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We describe redMaPPer, a new red-sequence cluster finder specifically designed to make optimal use of ongoing and near-future large photometric surveys. The algorithm has multiple attractive features: (1) It can iteratively self-train the red-sequence model based on minimal spectroscopic training sample, an important feature for high redshift surveys; (2) It can handle complex masks with varying depth; (3) It produces cluster-appropriate random points to enable large-scale structure studies; (4) All clusters are assigned a full redshift probability distribution P(z); (5) Similarly, clusters can have multiple candidate central galaxies, each with corresponding centering probabilities; (6) The algorithm is parallel and numerically efficient: it can run a Dark Energy Survey-like catalog in ~500 CPU hours; (7) The algorithm exhibits excellent photometric redshift performance, the richness estimates are tightly correlated with external mass proxies, and the completeness and purity of the corresponding catalogs is superb. We apply the redMaPPer algorithm to ~10,000 deg^2 of SDSS DR8 data, and present the resulting catalog of ~25,000 clusters over the redshift range 0.08<z<0.55. The redMaPPer photometric redshifts are nearly Gaussian, with a scatter sigma_z ~ 0.006 at z~0.1, increasing to sigma_z~0.02 at z~0.5 due to increased photometric noise near the survey limit. The median value for |Delta z|/(1+z) for the full sample is 0.006. The incidence of projection effects is low (<=5%). Detailed performance comparisons of the redMaPPer DR8 cluster catalog to X-ray and SZ catalogs are presented in a companion paper (Rozo & Rykoff 2014).
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In order to place constraints on cosmology through optical surveys of galaxy clusters, one must first understand the properties of those clusters. To this end, we introduce the Mass Analysis Tool for Chandra (MATCha), a pipeline which uses a parallellized algorithm to analyze archival Chandra data. MATCha simultaneously calculates X-ray temperatures and luminosities and performs centering measurements for hundreds of potential galaxy clusters using archival X-ray exposures. We run MATCha on the redMaPPer SDSS DR8 cluster catalog and use MATChas output X-ray temperatures and luminosities to analyze the galaxy cluster temperature-richness, luminosity-richness, luminosity-temperature, and temperature-luminosity scaling relations. We detect 447 clusters and determine 246 r2500 temperatures across all redshifts. Within 0.1 < z < 0.35 we find that r2500 Tx scales with optical richness as ln(kB Tx / 1.0 keV) = (0.52 pm 0.05) ln({lambda}/70) + (1.85 pm 0.03) with intrinsic scatter of 0.27 pm 0.02 (1 {sigma}). We investigate the distribution of offsets between the X-ray center and redMaPPer center within 0.1 < z < 0.35, finding that 68.3 pm 6.5% of clusters are well-centered. However, we find a broad tail of large offsets in this distribution, and we explore some of the causes of redMaPPer miscentering.
We present a calibration of the fundamental plane using SDSS Data Release 8. We analysed about 93000 elliptical galaxies up to $z<0.2$, the largest sample used for the calibration of the fundamental plane so far. We incorporated up-to-date K-corrections and used GalaxyZoo data to classify the galaxies in our sample. We derived independent fundamental plane fits in all five Sloan filters u, g, r, i and z. A direct fit using a volume-weighted least-squares method was applied to obtain the coefficients of the fundamental plane, which implicitly corrects for the Malmquist bias. We achieved an accuracy of 15% for the fundamental plane as a distance indicator. We provide a detailed discussion on the calibrations and their influence on the resulting fits. These re-calibrated fundamental plane relations form a well-suited anchor for large-scale peculiar-velocity studies in the nearby universe. In addition to the fundamental plane, we discuss the redshift distribution of the elliptical galaxies and their global parameters.
