The Dust Content of Galaxy Clusters

We report on the detection of reddening toward z ~ 0.2 galaxy clusters. This is measured by correlating the Sloan Digital Sky Survey cluster and quasar catalogs and by comparing the photometric and spectroscopic properties of quasars behind the clusters to those in the field. We find mean E(B-V) values of a few times 10^-3 mag for sight lines passing ~Mpc from the clusters' center. The reddening curve is typical of dust but cannot be used to distinguish between different dust types. The radial dependence of the extinction is shallow near the cluster center suggesting that most of the detected dust lies at the outskirts of the clusters. Gravitational magnification of background z ~ 1.7 sources seen on Mpc (projected) scales around the clusters is found to be of order a few per cent, in qualitative agreement with theoretical predictions. Contamination by different spectral properties of the lensed quasar population is unlikely but cannot be excluded.Comment: 4 pages, 3 figure

Cross-correlation Weak Lensing of SDSS galaxy Clusters II: Cluster Density Profiles and the Mass--Richness Relation

We interpret and model the statistical weak lensing measurements around 130,000 groups and clusters of galaxies in the Sloan Digital Sky Survey presented by Sheldon et al. 2007 (Paper I). We present non-parametric inversions of the 2D shear profiles to the mean 3D cluster density and mass profiles in bins of both optical richness and cluster i-band luminosity. We correct the inferred 3D profiles for systematic effects, including non-linear shear and the fact that cluster halos are not all precisely centered on their brightest galaxies. We also model the measured cluster shear profile as a sum of contributions from the brightest central galaxy, the cluster dark matter halo, and neighboring halos. We infer the relations between mean cluster virial mass and optical richness and luminosity over two orders of magnitude in cluster mass; the virial mass at fixed richness or luminosity is determined with a precision of 13% including both statistical and systematic errors. We also constrain the halo concentration parameter and halo bias as a function of cluster mass; both are in good agreement with predictions of LCDM models. The methods employed here will be applicable to deeper, wide-area optical surveys that aim to constrain the nature of the dark energy, such as the Dark Energy Survey, the Large Synoptic Survey Telescope and space-based surveys

Constraining the Scatter in the Mass-Richness Relation of maxBCG Clusters With Weak Lensing and X-ray Data

We measure the logarithmic scatter in mass at fixed richness for clusters in the maxBCG cluster catalog, an optically selected cluster sample drawn from SDSS imaging data. Our measurement is achieved by demanding consistency between available weak lensing and X-ray measurements of the maxBCG clusters, and the X-ray luminosity--mass relation inferred from the 400d X-ray cluster survey, a flux limited X-ray cluster survey. We find \sigma_{\ln M|N_{200}}=0.45^{+0.20}_{-0.18} (95% CL) at N_{200} ~ 40, where N_{200} is the number of red sequence galaxies in a cluster. As a byproduct of our analysis, we also obtain a constraint on the correlation coefficient between \ln Lx and \ln M at fixed richness, which is best expressed as a lower limit, r_{L,M|N} >= 0.85 (95% CL). This is the first observational constraint placed on a correlation coefficient involving two different cluster mass tracers. We use our results to produce a state of the art estimate of the halo mass function at z=0.23 -- the median redshift of the maxBCG cluster sample -- and find that it is consistent with the WMAP5 cosmology. Both the mass function data and its covariance matrix are presented.Comment: 14 pages, 6 figures, submitted to Ap

Precision Measurements of the Cluster Red Sequence using an Error Corrected Gaussian Mixture Model

The red sequence is an important feature of galaxy clusters and plays a crucial role in optical cluster detection. Measurement of the slope and scatter of the red sequence are affected both by selection of red sequence galaxies and measurement errors. In this paper, we describe a new error corrected Gaussian Mixture Model for red sequence galaxy identification. Using this technique, we can remove the effects of measurement error and extract unbiased information about the intrinsic properties of the red sequence. We use this method to select red sequence galaxies in each of the 13,823 clusters in the maxBCG catalog, and measure the red sequence ridgeline location and scatter of each. These measurements provide precise constraints on the variation of the average red galaxy populations in the observed frame with redshift. We find that the scatter of the red sequence ridgeline increases mildly with redshift, and that the slope decreases with redshift. We also observe that the slope does not strongly depend on cluster richness. Using similar methods, we show that this behavior is mirrored in a spectroscopic sample of field galaxies, further emphasizing that ridgeline properties are independent of environment.Comment: 33 pages, 14 Figures; A typo in Eq.A11 is fixed. The C++/Python codes for ECGMM can be downloaded from: https://sites.google.com/site/jiangangecgmm

Cosmological Constraints from the SDSS maxBCG Cluster Catalog

We use the abundance and weak lensing mass measurements of the SDSS maxBCG cluster catalog to simultaneously constrain cosmology and the richness--mass relation of the clusters. Assuming a flat \LambdaCDM cosmology, we find \sigma_8(\Omega_m/0.25)^{0.41} = 0.832\pm 0.033 after marginalization over all systematics. In common with previous studies, our error budget is dominated by systematic uncertainties, the primary two being the absolute mass scale of the weak lensing masses of the maxBCG clusters, and uncertainty in the scatter of the richness--mass relation. Our constraints are fully consistent with the WMAP five-year data, and in a joint analysis we find \sigma_8=0.807\pm 0.020 and \Omega_m=0.265\pm 0.016, an improvement of nearly a factor of two relative to WMAP5 alone. Our results are also in excellent agreement with and comparable in precision to the latest cosmological constraints from X-ray cluster abundances. The remarkable consistency among these results demonstrates that cluster abundance constraints are not only tight but also robust, and highlight the power of optically-selected cluster samples to produce precision constraints on cosmological parameters.Comment: comments welcom

