HST Observations of the Gravitationally Lensed Cloverleaf Broad Absorption Line QSO H1413+1143: Modeling the Lens

We investigate gravitational lens models for the quadruply-lensed Cloverleaf BAL QSO H1413+1143 based on the HST WFPC/WFPC2 astrometric and photometric data of the system by Turnshek et al. and the HST NICMOS-2 data by Falco et al. The accurate image positions and the dust-extinction-corrected relative amplifications, along with a possible detection of the lensing galaxy in the infrared, permit more accurate lens models than were previously possible. While more recent models are qualitatively consistent with the HST data, none of the previous models considered the dust-extinction-corrected relative amplifications of the image components. We use the power-law elliptical mass model to fit the HST data. We find that a single elliptical galaxy perturbed by an external shear can fit the image positions within the observational uncertainties; however, the predicted relative magnifications are only roughly consistent with the observational relative amplifications. We find that a primary galaxy combined with a secondary galaxy in the vicinity of the Cloverleaf or a cluster centered (south-)west of the Cloverleaf can fit both the image positions and relative amplifications within the observational uncertainties. We discuss future observations which could be used to test and/or further constrain lens models of the Cloverleaf.Comment: 23 pages (in aaspp.sty) including 5 tables and 3 figures, Accepted for publication in the Astrophysical Journa

The velocity and mass distribution of clusters of galaxies from the CNOC1 cluster redshift survey

In the context of the CNOC1 cluster survey, redshifts were obtained for galaxies in 16 clusters. The resulting sample is ideally suited for an analysis of the internal velocity and mass distribution of clusters. Previous analyses of this dataset used the Jeans equation to model the projected velocity dispersion profile. However, the results of such an analysis always yield a strong degeneracy between the mass density profile and the velocity dispersion anisotropy profile. Here we analyze the full (R,v) dataset of galaxy positions and velocities in an attempt to break this degeneracy. We build an `ensemble cluster' from the individual clusters under the assumption that they form a homologous sequence. To interpret the data we study a one-parameter family of spherical models with different constant velocity dispersion anisotropy. The best-fit model is sought using a variety of statistics, including the overall likelihood of the dataset. Although the results of our analysis depend slightly on which statistic is used to judge the models, all statistics agree that the best-fit model is close to isotropic. This result derives primarily from the fact that the observed grand-total velocity histogram is close to Gaussian, which is not expected to be the case for a strongly anisotropic model. The best-fitting models have a mass-to-number-density ratio that is approximately independent of radius over the range constrained by the data. They also have a mass-density profile that is consistent with the dark matter halo profile advocated by Navarro, Frenk & White, in terms of both the profile shape and the characteristic scale length. This adds important new weight to the evidence that clusters do indeed follow this proposed universal mass density profile. [Abridged]Comment: 37 pages, LaTeX, with 11 PostScript figures. Accepted by the Astronomical Journal, to appear in the May 2000 issue. This replacement version contains an additional Appendix and one additional Figure with respect to the version submitted to astro-ph originall

Cluster Alignments and Ellipticities in LCDM Cosmology

The ellipticities and alignments of clusters of galaxies, and their evolution with redshift, are examined in the context of a Lambda-dominated cold dark matter cosmology. We use a large-scale, high-resolution N-body simulation to model the matter distribution in a light cone containing ~10^6 clusters out to redshifts of z=3. Cluster ellipticities are determined as a function of mass, radius, and redshift, both in 3D and in projection. We find strong cluster ellipticities: the mean ellipticity increases with redshift from 0.3 at z=0 to 0.5 at z=3, for both 3D and 2D ellipticities; the evolution is well-fit by e=0.33+0.05z. The ellipticities increase with cluster mass and with cluster radius; the main cluster body is more elliptical than the cluster cores, but the increase of ellipticities with redshift is preserved. Using the fitted cluster ellipsoids, we determine the alignment of clusters as a function of their separation. We find strong alignment of clusters for separations <100 Mpc/h; the alignment increases with decreasing separation and with increasing redshift. The evolution of clusters from highly aligned and elongated systems at early times to lower alignment and elongation at present reflects the hierarchical and filamentary nature of structure formation. These measures of cluster ellipticity and alignment will provide a new test of the current cosmological model when compared with upcoming cluster surveys.Comment: 29 pages including 13 figures, to appear in ApJ Jan. 2005 (corrected typos, added reference

