We use the abundance and weak-lensing mass measurements of the Sloan Digital Sky Survey maxBCG cluster catalog to simultaneously constrain cosmology and the richness-mass relation of the clusters. Assuming a flat ΛCDM cosmology, we find σ 8 (Ω m /0.25) 0.41 = 0.832 ± 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 σ 8 = 0.807 ± 0.020 and Ω m = 0.265 ± 0.016, an improvement of nearly a factor of 2 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.

Imaging data from the Sloan Digital Sky Survey are used to characterize the population of galaxies in groups and clusters detected with the MaxBCG algorithm. We investigate the dependence of Brightest Cluster Galaxy (BCG) luminosity, and the distributions of satellite galaxy luminosity and satellite color, on cluster properties over the redshift range 0.1 ≤ z ≤ 0.3. The size of the dataset allows us to make measurements in many bins of cluster richness, radius and redshift. We find that, within r 200 of clusters with mass above 3×10 13 h −1 M ⊙ , the luminosity function of both red and blue satellites is only weakly dependent on richness. We further find that the shape of the satellite luminosity function does not depend on cluster-centric distance for magnitudes brighter than 0.25 M i -5log 10 h = −19. However, the mix of faint red and blue galaxies changes dramatically. The satellite red fraction is dependent on cluster-centric distance, galaxy luminosity and cluster mass, and also increases by ∼5% between redshifts 0.28 and 0.2, independent of richness. We find that BCG luminosity is tightly correlated with cluster richness, scaling as L BCG ∼ M 0.3 200 , and has a Gaussian distribution at fixed richness, with σ logL ∼ 0.17 for massive clusters. The ratios of BCG luminosity to total cluster luminosity and characteristic satellite luminosity scale strongly with cluster richness: in richer systems, BCGs contribute a smaller fraction of the total light, but are brighter compared to typical satellites. This study demonstrates the power of cross-correlation techniques for measuring galaxy populations in purely photometric data.

The Blanco Cosmology Survey (BCS) is a 60 night imaging survey of ∼80 deg 2 of the southern sky located in two fields: (α,δ)= (5 hr, −55 • ) and (23 hr, −55 • ). The survey was carried out between 2005 and 2008 in griz bands with the Mosaic2 imager on the Blanco 4m telescope. The primary aim of the BCS survey is to provide the data required to optically confirm and measure photometric redshifts for Sunyaev-Zel'dovich effect selected galaxy clusters from the South Pole Telescope and the Atacama Cosmology Telescope. We process and calibrate the BCS data, carrying out PSF corrected model fitting photometry for all detected objects. The median 10σ galaxy (point source) depths over the survey in griz are approximately 23.3 (23.9), 23.4 (24.0), 23.0 (23.6) and 21.3 (22.1), respectively. The astrometric accuracy relative to the USNO-B survey is ∼ 45 milli-arcsec. We calibrate our absolute photometry using the stellar locus in grizJ bands, and thus our absolute photometric scale derives from 2MASS which has ∼ 2% accuracy. The scatter of stars about the stellar locus indicates a systematics floor in the relative stellar photometric scatter in griz that is ∼1.9%, ∼2.2%, ∼2.7% and∼2.7%, respectively. A simple cut in the AstrOmatic star-galaxy classifier spread model produces a star sample with good spatial uniformity. We use the resulting photometric catalogs to calibrate photometric redshifts for the survey and demonstrate scatter δz/(1 + z) = 0.054 with an outlier fraction η < 5% to z ∼ 1. We highlight some selected science results to date and provide a full description of the released data products.

Imaging data from the Sloan Digital Sky Survey is used to measure the empirical size-richness relation for a large sample of galaxy clusters. Using population subtraction methods, we determine the radius at which the cluster galaxy number density is 200Ω −1 m times the mean galaxy density, without assuming a model for the radial distribution of galaxies in clusters. If these galaxies are unbiased on Mpc scales, this galaxy-density-based R 200 reflects the characteristic radii of clusters. We measure the scaling of this characteristic radius with richness over an order of magnitude in cluster richness, from rich clusters to poor groups. We use this information to examine the radial profiles of galaxies in clusters as a function of cluster richness, finding that the concentration of the galaxy distribution decreases with richness and is systematically lower than the concentrations measured for dark matter profiles in N-body simulations. Using these scaled radii, we investigate the behavior of the cluster luminosity function, and find that it is well matched by a Schechter function for galaxies brighter than M r = −18 only after the central galaxy has been removed. We find that the luminosity function varies with richness and with distance from the cluster center, underscoring the importance of using an aperture that scales with cluster mass to compare physically equivalent regions of these different systems. We note that the lowest richness systems in our catalog have properties consistent with those expected of the earliest-forming halos; our cluster-finding algorithm, in addition to reliably finding clusters, may be efficient at finding fossil groups.