Strong Lens Models for 37 Clusters of Galaxies from the SDSS Giant Arcs Survey

We present strong gravitational lensing models for 37 galaxy clusters from the SDSS Giant Arcs Survey. We combine data from multi-band Hubble Space Telescope WFC3imaging, with ground-based imaging and spectroscopy from Magellan, Gemini, APO, and MMT, in order to detect and spectroscopically confirm new multiply-lensed background sources behind the clusters. We report spectroscopic or photometric redshifts of sources in these fields, including cluster galaxies and background sources. Based on all available lensing evidence, we construct and present strong lensing mass models for these galaxy clusters.Comment: 53 pages; submitted to ApJ

MaxBCG: A Red Sequence Galaxy Cluster Finder

Measurements of galaxy cluster abundances, clustering properties, and mass to- light ratios in current and future surveys can provide important cosmological constraints. Digital wide-field imaging surveys, the recently-demonstrated fidelity of red-sequence cluster detection techniques, and a new generation of realistic mock galaxy surveys provide the means for construction of large, cosmologicallyinteresting cluster samples, whose selection and properties can be understood in unprecedented depth. We present the details of the "maxBCG" algorithm, a cluster-detection technique tailored to multi-band CCD-imaging data. MaxBCG primarily relies on an observational cornerstone of massive galaxy clusters: they are marked by an overdensity of bright, uniformly red galaxies. This detection scheme also exploits classical brightest cluster galaxies (BCGs), which are often found at the center of these same massive clusters. (ABRIDGED)Comment: 39 pages, 16 figures, 1 table. Accepted to Ap

Alignment of Brightest Cluster Galaxies with their Host Clusters

We examine the alignment between Brightest Cluster Galaxies (BCGs) and their host clusters in a sample of 7031 clusters with 0.08<z<0.44 found using a matched-filter algorithm and an independent sample of 5744 clusters with 0.1<z<0.3 selected with the maxBCG algorithm, both extracted from the Sloan Digital Sky Survey Data Release 6 imaging data. We confirm that BCGs are preferentially aligned with the cluster's major axis; clusters with dominant BCGs (>0.65 mag brighter than the mean of the second and third ranked galaxies) show stronger alignment than do clusters with less dominant BCGs at the 4.4 sigma level. Rich clusters show a stronger alignment than do poor clusters at the 2.3 sigma level. Low redshift clusters (z<0.26) show more alignment than do high redshift (z>0.26) clusters, with a difference significant at the 3.0 sigma level. Our results do not depend on the algorithm used to select the cluster sample, suggesting that they are not biased by systematics of either algorithm. The correlation between BCG dominance and cluster alignment may be a consequence of the hierarchical merging process which forms the cluster. The observed redshift evolution may follow from secondary infall at late redshifts.Comment: 15 pages, 12 Figures, 10 Tables, Accepted for publication in MNRA

Cosmological Constraints from Galaxy Clustering and the Mass-to-Number Ratio of Galaxy Clusters

We place constraints on the average density (Omega_m) and clustering amplitude (sigma_8) of matter using a combination of two measurements from the Sloan Digital Sky Survey: the galaxy two-point correlation function, w_p, and the mass-to-galaxy-number ratio within galaxy clusters, M/N, analogous to cluster M/L ratios. Our w_p measurements are obtained from DR7 while the sample of clusters is the maxBCG sample, with cluster masses derived from weak gravitational lensing. We construct non-linear galaxy bias models using the Halo Occupation Distribution (HOD) to fit both w_p and M/N for different cosmological parameters. HOD models that match the same two-point clustering predict different numbers of galaxies in massive halos when Omega_m or sigma_8 is varied, thereby breaking the degeneracy between cosmology and bias. We demonstrate that this technique yields constraints that are consistent and competitive with current results from cluster abundance studies, even though this technique does not use abundance information. Using w_p and M/N alone, we find Omega_m^0.5*sigma_8=0.465+/-0.026, with individual constraints of Omega_m=0.29+/-0.03 and sigma_8=0.85+/-0.06. Combined with current CMB data, these constraints are Omega_m=0.290+/-0.016 and sigma_8=0.826+/-0.020. All errors are 1-sigma. The systematic uncertainties that the M/N technique are most sensitive to are the amplitude of the bias function of dark matter halos and the possibility of redshift evolution between the SDSS Main sample and the maxBCG sample. Our derived constraints are insensitive to the current level of uncertainties in the halo mass function and in the mass-richness relation of clusters and its scatter, making the M/N technique complementary to cluster abundances as a method for constraining cosmology with future galaxy surveys.Comment: 23 pages, submitted to Ap

Cosmological Constraints from SDSS maxBCG Cluster Abundances

We perform a maximum likelihood analysis of the cluster abundance measured in the SDSS using the maxBCG cluster finding algorithm. Our analysis is aimed at constraining the power spectrum normalization $\sigma_8$, and assumes flat cosmologies with a scale invariant spectrum, massless neutrinos, and CMB and supernova priors Omega_m*h^2=0.128+/-0.01 and h=0.72+/-0.05 respectively. Following the method described in the companion paper Rozo et al. 2007, we derive \sigma_8=0.92+/-0.10$ (1-sigma) after marginalizing over all major systematic uncertainties. We place strong lower limits on the normalization, sigma_8>0.76 (95% CL) (>0.68 at 99% CL). We also find that our analysis favors relatively low values for the slope of the Halo Occupation Distribution (HOD), alpha=0.83+/-0.06. The uncertainties of these determinations will substantially improve upon completion of an ongoing campaign to estimate dynamical, weak lensing, and X-ray cluster masses in the SDSS maxBCG cluster sample.Comment: 10 pages, 6 figures, ApJ Submitte