object positions from the original catalog, but randomly assigning a new q value to each object, drawn randomly without replacement from the pool of q values in the original catalog. Each of these random catalogs was then used to generate a mass map with the same resolution as the real mass maps. We could then estimate the significance of peaks in the mass maps by looking at the scatter of the values at the corresponding position in the randomized mass maps. The rms spread in had values in the range , the former being typical for data obtained in 0>8 seeing, and the latter being typical for data obtained in 1>0 seeing. In Figure 48, a representative random shear reconstruction from UH8K data is shown for the cluster A959. This illustrates the typical noise level in the reconstructed images and gives an indication of the significance of the peaks seen in the mass maps. The two highest peaks in Figure 48 are at the 2 level. The typical significance of the cluster mass peaks is around 4, with A1351 displaying the most significant peak, at 10. As mentioned above, the reconstruction algorithm will set the net mass inside the field to zero, and this will, in the presence of real mass concentrations in the fields, bias the

20 332 DAHLE ET AL. Vol. 139 Fig. 15. A1576 height of the mass peaks downward with respect to the random shear reconstructions. The strength of this bias will obviously depend on the true mass content of the field. We have adjusted Figure 48 for this effect by adding a small constant negative value to the image, such that it has the same lower quartile value as the reconstruction in the upper right panel of Figure Aperture Densitometry From Gauss s law, it can be shown that the tangential component of the shear averaged along a circular path of radius r is related to the mean surface density inside r by h T i ¼ 1 d ð15þ 2 d ln r (Squires & Kaiser 1996). By integrating this over a range of radii, a useful aperture densitometry statistic can be formed, as derived by Kaiser et al. (1994): 2 ðr 1 ; R 2 Þ ¼ ðr 1 Þ ðr 1 ; R 2 Þ ¼ 1 R 2 1 =R2 2 Z R2 T R 1 h id ln r : ð16þ This statistic measures the mean dimensionless surface density within an aperture R 1 minus the average density in a control annulus between R 1 and a larger radius R 2. An error estimate is obtained by replacing 1 with 2 and 2 with 1, which rotates the source galaxies by 45 and cancels the true shear signal. This method is less useful in cases in which there are multiple mass peaks present in the field, since the mass peaks will bias each other s statistic when situated within the control annulus. In addition, unless there is no mass at all in the control annulus, the measurement will

21 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 333 Fig. 16. A1705 only provide a lower limit to the total mass within R 1.However, for a large field with a single mass concentration, should approach the true value for the contained mass when R 1 5 R 2. Figure 49 shows the result of aperture densitometry using the V þ I catalog of the very massive cluster A1351. On the left-hand side, from top to bottom, are plots of the tangential distortion [hg T i¼h T i=ð1 Þ h T i in the weak lensing regime] as a function of radius, the statistic as a function of r ¼ R 1 (for R 2 ¼ ), and a mass estimate M ap ¼ r 2 crit within this radius. On the right-hand side are corresponding control plots, derived by swapping the components of as described above. In Figures 50 and 51 we plot aperture mass estimates based on UH8K and 2k data, respectively. For some clusters, e.g., A922 and A1722, the presence of strong secondary mass peaks in the field tends to bias the aperture mass estimates downward. The mass estimates presented in Figures 50 and 51 depend on the background galaxy redshifts which enter into the expression for crit through the parameter, which is a function of the angular diameter distances ( D ls =D s ). Hence, some information about the redshift distribution n(z) of faint galaxies is required, and even very basic constraints are useful, since the lensing signal from clusters in our sample is relatively insensitive to n(z), particularly at the low-redshift end of our sample. We estimated hi from the photometric redshifts measured by Sawicki, Lin, & Yee (1997) in the Hubble Deep Field (HDF) (North). 5 The background galaxies were 5 We converted I F814W AB magnitudes to Cousins I using I I F814W;ST ¼ 1:22 (Biretta et al. 2000) and adopted the I F814W ABMAG STMAG ¼ 0:819 conversion tabulated in the HDF Web site (see

22 334 DAHLE ET AL. Vol. 139 Fig. 17. A1722 binned by magnitude as follows: one bin with I < 21:0, one bin with I > 25:0, and bins of DI ¼ 0:5 covering the interval between these two values (essentially all of the measured shear signal comes from galaxies within the 21:0 < I < 25:0 interval). For each bin, the corresponding magnitude cuts were made in the HDF catalog, and the average (from the HDF photometric redshifts) and the average weight hq 2 iof the N gi galaxies in that bin were calculated. The average hi for the whole galaxy sample was then computed as hi ¼ X Nbins N i¼1 g i hi i Q 2 i X : ð17þ Q 2 For the data presented in this paper, hi as a function of lens redshift was adequately approximated (for an Einstein de Sitter cosmology) by the empirical relation hi ¼ 1:40z l þ 0:91 in the 0:15 < z l < 0:35 range. This is equivalent to having a single-screen source population at an effective redshift of 0.77 and 0.72 for a lens redshift of z l ¼ 0:35 and 0.15, respectively. For a low-density cosmology with m ¼ 0:3, ¼ 0, the corresponding values for hi will increase by up to 5%, and for a spatially flat cosmology with ¼ 0:7, the value for hi will increase by about 10% for the most distant clusters in our sample. The mass values given here may easily be scaled with updated hi values when more precise information becomes available about cosmological parameters and the redshift distribution of faint galaxies. The dominant random noise contribution to our mass measurements comes from the intrinsic spread in galaxy shapes. In addition to the random uncertainty, there are several systematic effects that may significantly affect our weak lensing mass measurements. Some effects that may affect