We search for the presence of substructure, a non-Gaussian, asymmetrical velocity distribution of galaxies, and large peculiar velocities of the main galaxies in galaxy clusters with at least 50 member galaxies, drawn from the SDSS DR8. We employ a number of 3D, 2D, and 1D tests to analyse the distribution of galaxies in clusters: 3D normal mixture modelling, the Dressler-Shectman test, the Anderson-Darling and Shapiro-Wilk tests and others. We find the peculiar velocities of the main galaxies, and use principal component analysis to characterise our results. More than 80% of the clusters in our sample have substructure according to 3D normal mixture modelling, the Dressler-Shectman (DS) test shows substructure in about 70% of the clusters. The median value of the peculiar velocities of the main galaxies in clusters is 206 km/s (41% of the rms velocity). The velocities of galaxies in more than 20% of the clusters show significant non-Gaussianity. While multidimensional normal mixture modelling is more sensitive than the DS test in resolving substructure in the sky distribution of cluster galaxies, the DS test determines better substructure expressed as tails in the velocity distribution of galaxies. Richer, larger, and more luminous clusters have larger amount of substructure and larger (compared to the rms velocity) peculiar velocities of the main galaxies. Principal component analysis of both the substructure indicators and the physical parameters of clusters shows that galaxy clusters are complicated objects, the properties of which cannot be explained with a small number of parameters or delimited by one single test. The presence of substructure, the non-Gaussian velocity distributions, as well as the large peculiar velocities of the main galaxies, shows that most of the clusters in our sample are dynamically young.
The accurate determination of the galaxy cluster mass-observable relations is one of the major challenge of modern astrophysics and cosmology. We present a new statistical methodology to constrain the evolution of the mass-observable relations. Instead of measuring individual mass of galaxy clusters, we only consider large scale homogeneity of the Universe. In this case, we expect the present galaxy cluster mass function to be the same everywhere in the Universe. Using relative abundance matching, we contraint the relation between the richness, $lambda(z)$, and the expected present mass, $M(t_0)$, of galaxy clusters. We apply this approach to the redMaPPer galaxy cluster catalogue in 10 redshift bins from $z=0.1$ to $0.6$. We found that the $lambda(z)$-$M(t_0)$ relation is not evolving from $z=0.1$ to $0.4$, whereas it starts to significantly evolve at higher redshift. This results implies that the redMaPPer richness appears to be a better proxy for the expected present-day galaxy cluster mass than for the mass at the observational redshift. Assuming cosmology and galaxy cluster mass accretion history, it is possible to convert $M(t_0)$ to the mass at the galaxy cluster redshift $M(t_z)$. We found a significant evolution of the $lambda(z)$-$M(t_z)$ over all the covered redshift range. Consequently, we provide a new redshift-dependent richness-mass relation for the redMaPPer galaxy cluster catalogue. This results demonstrates the efficiency of this new methodology to probe the evolution of scaling relations compared to individual galaxy cluster mass estimation.
We describe updates to the redmapper{} algorithm, a photometric red-sequence cluster finder specifically designed for large photometric surveys. The updated algorithm is applied to $150,mathrm{deg}^2$ of Science Verification (SV) data from the Dark Energy Survey (DES), and to the Sloan Digital Sky Survey (SDSS) DR8 photometric data set. The DES SV catalog is locally volume limited, and contains 786 clusters with richness $lambda>20$ (roughly equivalent to $M_{rm{500c}}gtrsim10^{14},h_{70}^{-1},M_{odot}$) and $0.2<z<0.9$. The DR8 catalog consists of 26311 clusters with $0.08<z<0.6$, with a sharply increasing richness threshold as a function of redshift for $zgtrsim 0.35$. The photometric redshift performance of both catalogs is shown to be excellent, with photometric redshift uncertainties controlled at the $sigma_z/(1+z)sim 0.01$ level for $zlesssim0.7$, rising to $sim0.02$ at $zsim0.9$ in DES SV. We make use of emph{Chandra} and emph{XMM} X-ray and South Pole Telescope Sunyaev-Zeldovich data to show that the centering performance and mass--richness scatter are consistent with expectations based on prior runs of redmapper{} on SDSS data. We also show how the redmapper{} photoz{} and richness estimates are relatively insensitive to imperfect star/galaxy separation and small-scale star masks.
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