Cluster Ellipticities as a Cosmological Probe

We investigate the dependence of ellipticities of clusters of galaxies on cosmological parameters using large-scale cosmological simulations. We determine cluster ellipticities out to redshift unity for LCDM models with different mean densities $\Omega_m$ and amplitudes of mass fluctuation $\sigma_{8,0}$. The mean ellipticity increases monotonically with redshift for all models. Larger values of $\sigma_{8,0}$, i.e., earlier cluster formation time, produce lower ellipticities. The dependence of ellipticity on $\Omega_m$ is relatively weak in the range $0.2 \leq \Omega_m \leq 0.5$ for high mass clusters. The mean ellipticity $\bar{e}(z)$ decreases linearly with the amplitude of fluctuations at the cluster redshift $z$, nearly independent of $\Omega_m$; on average, older clusters are more relaxed and are thus less elliptical. The distribution of ellipticities about the mean is approximated by a Gaussian, allowing a simple characterization of the evolution of ellipticity with redshift as a function of cosmological parameters. At $z=0$, the mean ellipticity of high mass clusters is approximated by $\bar{e}(z=0) = 0.248-0.069 \sigma_{8,0} + 0.013 \Omega_{m,0}$. This relation opens up the possibility that, when compared with future observations of large cluster samples, the mean cluster ellipticity and its evolution could be used as a new, independent tool to constrain cosmological parameters, especially the amplitude of mass fluctuations, $\sigma_{8,0}$.Comment: 16 pages, 4 figure

Weak lensing surveys and the intrinsic correlation of galaxy ellipticities

We explore the possibility that an intrinsic correlation between galaxy ellipticities arising during the galaxy formation process may account for part of the shear signal recently reported by several groups engaged in weak lensing surveys. Using high resolution N-body simulations we measure the projected ellipticities of dark matter halos and their correlations as a function of pair separation. With this simplifying, but not necessarily realistic assumption (halo shapes as a proxy for galaxy shapes), we find a positive detection of correlations up to scales of at least 20 h^-1mpc (limited by the box size). The signal is not strongly affected by variations in the halo finding technique, or by the resolution of the simulations. We translate our 3d results into angular measurements of ellipticity correlation functions and shear variance which can be directly compared to observations. We also measure similar results from simulated angular surveys made by projecting our simulation boxes onto the plane of the sky and applying a radial selection function. Interestingly, the shear variance we measure is a small, but not entirely negligible fraction (from ~10-20 %) of that seen by the observational groups, and the ellipticity correlation functions approximately mimic the functional form expected to be caused by weak lensing. The amplitude depends on the width in redshift of the galaxy distribution. If photometric redshifts are used to pick out a screen of background galaxies with a small width, then the intrinsic correlation may become comparable to the weak lensing signal. Although we are dealing with simulated dark matter halos, whether there is a signal from real galaxies could be checked with a nearby sample with known redshifts.Comment: 12 pages, 11 ps figures, emulateapj.sty, submitted to Ap

Measuring the Three-Dimensional Structure of Galaxy Clusters. II. Are clusters of galaxies oblate or prolate?

The intrinsic shape of galaxy clusters can be obtained through a combination of X-ray and Sunyaev-Zeldovich effect observations once cosmological parameters are assumed to be known. In this paper we discuss the feasibility of modelling galaxy clusters as either prolate or oblate ellipsoids. We analyze the intra-cluster medium distribution for a sample of 25 X-ray selected clusters, with measured Sunyaev-Zeldovich temperature decrements. A mixed population of prolate and oblate ellipsoids of revolution fits the data well, with prolate shapes preferred on a 60-76% basis. We observe an excess of clusters nearly aligned along the line of sight, with respect to what is expected from a randomly oriented cluster population, which might imply the presence of a selection bias in our sample. We also find signs that a more general triaxial morphology might better describe the morphology of galaxy clusters. Additional constraints from gravitational lensing could disentangle the degeneracy between an ellipsoidal and a triaxial morphology, and could also allow an unbiased determination of the Hubble constant.Comment: 9 pages, 8 figures, accepted for publication in Astrophys.