23 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 335 Fig. 18. A1995 our results at the 10% 20% level include uncertainties in our knowledge of the faint galaxy redshift distribution and the underlying cosmological model (both briefly discussed above) and possible contamination of cluster galaxies in the faint galaxy catalogs, which will be discussed in detail in a future paper concerning the average mass density profile of cluster halos. In addition, a false shear signal would arise from intrinsic alignments of galaxy orientations. Several recent studies (e.g., Croft & Metzler 2000; Brown et al. 2000) indicate that this will only be a minor effect for our data set, given the broad redshift distribution of the faint galaxies and the relatively high median redshift of our faint galaxy catalogs (z m ¼ 0:85). To facilitate the comparison of our results to cluster mass estimates from virial analysis, we fitted our measurements of hg T i to a singular isothermal sphere (SIS) model. The resulting weak lensing estimates of the cluster velocity dispersion WL are listed in Table CLUSTER PROPERTIES In this section we provide brief notes on the properties of individual clusters. For information on individual clusters, the reader is also referred to the maps in Figures 7 45, the aperture mass plots in Figures 50 and 51, and the SIS mass profile fits in Table A68 About a dozen strongly gravitationally lensed arcs and arclets are visible in the central regions of this cluster, surrounding both of the two brightest cluster galaxies, which are separated by about 1<5. The mass distribution is strongly elongated along the axis joining these two galaxies, indicating a possible ongoing merger of two mass concentrations. The peak positions of the mass, light, and number density distributions coincide well, but the mass distribution appears more elongated than the light and number density

24 336 DAHLE ET AL. Vol. 139 TABLE 2 SIS Model Fit to Radial Shear Profile Designation WL v 2 /dof (dof) A (5) A þ (5) A (9) A þ (9) A þ (9) A (9) A þ (5) A þ (5) A þ (5) Zw þ (5) A þ (5) A þ (9) A þ (9) A þ (9) A þ (9) A þ (9) A þ (5) Zw þ (5) A (9) A þ (5) A þ (9) A (9) A þ (5) A þ (5) A þ (5) A þ (5) A (9) Zw (5) RX J þ (5) A þ (5) A (5) A þ (5) A þ (5) RX J þ (5) A þ (5) A þ (5) RX J þ (5) A þ (9) distributions. As indicated by Figure 51 and Table 2, this is one of the most massive clusters in our observed sample A115 As shown by Shibata et al. (1999), this cluster is probably undergoing a major merger of two subconcentrations. The temperatures of the two peaks seen in their ASCA X-ray data are similar, but the northern peak has about twice the X-ray luminosity of the southern peak. The region between the two peaks has a significantly higher temperature, probably caused by shock heating in connection with the merger. Unfortunately, the field of view of the 2k images analyzed here only includes the southern peak (labeled region C by Shibata et al. 1999) which is estimated to be less massive than the northern peak, which is outside the field of view. The highest peak in our mass map is well aligned with the brightest galaxy of the southern peak. The mass distribution in the field has a strongly extended, filamentary morphology with four apparent subpeaks. As noted in x 4.2, the presence of such subpeaks in the area covered by the control annulus will bias downward the estimated aperture mass plotted in Figure 51. Two of the subpeaks, situated north and northwest of the strongest mass peak, are well aligned with subpeaks in the cluster light distribution. The overall appearance of this cluster is indicative of an unrelaxed system A141 Judging from the optical images, this cluster does not appear to have a well-defined center. The galaxy distribution is elongated roughly along a north-south axis, and there is an 2 0 offset between the highest peaks in the cluster light and galaxy density distributions. The latter is situated closer to the mass peak (see Figs. 7 and 21), although the mass distribution in Figure 21 also shows a second, lower peak closer to the peak in the light distribution. As noted in x 2.3.3, the UH8K data for A141 were obtained in strongly variable observing conditions, and as a result of this the mass map in Figure 7 has significantly higher noise than the mass map in Figure 21. A bright cluster galaxy located close to the peak in the cluster mass distribution is surrounded by a system of faint arc(let)s. A bright galaxy situated further toward the southeast, near the dominant peak in the galaxy light distribution, has an asymmetric, apparently disturbed, envelope indicative of recent merger activity A209 This cluster is dominated by a central cd galaxy. The peak in the cluster mass distribution is close to this galaxy (see Fig. 8), and a candidate gravitational arc is visible inside the cd halo. The mass, light, and number density distributions all show an extension to the south from the cluster center. A second, lower mass peak about 5 0 north of the cluster center corresponds to a peak in the galaxy density distribution but does not contribute significantly to the galaxy flux in the field. This peak could be associated with a high-redshift cluster, but this feature lies outside the area covered by our V-band observations, and the lack of color information makes it difficult to assess the nature of this feature. ROSAT HRI data of this cluster indicate an irregular X-ray morphology with significant substructure (Rizza et al. 1998) A267 This cluster appears as a relaxed system, with a center dominated by a giant cd galaxy. The peaks in the mass, light, and number density distributions are all very well aligned with this galaxy. A bright arc candidate is visible about north-northwest of the cd galaxy. A foreground cluster identified by Bade et al. (1998), RX J , is centered around ¼ 01 h 53 m 15 s, ¼ 1 02<5, near the southern end of chip 4, and is responsible for the second highest peak in the predicted map shown in Figure 9. The redshift of RX J is currently unknown A520 This cluster, also known as MS , appears complex, with no well-defined center judging from the optical images. A giant arc discovered by Le Fèvre et al. (1994) is visible around a giant elliptical galaxy at ¼ 04 h 54 m 20 s, ¼ 2 57<7. This galaxy is offset toward the northeast from the peaks in the mass, light, and galaxy distributions. The mass distribution derived from UH8K data has three main peaks, two of which coincide

