redMaPPer III: A Detailed Comparison of the Planck 2013 and SDSS DR8 RedMaPPer Cluster Catalogs

We compare the Planck Sunyaev-Zeldovich (SZ) cluster sample (PSZ1) to the Sloan Digital Sky Survey (SDSS) redMaPPer catalog, finding that all Planck clusters within the redMaPPer mask and within the redshift range probed by redMaPPer are contained in the redMaPPer cluster catalog. These common clusters define a tight scaling relation in the richness-SZ mass ($\lambda$--$M_{SZ}$) plane, with an intrinsic scatter in richness of $\sigma_{\lambda|M_{SZ}} = 0.266 \pm 0.017$. The corresponding intrinsic scatter in true cluster halo mass at fixed richness is $\approx 21\%$. The regularity of this scaling relation is used to identify failures in both the redMaPPer and Planck cluster catalogs. Of the 245 galaxy clusters in common, we identify three failures in redMaPPer and 36 failures in the PSZ1. Of these, at least 12 are due to clusters whose optical counterpart was correctly identified in the PSZ1, but where the quoted redshift for the optical counterpart in the external data base used in the PSZ1 was incorrect. The failure rates for redMaPPer and the PSZ1 are $1.2\%$ and $14.7\%$ respectively, or 9.8% in the PSZ1 after subtracting the external data base errors. We have further identified 5 PSZ1 sources that suffer from projection effects (multiple rich systems along the line-of-sight of the SZ detection) and 17 new high redshift ($z\gtrsim 0.6$) cluster candidates of varying degrees of confidence. Should all of the high-redshift cluster candidates identified here be confirmed, we will have tripled the number of high redshift Planck clusters in the SDSS region. Our results highlight the power of multi-wavelength observations to identify and characterize systematic errors in galaxy cluster data sets, and clearly establish photometric data both as a robust cluster finding method, and as an important part of defining clean galaxy cluster samples.Comment: comments welcom

redMaPPer II: X-ray and SZ Performance Benchmarks for the SDSS Catalog

We evaluate the performance of the SDSS DR8 redMaPPer photometric cluster catalog by comparing it to overlapping X-ray and SZ selected catalogs from the literature. We confirm the redMaPPer photometric redshifts are nearly unbiased ( < 0.005), have low scatter (\sigma_z ~ 0.006-0.02, depending on redshift), and have a low catastrophic failure rate (~ 1%). Both the T_X-\lambda\ and Mgas-\lambda\ scaling relations are consistent with a mass scatter of \sigma_{\ln M|\lambda} ~ 25%, albeit with a ~ 1% outlier rate due to projection effects. This failure rate is somewhat lower than that expected for the full cluster sample, but is consistent with the additional selection effects introduced by our reliance on X-ray and SZ selected reference cluster samples. Where the redMaPPer DR8 catalog is volume limited (z < 0.35), the catalog is 100% complete above T_X > 3.5 keV, and L_X > 2\times 10^{44} erg/s, decreasing to 90% completeness at L_X ~ 10^{43} erg/s. All rich (\lambda > 100), low redshift (z < 0.25) redMaPPer clusters are X-ray detected in the ROSAT All Sky Survey (RASS), and 86% of the clusters are correctly centered. Compared to other SDSS photometric cluster catalogs, redMaPPer has the highest completeness and purity, and the best photometric redshift performance, though some algorithms do achieve comparable performance to redMaPPer in subsets of the above categories and/or in limited redshift ranges. The redMaPPer richness is clearly the one that best correlates with X-ray temperature and gas mass. Most algorithms (including redMaPPer) have very similar centering performance, with only one exception which performs worse.Comment: comments welcom

Constraining the Mass-Richness Relationship of redMaPPer Clusters with Angular Clustering