The Velocity Dispersion of MS1054-03: A Massive Galaxy Cluster at High Redshift

We present results from a dynamical study of the high redshift, massive, X-ray luminous galaxy cluster MS1054--03. We significantly increase the number of confirmed cluster members by adding 20 to an existing set of twelve; using the confirmed members, we estimate MS1054--03's redshift, velocity dispersion, and mass. We find that z=0.8329 +/- 0.0017, sigma = 1170 +/- 150 km/s, and the central mass is approximately 1.9 +/- 0.5 x 10^{15} h^{-1} M_{odot} (within R=1 h^{-1} Mpc; H_0 =100h km s^{-1} Mpc^{-1}, q_0=0.5). MS1054--03 is one of a handful of high redshift (z>0.5) clusters known that also has X-ray and weak-lensing observations (Donahue et al. 1998; Luppino & Kaiser 1997); we find our dynamical mass agrees with mass estimates from both studies. The confirmation of MS1054--03 as a massive cluster at z~0.8 is consistent with an open (Omega_M~0.3) or flat, Lambda-dominated (Omega_M+Omega_{Lambda}=1) universe. In addition, we compare MS1054--03's velocity dispersion and X-ray temperature to a sample of low and intermediate redshift galaxy clusters to test for evolution in the sigma - T_x relation; we find no evidence for evolution in this relation to z~0.8.Comment: 13 pages, 3 figures, LaTex; Accepted for Publication in the Astrophysical Journa

HST Photometry and Keck Spectroscopy of the Rich Cluster MS1054-03: Morphologies, Butcher-Oemler Effect and the Color-Magnitude Relation at z=0.83

We present a study of 81 I selected, spectroscopically-confirmed members of the X-ray cluster MS1054-03 at z=0.83. Redshifts and spectral types were determined from Keck spectroscopy. Morphologies and accurate colors were determined from a large mosaic of HST WFPC2 images in F606W and F814W. Early-type galaxies constitute only 44% of this galaxy population. Thirty-nine percent are spiral galaxies, and 17% are mergers. The early-type galaxies follow a tight and well-defined color-magnitude relation, with the exception of a few outliers. The observed scatter is 0.029 +- 0.005 magnitudes in restframe U-B. Most of the mergers lie close to the CM relation defined by the early-type galaxies. They are bluer by only 0.07 +- 0.02 magnitudes, and the scatter in their colors is 0.07 +- 0.04 magnitudes. Spiral galaxies in MS1054-03 exhibit a large range in their colors. The bluest spiral galaxies are 0.7 magnitudes bluer than the early-type galaxies, but the majority is within +- 0.2 magnitudes of the early-type galaxy sequence. The red colors of the mergers and the majority of the spiral galaxies are reflected in the fairly low Butcher-Oemler blue fraction of MS1054-03: f_B=0.22 +- 0.05. The slope and scatter of the CM relation of early-type galaxies are roughly constant with redshift, confirming previous studies that were based on ground-based color measurements and very limited membership information. However, the scatter in the combined sample of early-type galaxies and mergers is twice as high as the scatter of the early-type galaxies alone. This is a direct demonstration of the ``progenitor bias'': high redshift early-type galaxies seem to form a homogeneous, old population because the progenitors of the youngest present-day early-type galaxies are not included in the sample.Comment: Accepted for publication in the ApJ. At http://astro.caltech.edu/~pgd/cm1054/ color figures can be obtaine

The Apparent and Intrinsic Shape of the APM Galaxy Clusters

We estimate the distribution of intrinsic shapes of APM galaxy clusters from the distribution of their apparent shapes. We measure the projected cluster ellipticities using two alternative methods. The first method is based on moments of the discrete galaxy distribution while the second is based on moments of the smoothed galaxy distribution. We study the performance of both methods using Monte Carlo cluster simulations covering the range of APM cluster distances and including a random distribution of background galaxies. We find that the first method suffers from severe systematic biases, whereas the second is more reliable. After excluding clusters dominated by substructure and quantifying the systematic biases in our estimated shape parameters, we recover a corrected distribution of projected ellipticities. We use the non-parametric kernel method to estimate the smooth apparent ellipticity distribution, and numerically invert a set of integral equations to recover the corresponding distribution of intrinsic ellipticities under the assumption that the clusters are either oblate or prolate spheroids. The prolate spheroidal model fits the APM cluster data best.Comment: 8 pages, including 7 figures, accepted for publication in MNRA