25 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 337 Fig. 19. Mass, light, and galaxy number density distributions in the field of A68. In the upper left plot, all galaxies with M B < 15:0 þ 5logh are plotted as circles, with areas proportional to the flux. The circles are shaded according to the V I colors of the galaxies, with darker shades indicating redder galaxies. The circles above the plot indicate the no-evolution prediction for the fluxes and colors of E0-, Sbc-, and Scd-type galaxies with M B ¼ 19:68 þ 5logh as a function of redshift. The upper right plot shows the projected mass density in the field, inferred using the maximum probability method of Squires & Kaiser (1996). The scale bar on the right runs from zero to the highest value. The lower left plot shows a prediction of the surface mass density in the field, based on galaxy photometry in the field. The contour levels are the same as in the upper right figure. The lower right plot shows the number density of galaxies in the field. The three surface density plots have all been smoothed with a Gaussian filter of the same size (see xx and 4.1 for further details). The plots in Figs contain the same information as this figure for other clusters. closely with peaks in the light and number density distributions. According to Le Fèvre et al. (1994), this cluster has a complex X-ray structure, and it may still be forming, with subcluster concentrations in the process of merging. However, our estimated velocity dispersion of km s 1 is consistent with the spectroscopically measured value of km s 1 (Carlberg et al. 1996). The field of this cluster is rich in stars and is well suited to study the PSF anisotropy and distortion at the Cassegrain focus of the UH 2.24 m (see Figs. 2 and 5) A586 A586 is one of the most massive clusters in our observed sample. A very strong, single mass peak is seen in this field,

26 338 DAHLE ET AL. Vol. 139 Fig. 20. A115 closely aligned with the central galaxy. The cluster appears completely relaxed, with a core dominated by a central cd galaxy. There is a long faint blue arc (with some foreground galaxies superposed on it) to the northwest of the central galaxy. Buote & Tsai (1996) study the morphology of this cluster in ROSAT PSPC images and find that it is likely to be a relaxed system. As indicated by Figure 51 and Table 2, this is one of the most massive clusters in our observed sample A665 This cluster is notable as the only one classified by Abell as R ¼ 5, although Oegerle et al. (1991), who measure a galaxy velocity dispersion of 1201 þ km s 1, see a foreground structure at z 0:12 which may be responsible for boosting the apparent richness. Yee & López-Cruz (1999) show that the richness has been significantly overestimated by Abell and that there are a number of Abell clusters which have similar richness to A665. Buote & Tsai (1996) suggest that the X-ray emitting gas in A665 may be in a short-lived transition phase going from following a distribution similar to the distribution of dissipationless matter (or being in virial equilibrium in several subcluster-sized clumps) to a distribution following the overall cluster potential. The dynamical study of Oegerle et al. (1991) seems consistent with this picture: the distribution

27 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 339 Fig. 21. A141 of 33 observed radial velocities is consistent with a Gaussian, and no significant spatial velocity correlations are seen, but other statistical tests indicate the presence of substructure in the cluster, and the brightest cluster member has a velocity which deviates at the greater than 2 level from the median cluster velocity. Chandra ACIS-I data show a highly non-isothermal temperature structure in the center of this cluster (Markevitch & Vikhlinin 2001). The X-ray luminosity distribution has an extension toward north-northwest, and there is a hot bow shock region southeast of the core, indicating an ongoing merger. Our mass map shows a mass peak well aligned with the central, brightest cluster member galaxy, and the mass distribution appears to have a position angle similar to that of the central galaxy. The mass distribution shows an extension toward north-northwest, similar to what is seen in the Chandra X-ray luminosity distribution. There are several faint arc candidates in the field A697 This is one of the most massive clusters in our sample. The halo of the central cd galaxy in this cluster has a peculiar disturbed morphology, indicative of a recent merger. There are two arc candidates in this cluster, discovered by Metzger & Ma (2000). The positions of the peaks in the mass, light, and number density distributions coincide very

28 340 DAHLE ET AL. Vol. 139 Fig. 22. A586 well, although the mass distribution is more elongated than the latter two. The mass distribution is elongated along the major axis of the faint, outer parts of the cd halo (which shows strongly twisting isophotes), and this may indicate a recent head-on collision of two mass clumps along this axis. The central cd galaxy has a double nucleus, which also supports the merger hypothesis. An X-ray image from a 28 ks ROSAT HRI exposure shows an elliptical X-ray luminosity distribution with a position angle similar to that of the dark matter. A comparison of the mass and light maps in Figure 24 clearly shows that A697 has an unusually high mass-tolight ratio (see also H. Dahle et al. 2002c, in preparation). A697 also has the lowest SZ-derived gas mass fraction of the 18 clusters measured by Grego et al. (2001), raising the interesting possibility that this is an unusually baryonpoor cluster A773 This cluster has a center which is extremely optically rich and contains almost only early-type galaxies. There is a strong peak in the mass map, offset to the southwest from the optical cluster center by about 1 0. A 16 ks ROSAT HRI exposure of this field shows an X-ray luminosity peak which