Reducing the scatter between cluster mass and optical richness is a key goal for cluster cosmology from photometric catalogs. We consider various modifications to the red-sequence matched filter richness estimator of Rozo et al. (2009b), and evaluate their impact on the scatter in X-ray luminosity at fixed richness. Most significantly, we find that deeper luminosity cuts can reduce the recovered scatter, finding that σ ln LX |λ = 0.63 ± 0.02 for clusters with M 500c 1.6 × 10 14 h −1 70 M ⊙ . The corresponding scatter in mass at fixed richness is σ ln M|λ ≈ 0.2 − 0.3 depending on the richness, comparable to that for total X-ray luminosity. We find that including blue galaxies in the richness estimate increases the scatter, as does weighting galaxies by their optical luminosity. We further demonstrate that our richness estimator is very robust. Specifically, the filter employed when estimating richness can be calibrated directly from the data, without requiring a-priori calibrations of the red-sequence. We also demonstrate that the recovered richness is robust to up to 50% uncertainties in the galaxy background, as well as to the choice of photometric filter employed, so long as the filters span the 4000Å break of red-sequence galaxies. Consequently, our richness estimator can be used to compare richness estimates of different clusters, even if they do not share the same photometric data. Appendix A includes "easy-bake" instructions for implementing our optimal richness estimator, and we are releasing an implementation of the code that works with SDSS data, as well as an augmented maxBCG catalog with the λ richness measured for each cluster. 15 As discussed in Rozo et al. (2009b), throughout this work the word "richness" is meant to be understood as "optical mass tracer," and is not necessarily the actual number of cluster galaxies within the virialized region of a cluster or the total optical luminosity of the cluster.

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 σ ln M|N200 = 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 L X 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. 13 σ 8 is formally defined as the variance of the linear matter density averaged over spheres with radius R = 8 h −1 Mpc.

Minimizing the scatter between cluster mass and accessible observables is an important goal for cluster cosmology. In this work, we introduce a new matched filter richness estimator, and test its performance using the maxBCG cluster catalog. Our new estimator significantly reduces the variance in the L X-richness relation, from σ 2 ln L X = (0.86 ± 0.02) 2 to σ 2 ln L X = (0.69 ± 0.02) 2. Relative to the maxBCG richness estimate, it also removes the strong redshift dependence of the L X-richness scaling relations, and is significantly more robust to photometric and redshift errors. These improvements are largely due to the better treatment of galaxy color data. We also demonstrate the scatter in the L X-richness relation depends on the aperture used to estimate cluster richness, and introduce a novel approach for optimizing said aperture which can easily be generalized to other mass tracers.

We present measurements of the excess mass-to-light ratio measured around MaxBCG galaxy clusters observed in the SDSS. This red sequence cluster sample includes objects from small groups with M 200 ∼ 5 × 10 12 h −1 M ⊙ to clusters with M 200 ∼ 10 15 h −1 M ⊙ . Using cross-correlation weak lensing, we measure the excess mass density profile above the universal mean ∆ρ(r) = ρ(r) −ρ for clusters in bins of richness and optical luminosity. We also measure the excess luminosity density ∆ℓ(r) = ℓ(r) −l measured in the z = 0.25 i-band. For both mass and light, we de-project the profiles to produce 3D mass and light profiles over scales from 25h −1 kpc to 22h −1 Mpc. From these profiles we calculate the cumulative excess mass ∆M (r) and excess light ∆L(r) as a function of separation from the BCG. On small scales, where ρ(r) ≫ρ, the integrated mass-to-light profile (∆M/∆L)(r) may be interpreted as the cluster mass-to-light ratio. We find the (∆M/∆L) 200 , the mass-to-light ratio within r 200 , scales with cluster mass as a power law with index 0.33 ± 0.02. On large scales, where ρ(r) ∼ρ, the ∆M/∆L approaches an asymptotic value independent of cluster richness. For small groups, the mean (∆M/∆L) 200 is much smaller than the asymptotic value, while for large clusters (∆M/∆L) 200 is consistent with the asymptotic value. This asymptotic value should be proportional to the mean mass-to-light ratio of the universe M/L . We find M/L b −2 M/L = 362 ± 54h (statistical). There is additional uncertainty in the overall calibration at the ∼10% level. The parameter b 2 M/L is primarily a function of the bias of the L L * galaxies used as light tracers, and should be of order unity. Multiplying by the luminosity density in the same bandpass we find Ω m b −2 M/L = 0.20 ± 0.03, independent of the Hubble parameter.