The potential of using cluster clustering for calibrating the mass-observable relation of galaxy clusters has been recognized theoretically for over a decade. Here, we demonstrate the feasibility of this technique to achieve high precision mass calibration using redMaPPer clusters in the Sloan Digital Sky Survey North Galactic Cap. By including cross-correlations between several richness bins in our analysis we significantly improve the statistical precision of our mass constraints. The amplitude of the mass-richness relation is constrained to 7% statistical precision. However, the error budget is systematics dominated, reaching an 18% total error that is dominated by theoretical uncertainty in the bias-mass relation for dark matter halos. We perform a detailed treatment of the effects of assembly bias on our analysis, finding that the contribution of such effects to our parameter uncertainties is somewhat greater than that of measurement noise. We confirm the results from Miyatake et al. (2015) that the clustering amplitude of redMaPPer clusters depends on galaxy concentration, and provide additional evidence in support of this effect being due to some form of assembly bias. The results presented here demonstrate the power of cluster clustering for mass calibration and cosmology provided the current theoretical systematics can be ameliorated.Comment: 18 pages, 9 figure

Galaxy Cluster Mass Estimation from Stacked Spectroscopic Analysis

We use simulated galaxy surveys to study: i) how galaxy membership in redMaPPer clusters maps to the underlying halo population, and ii) the accuracy of a mean dynamical cluster mass, $M_\sigma(\lambda)$, derived from stacked pairwise spectroscopy of clusters with richness $\lambda$. Using $\sim\! 130,000$ galaxy pairs patterned after the SDSS redMaPPer cluster sample study of Rozo et al. (2015 RMIV), we show that the pairwise velocity PDF of central--satellite pairs with $m_i < 19$ in the simulation matches the form seen in RMIV. Through joint membership matching, we deconstruct the main Gaussian velocity component into its halo contributions, finding that the top-ranked halo contributes $\sim 60\%$ of the stacked signal. The halo mass scale inferred by applying the virial scaling of Evrard et al. (2008) to the velocity normalization matches, to within a few percent, the log-mean halo mass derived through galaxy membership matching. We apply this approach, along with mis-centering and galaxy velocity bias corrections, to estimate the log-mean matched halo mass at $z=0.2$ of SDSS redMaPPer clusters. Employing the velocity bias constraints of Guo et al. (2015), we find $\langle \ln(M_{200c})|\lambda \rangle = \ln(M_{30}) + \alpha_m \ln(\lambda/30)$ with $M_{30} = 1.56 \pm 0.35 \times 10^{14} M_\odot$ and $\alpha_m = 1.31 \pm 0.06_{stat} \pm 0.13_{sys}$. Systematic uncertainty in the velocity bias of satellite galaxies overwhelmingly dominates the error budget.Comment: 14 pages, 7 figure

Intrinsic Alignment in redMaPPer clusters -- II. Radial alignment of satellites toward cluster centers

We study the orientations of satellite galaxies in redMaPPer clusters constructed from the Sloan Digital Sky Survey at $0.1<z<0.35$ to determine whether there is any preferential tendency for satellites to point radially toward cluster centers. We analyze the satellite alignment (SA) signal based on three shape measurement methods (re-Gaussianization, de Vaucouleurs, and isophotal shapes), which trace galaxy light profiles at different radii. The measured SA signal depends on these shape measurement methods. We detect the strongest SA signal in isophotal shapes, followed by de Vaucouleurs shapes. While no net SA signal is detected using re-Gaussianization shapes across the entire sample, the observed SA signal reaches a statistically significant level when limiting to a subsample of higher luminosity satellites. We further investigate the impact of noise, systematics, and real physical isophotal twisting effects in the comparison between the SA signal detected via different shape measurement methods. Unlike previous studies, which only consider the dependence of SA on a few parameters, here we explore a total of 17 galaxy and cluster properties, using a statistical model averaging technique to naturally account for parameter correlations and identify significant SA predictors. We find that the measured SA signal is strongest for satellites with the following characteristics: higher luminosity, smaller distance to the cluster center, rounder in shape, higher bulge fraction, and distributed preferentially along the major axis directions of their centrals. Finally, we provide physical explanations for the identified dependences, and discuss the connection to theories of SA.Comment: 25 pages, 16 figures, 7 tables, accepted to MNRAS. Main statistical analysis tool changed, with the results remain simila