29 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 341 Fig. 23. A665 is situated between the peaks in the mass and light distributions (Saunders et al. 2001). However, the X-ray morphology of this cluster displays extreme amounts of substructure, according to Rizza et al. (1998). The mass appears elongated in a different direction than the light and number density distributions. Several faint candidate arc(let)s are visible in the central regions of the cluster A914 and A922 A914 and A922 are at very similar redshifts (0.193 and 0.189, respectively) and are separated by only 11 0 in the plane of the sky, corresponding to a projected distance of 1.4 h 1 Mpc at the redshift of the clusters. Numerical simulations of structure formation and other theoretical work (Bond, Kofman, & Pogosyan 1996) predict that pairs of clusters like A914 and A922 are connected by filaments of gas and dark matter, but such a filament is not convincingly seen in the weak lensing data. Although A914 has an X-ray luminosity more than 3 times that of A922 (Briel & Henry 1993), A922 is associated with the strongest mass peak in the field. However, a comparison of the surface density plots in Figure 11 shows that the two clusters have similar richness and total luminosity. In Figure 50 we plot the aperture mass profile of the most massive of the two clusters, but the aperture mass of A922 is biased downward by the presence of A914 inside the control annulus.

30 342 DAHLE ET AL. Vol. 139 Fig. 24. A A959 The published redshift of z ¼ 0:35 for this cluster is incorrect, the correct value being z ¼ 0:285 (R. J. Irgens et al. 2002, in preparation); hence, its X-ray luminosity is somewhat lower than the value listed by Briel & Henry (1993). The cluster is not dominated by any single galaxy, but it has a core region consisting of many early-type galaxies of similar brightnesses. A highly significant mass peak is seen in both the 2k and 8k mass maps, and the dark matter distribution appears to resemble the cluster light and mass distributions. The mass distribution in Figure 12 has two peaks near the cluster center, but the noise in the mass reconstruction may be responsible for splitting the central cluster mass into two peaks. A third mass peak is visible about 6 0 southwest of the optical cluster center. The mass reconstruction based on 2k data plotted in Figure 26 only shows a single peak which is elongated in the same direction as the peaks in the light and number density distributions. The aperture mass plot in Figure 50 shows this cluster to be very massive, in

31 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 343 Fig. 25. A773 spite of the modest value for the WL value listed in Table 2. However, this WL value is not very meaningful, since the cluster is very poorly fit by an SIS-type profile A963 Lavery & Henry (1998) report a measured velocity dispersion of 1350 þ km s 1 for this cluster. They also find that the X-ray emitting gas has an elliptical distribution with position angle similar to that of the central cd galaxy. The innermost isodensity contour in the mass map is also aligned along this axis. There are two arcs on opposite sides of the cd galaxy, discovered by Lavery & Henry (1988). The relatively short exposure times for this cluster give a noisier mass map than for most other clusters. There is a mass peak coincident with the position of the central cd in the cluster, but the S/N level is rather low (around 2 ) A1351 A1351 has an elongated luminosity distribution indicating a possible ongoing merger. Other evidence for this comes from the unusually high velocity dispersion of 1680 km s 1 measured by R. J. Irgens et al. (2002, in preparation) and the presence of a bright red gravitational arc offset from the cluster light center. A1351 appears to be the most massive of the clusters observed with the UH8K, and it gives the most significant zero-lag peak (13 ) resulting from a two-

32 344 DAHLE ET AL. Vol. 139 Fig. 26. A959 dimensional cross-correlation of the mass and light distributions in the field (H. Dahle et al. 2002c, in preparation). The position and position angle of the peak in the mass distribution both closely match the light and number density distributions in this field. A possible mass filament appears to extend from the cluster center toward the southeast A1423 The cluster center is dominated by a single large cd galaxy. The cluster is close to the lower X-ray luminosity cutoff for the cluster sample selection and shows only a modest weak lensing signal. A few candidate arc(let)s are visible around the central galaxy. There is some confusion regarding the correct redshift of this cluster. The redshift value listed in Table 1 is the redshift measured by Crawford et al. (1995) for the brightest galaxy within our observed field. Postman, Huchra, & Geller (1992) obtain a much lower redshift of z ¼ 0:0761 for A1423, based on spectroscopic measurements of three galaxies. If a significant part of the measured X-ray flux originates at this lower redshift, the X- ray luminosity given in Table 1 would be significantly overestimated, and the cluster would also be a much less effective lens at this lower redshift. In this field, we measure a median color of bright (I < 21) galaxies of V I ¼ 1:44, consistent with predictions for the color of the early-type galaxy sequence at z ¼ 0:213 and greater than 0.2 mag redder than the predicted color of early-type galaxies at z ¼ 0:0761 (see Fig. 47).

33 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 345 Fig. 27. A A1576 There are about half a dozen faint blue arclets surrounding the cluster core of A1576. The central brightest cluster member has three bright nuclei embedded in a common envelope, indicative of a merger in an advanced stage. The radial shear profile is very poorly fit by an SIS-type model, also indicating significant dynamical activity in this cluster. The light, mass, and galaxy density distributions (Fig. 15) indicate the presence of multiple peaks in this cluster, although the position of the peaks differs somewhat in the three maps. The strongest peak in the galaxy light distribution is offset by about 3 0 from the peak in the galaxy number density distribution. The highest mass peak coincides most closely with the light peak but shows an extension toward the peak in the number density distribution. Several additional subpeaks in the field are visible in all three maps, with good positional agreement. A two-dimensional crosscorrelation of the mass and light distributions in this field gives a zero-lag significance of 7, but the mass appears to be significantly more concentrated than the light (H. Dahle et al. 2002c, in preparation) A1682 This cluster appears very rich in the optical images. The light in the cluster center is dominated by two bright elliptical galaxies, but there is also an additional dense concentra-

34 346 DAHLE ET AL. Vol. 139 Fig. 28. A1682 tion of galaxies about 2 0 southeast of the two bright ellipticals. The binary nature of this cluster is also evident in the mass map (Fig. 28), which shows one peak located between the two bright E galaxies and a second peak which closely coincides with the dominant peak in the galaxy number density distribution A1705 The reconstruction of this field (see Fig. 16) shows a number of secondary peaks in addition to the highest mass peak, which is associated with the center of A1705. Some of the other mass peaks are clearly associated with structures at different redshifts, and this cluster field will be the subject of a separate paper in this series, along with the field of A A1722 As shown in the mass map (Fig. 17), there is a second peak in the mass distribution which is almost as significant as the A1722 mass peak itself. The nature of this feature will be discussed in a separate paper A1758 In our optical images, A1758 appears as a double cluster which is possibly in the process of merging into a single massive cluster. Both subclumps appear locally relaxed and

35 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 347 Fig. 29. A1758 strongly concentrated around a bright early-type galaxy. There is an apparent blue arc associated with the northwest mass clump. The mass map shows a highly elongated mass concentration, bridging the gap between the two subclusters. The total mass of this cluster is very high, as indicated by the aperture mass plot in Figure 51 and the WL value in Table 2. A third galaxy concentration is located about 4 0 south of the edge of the field. Observations of a 30 0 field centered on this triple cluster have been obtained with the 3.6 m CFHT, and the results will be described in a future paper A1763 The cluster center is well defined and dominated by a cd galaxy. The peak in the mass distribution is situated at the position of the central cd galaxy. The mass, light, and number density distributions all give the appearance of a relaxed system A1835 A1835 is the most X-ray luminous cluster of galaxies in the XBAC and BCS catalogs. From an analysis of 30 ks of

36 348 DAHLE ET AL. Vol. 139 Fig. 30. A1763 Chandra observations of this cluster, Schmidt, Allen, & Fabian (2001) find a steep drop in the X-ray gas temperature from kt 12 kev at 0.5 h 1 Mpc to kt 4 kev at the cluster core, and they find a cooling flow with a mass deposition rate of 230 þ80 50 M yr 1. The cluster has a regular morphology in the X-ray image, indicating that A1835 is a relaxed system. The presence of the cooling flow and the optical appearance of the cluster also indicate that all the constituents (galaxies, the hot intracluster medium [ICM], and dark matter) of the cluster are in dynamical equilibrium. The light map in Figure 31 is contaminated by a bright foreground galaxy close to the north edge of the field. The mass map shows a strong peak, well aligned with the position of the central cd galaxy, and similar peaks in the light and number density distributions. Several blue arcs are visible around the cluster center. By fitting the X-ray gas temperature profile to a Navarro, Frenk, & White (1997) model of the mass density distribution, Schmidt et al. (2001) obtain an effective velocity dispersion ¼ 1275 þ km s 1, consistent with, but slightly higher than, our SIS model fit result given in Table 2. Schmidt et al. (2001) also obtain a similar result by fitting their X-ray data to a nonsingular isothermal sphere model, and the mass values we plot in Figure 51 are also in good agreement with the best-fit Navarro et al. (1997) model derived by Schmidt et al. (2001) for the radial mass profile.

37 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 349 Fig. 31. A A1914 The mass peak is located inside the triangle formed by the three brightest early-type cluster members and appears to have extensions toward each of these galaxies. Both the light distribution and the galaxy number density distribution in the cluster are highly elongated, and both have peaks that coincide closely with the mass peak. An analysis of the X-ray morphology of this cluster by Buote & Tsai (1996) indicated that A1914 is a relaxed system, but Jones et al. (2001) point to several pieces of evidence that suggest otherwise, including the absence of a cooling flow, the high X-ray temperature, the lack of a well-defined center in optical images, and the fact that the X-ray data are very poorly fitted by a model. Furthermore, Jones et al. (2001) derive a Hubble constant H 0 ¼ 119 þ46 38 km s 1 Mpc 1 from SZ measurements in this cluster, 1.6 above the mean H 0 value obtained from their sample of five clusters. Our mass map also seems to indicate an unrelaxed system, with a mass center that is significantly offset from the brightest cluster galaxy. Several red and blue arc candidates are visible near the mass center and around the brightest cluster galaxy A1995 The light distribution in this cluster is quite strongly elongated in the northeast-southwest direction, but the mass distribution in A1995 is more circularly symmetric and

38 350 DAHLE ET AL. Vol. 139 Fig. 32. A1914 concentrated than the light distribution. The X-ray morphology in a 37 ks ROSAT HRI exposure analyzed by Patel et al. (2000) appears very similar to our mass map. The aperture mass plot in Figure 50 shows that almost all the mass in A1995 appears to be contained within the innermost (0.6 h 1 Mpc). This peculiar feature cannot be easily explained by a bias caused by secondary mass peaks in the control annulus, since the mass map in Figure 18 shows little evidence for significant additional mass concentrations in this field. Other clusters such as A959 or A1351 show a very different behavior in Figure 50, their masses increasing with radius, even at large radii. We have recently obtained data with the CFH12K camera on the 3.6 m CFHT covering larger fields around A1351 and A1995, and we plan to investigate whether this discrepancy becomes even more conspicuous with increasing radius. There are several blue arcs visible in this cluster, including one arc associated with a group of galaxies 2 0 southwest of the cluster center. A bright foreground galaxy, IRAS F , has a strongly disturbed outer halo with antenna-like tidal tails A2104 There is a bright, very red arc discovered by Pierre et al. (1994) visible through the halo of the central cd galaxy. This galaxy is well aligned with the peaks in the mass, light,

39 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 351 Fig. 33. A2104 and galaxy number density distributions. The mass distribution and light distribution both appear elliptical, but they are elongated in almost perpendicular directions. Although this cluster is below the X-ray luminosity cutoff for the cluster sample selection, it has an estimated mass above the sample average (see Table 2). The measured cluster galaxy velocity dispersion of km s 1 (Liang et al. 2000) is reasonably consistent with our estimate A2111 Henriksen, Wang, & Ulmer (1999) use ASCA and ROSAT PSPC data to detect a highly significant temperature gradient in A2111, with a higher temperature cluster core (kt ¼ 6:46 0:87 kev at R < 3 0 ) surrounded by a cooler region (kt ¼ 3:10 1:19 kev at 3 0 < R < 6 0 ). The non-isothermality of the ICM may indicate a system which has undergone a recent merger which heated the ICM in the cluster center, or it may be due to the gravitational potential of the cluster. In optical images, the cluster core is dominated by two bright early-type galaxies separated by about 1 0. The mass map shows a peak situated between the two brightest cluster galaxies, but closer to the brightest galaxy of the pair. The light and number density distributions both have a much more elongated morphology than the mass distribution. By itself, the cluster mass distribution does not provide any strong evidence for significant dynamical activity within this cluster. There are several very red arc candi-

40 352 DAHLE ET AL. Vol. 139 Fig. 34. A2111 dates around the mass center. A secondary mass peak in the northeast corner of our image is most likely an artifact, given its proximity to the corner and the absence of any corresponding peaks in the light and number density distributions A2204 This cluster constitutes a difficult target for optical observations, as there is a strong gradient in the background light, caused by the bright foreground star PPM (V ¼ 5:6), situated only 4 0 southwest of the cluster center. Most of the gradient was removed by subtracting a highly smoothed version of the sky. A2204 has a massive cooling flow (Peres et al. 1998), indicating a dynamically relaxed system. The innermost contours in the mass, light, and number density distributions are all elongated roughly in the eastwest direction, and so is the halo of the central galaxy, which has two nuclei of similar brightness embedded in a common envelope. There are about a dozen red and blue arcs and arclets surrounding the central cluster galaxy A2219 This cluster has a pair of strongly lensed arcs, discovered by Smail et al. (1995b). Bézecourt et al. (2000) fitted an SIS-

41 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 353 Fig. 35. A2204 type model to weak shear measurements around A2219 to obtain DM ¼ , consistent with our result. The mass distribution we obtain from our weak lensing analysis peaks close to the peaks in the light and number density distributions but appears significantly more elongated than either of these. The mass maps derived by Bézecourt et al. (2000) from strong and weak gravitational lensing also show significant substructure in the mass distribution of this cluster A2261 This cluster has a similar appearance to A586: the galaxy light distribution is circularly symmetric, and the cluster center is dominated by a bright cd galaxy. The mass and number density distributions are both more elongated than the light distribution, and they are both extended roughly in the same direction, although the mass peak is offset by about 1 0 northwest from the light and number density peaks. There is a bright, thin blue arc southwest of the cd galaxy A2345 The cluster has a well-defined core dominated by a cd galaxy, and the light and number density distributions both have peaks situated close to the central cd. A2345 has an X-ray luminosity which is marginally below the nominal

42 354 DAHLE ET AL. Vol. 139 Fig. 36. A2219 cutoff limit for our sample selection (see x 2.1). We therefore expect it to be one of the least massive clusters in our sample, and this is confirmed by the relatively modest value for WL in Table 2. An archival ROSAT HRI exposure of 12 ks shows a very large amount of substructure in this cluster, with multiple subpeaks, indicating that it may be a dynamically young system. The highest peak in our mass map is offset to the east from the central cd by 1<5, although a secondary peak lies much closer to the cd. A cross-correlation of the light and mass distributions in this field gives a 2 peak at zero lag (H. Dahle et al. 2002c, in preparation) A2537 This cluster has several red and blue arcs, mostly surrounding the central cd galaxy, but there are also some arcs associated with the second brightest cluster galaxy which is situated 1 0 southeast of the cluster center. The mass distribu-

43 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 355 Fig. 37. A2261 tion is extended in a different direction than the light and galaxy number density distributions, but the positions of the central peaks coincide well with each other in all three surface density plots in Figure RX J This cluster has a compact core with an unusually blue brightest cluster galaxy in the center surrounded by fainter, redder galaxies. The mass, light, and number density distributions match each other very well both in morphology and peak position. A second light peak toward northeast may be associated with foreground galaxies, since there is no similar peak in the mass and number density distributions, although both distributions show an extension toward northeast. The high value for WL in Table 2 indicate that RX J is one of the most massive clusters in our sample RX J The cluster core is dominated by a single galaxy with an extended envelope, and the cluster has an optical appearance similar to A586 and A2261. The peaks in the mass, light, and number density distributions all coincide well with the position of the central galaxy. Mazzotta et al.

44 356 DAHLE ET AL. Vol. 139 Fig. 38. A2345 (2001b) analyze Chandra data of this cluster and find an X- ray surface brightness peak situated at the position of the central cluster galaxy. The X-ray surface brightness contours at large radii have a regular appearance typical for a relaxed system, but there is a sharp edge 125 h 1 kpc southeast of the cluster center and a plateau at the opposite, northwest side of the center. These features mark the extent of a central, dense cold (kt 4 kev) gas cloud surrounded by a much hotter region with kt 10 kev. Mazzotta et al. (2001b) interpret this peculiar system as either the result of a merger in a very late stage or the result of having a groupsized density perturbation collapse almost at the same location as a more massive cluster in a way that has preserved the cooler gas halo of the group-sized perturbation. A mass estimate assuming hydrostatic equilibrium and using the gas density properties of a sector located northwest of the cluster center is consistent with our weak lensing mass measurements for RX J shown in Figure 51, but a similar estimate using the gas density properties in the southeast sector tends to strongly underestimate the cluster mass at small radii (Mazzotta et al. 2001b). The sharp jumps in density and X-ray temperature found by Mazzotta et al. (2001b) suggest a system in which the central cool gas cloud is moving with respect to the ambient medium. Such motions would invalidate the assumption of hydrostatic equilibrium, and Mazzotta et al. (2001b) suggest that this

45 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 357 Fig. 39. A2537 may be responsible for the discrepancy between X-ray mass estimates (based on hydrostatic equilibrium) and strong lensing mass estimates reported for some clusters. We find three strongly lensed images inside the envelope of the central galaxy, including a thin, highly elongated feature southwest of the cluster center. If we assume a redshift z s ¼ 1 for this galaxy and assume that it is located at the Einstein radius of a spherically symmetric gravitational lens, the projected mass within 20 h 1 kpc is 7: h 1 M, consistent with the mass estimate of Mazzotta et al. (2001b) using Chandra data in the northwest sector but much higher than their mass estimate using the southeast sector RX J The cluster core is dominated by a cd galaxy. The mass, light, and number density distributions all peak close to the cd and all show similar structure, with an extension toward southwest. The secondary peak in the mass map close to the northwest corner of the field is most likely an artifact. A bright secondary peak in the light map near the west edge of the field is due to a bright foreground galaxy Zw 2089 Zw 2089 lies close to the X-ray luminosity cutoff limit for our sample selection and was observed with the shortest

46 358 DAHLE ET AL. Vol. 139 Fig. 40. RX J exposure time of any of the clusters. The fact that we only had two exposures in each passband also made it difficult to completely remove artifacts such as cosmic rays. The cluster seems very extended in the northeast-southwest direction in the optical images, and this highly elongated morphology is also apparent in the light and galaxy number density distributions. This is the only cluster for which a two-dimensional cross-correlation of the light and mass distributions does not give a significant peak at zero lag (H. Dahle et al. 2002c, in preparation), which indicates that the mass map is dominated by noise Zw 5247 This cluster does not have a single, well-defined center but appears to consist of several subconcentrations. The light map shows three distinct peaks, but the southernmost peak is associated with a probable foreground galaxy which is significantly bluer than typical early-type cluster galaxies at the redshift of Zw 5247, although it has an early-type morphology. The densest galaxy concentration, in the northeast part of the image, closely matches similar peaks in the mass and light distributions. Another peak in the light distribution is

47 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 359 Fig. 41. RX J associated with the brightest cluster galaxy which is situated close to the center of our observed field. The highest peak in the mass map is located less than 1 0 southwest of this galaxy Zw 7160 This cluster, also designated MS , was one of the clusters targeted in the weak lensing study by Smail et al. (1995a). It has a possibly massive cooling flow (Allen et al. 1996), and it has one bright blue arc, discovered by Le Fèvre et al. (1994), plus several fainter red and blue arcs. A bright radial arc in the southern part of the cd halo was found by Newbury & Fahlman (1999), who also developed a strong lensing model for this system. The dominant peak in the light distribution in Figure 45 is caused by an elliptical galaxy which is likely to be a field galaxy in front of the cluster, since it has no associated X-ray emission (Smail et al. 1995a; Mazzotta et al. 2001a) and is slightly bluer than early-type galaxies at the cluster redshift. The data of Smail et al. (1995a) are based on a longer integration time on a larger telescope (the 4.2 m WHT), but with poorer seeing (0>9 in the I band vs. 0>7 for our data) and a less sensitive CCD. The V-band catalog used here actually has a slightly higher source density than the I-band catalog they used for their weak lensing measurements. The mass map presented here is similar to theirs and appears elongated in the same

48 360 DAHLE ET AL. Vol. 139 Fig. 42. RX J direction, but we see no evidence for the secondary dark peak visible in their mass maps. We conclude that this is probably a noise peak. The peak in the mass distribution is very closely centered on the cd galaxy in the cluster center, and the mass distribution is elongated in the same direction as the cd halo. Mazzotta et al. (2001a) analyze Chandra data of Zw 7160 and find it to have X-ray characteristics similar to RX J (see x 5.33) with a cool core bounded by sharp edges in the surface brightness distribution to the north and south of the cluster center. The most likely explanation for this structure is the movement of a cooler, group-sized subhalo along the major axis of the dark matter distribution in the cluster. As for RX J , Mazzotta et al. (2001a) propose that the cool core corresponds to an old group-sized halo which was formed almost at the same location as the cluster, instead of being a remnant of a recent merger event involving an infalling subhalo which was formed outside the main cluster. The main arguments against the latter scenario are the relaxed overall appearance of the X-ray surface brightness distribution and the possible presence of a massive cooling flow. However, given the highly elongated dark matter distribution seen in our mass map, it appears that a merger scenario cannot be ruled out. Carlberg et al. (1996) measure a velocity disper-

49 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 361 Fig. 43. Zw 2089 sion for Zw 7160 of km s 1, consistent with the result obtained from an SIS-type model fit to our weak lensing data. 6. CONCLUSIONS The data set presented here more than doubles the total number of galaxy clusters with a measured weak lensing signal. Furthermore, the cluster sample was generated using well-defined selection criteria, and the weak lensing data were reduced and analyzed in a consistent way for all the clusters, making the resulting data set very useful for statistical studies of cluster properties. In future papers we will further exploit this data set to study the relative amount and distribution of mass and light in the clusters (H. Dahle et al. 2002c, in preparation), measure the average cluster density profile and use it to constrain dark matter properties (H. Dahle et al. 2002d, in preparation), and measure the cluster mass function and its evolution at redshifts 0:1 < z < 0:3 (H. Dahle et al. 2002d, in preparation). We will also compare our weak lensing mass measurements to cluster mass determinations from virial analysis of a subset of our cluster sample (R. J. Irgens et al. 2002, in preparation). The data represent a total observing time of about 30 nights on the NOT and the UH 2.24 m telescope. The excellent image quality of these two telescopes is probably unique

50 362 DAHLE ET AL. Vol. 139 Fig. 44. Zw 5247 for 2 m class telescopes and has been a crucial factor in the success of this effort. All but one cluster in our X-ray selected cluster sample display a significant weak lensing signal, which demonstrates that high X-ray luminosity is an excellent criterion for selecting very massive clusters with deep potential wells. This is also demonstrated by the fact that more than 50% of the clusters display strongly lensed arcs and arclets. The mass distribution in the cluster fields shows a range of morphologies, from circularly symmetric, apparently relaxed, systems to clusters with multiple subconcentrations in various stages of mergers. About 30% of the clusters in our sample show clear indications of significant dynamical activity. Jones & Forman (1999) find that 15 of 38 X-ray luminous clusters at z < 0:2 contain substructure in their X- ray emission, in reasonable agreement with our weak lensing results. From a weak lensing study of six clusters at high redshifts (z > 0:5), Clowe et al. (2000) find that at least half of massive clusters appear not to have fully collapsed, but larger high-redshift cluster samples will be needed to draw firm conclusions about cluster evolution from weak lensing. We thank Harald Ebeling, Pat Henry, Klaus Hodapp, Gerry Luppino, Kristian Pedersen, Somak Raychaudhury, and Gillian Wilson for helpful comments and suggestions. We also thank Doug Clowe for letting us use some of his

51 No. 2, 2002 WEAK LENSING BY X-RAY LUMINOUS CLUSTERS. I. 363 Fig. 45. Zw 7160 observing time at the UH 2.24 m telescope in 1997 April/ May and Gerbs Bauer for obtaining an I-band image of A68. We thank the staff of the University of Hawaii 2.24 m telescope and the Nordic Optical Telescope for support during our observing runs. H. D. gratefully acknowledges support from a doctoral research fellowship awarded by the Research Council of Norway, project number /431. H. D., R. J. I., and P. B. L. thank the Research Council of Norway for travel support. Some of the data presented here have been taken using ALFOSC, which is owned by the Instituto de Astrofisica de Andalucia (IAA) and operated at the Nordic Optical Telescope under agreement between IAA and the NBIfAFG (Astronomical Observatory) of the University of Copenhagen. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

52 Fig. 46. Color-magnitude diagram for 10,686 galaxies in the field containing A914 (z ¼ 0:193) and A922 (z ¼ 0:189). Circled galaxies have been spectroscopically confirmed as cluster members by R. J. Irgens et al. (2002, in preparation). The almost horizontal sequence at V I ¼ 1:4 is formed by early-type cluster galaxies at z ¼ 0:19. The V I colors are measured within a fixed aperture of 2>7. Fig. 47. Johnson-Cousins V I color for different galaxy types as a function of redshift. The galaxy color predictions (solid line: E0; dot-dashed line: Sbc; dotted line: Scd; dashed line: Im) are based on the SEDs of Coleman et al. (1980). The open circles denote median measured colors for I < 21 galaxies in the observed cluster fields. The crosses represent galaxies with spectroscopically measured redshifts by R. J. Irgens et al. (2002, in preparation). The predicted curves are shifted by D(V IÞ ¼ 0:10 to match the observed colors. Fig. 48. KS93 reconstruction of the field of A959, based on a catalog with randomized shear values. This illustrates the typical noise level in the reconstructions displayed in the upper right panels of Figs The scale bar on the right runs from zero to the peak value of. 364