The Mean and Scatter of the Velocity Dispersion-Optical Richness Relation for maxBCG Galaxy Clusters

The distribution of galaxies in position and velocity around the centers of galaxy clusters encodes important information about cluster mass and structure. Using the maxBCG galaxy cluster catalog identified from imaging data obtained in the Sloan Digital Sky Survey, we study the BCG-galaxy velocity correlation function. By modeling its non-Gaussianity, we measure the mean and scatter in velocity dispersion at fixed richness. The mean velocity dispersion increases from 202+/-10 km/s for small groups to more than 854+/-102 km/s for large clusters. We show the scatter to be at most 40.5+/-3.5%, declining to 14.9+/-9.4% in the richest bins. We test our methods in the C4 cluster catalog, a spectroscopic cluster catalog produced from the Sloan Digital Sky Survey DR2 spectroscopic sample, and in mock galaxy catalogs constructed from N-body simulations. Our methods are robust, measuring the scatter to well within one-sigma of the true value, and the mean to within 10%, in the mock catalogs. By convolving the scatter in velocity dispersion at fixed richness with the observed richness space density function, we measure the velocity dispersion function of the maxBCG galaxy clusters. Although velocity dispersion and richness do not form a true mass-observable relation, the relationship between velocity dispersion and mass is theoretically well characterized and has low scatter. Thus our results provide a key link between theory and observations up to the velocity bias between dark matter and galaxies.Comment: 25 pages, 15 figures, 2 tables, published in Ap

Dynamical Confirmation of SDSS Weak Lensing Scaling Laws

Galaxy masses can be estimated by a variety of methods; each applicable in different circumstances, and each suffering from different systematic uncertainties. Confirmation of results obtained by one technique with analysis by another is particularly important. Recent SDSS weak lensing measurements of the projected-mass correlation function reveal a linear relation between galaxy luminosities and the depth of their dark matter halos (measured on 260 \hinv kpc scales). In this work we use an entirely independent dynamical method to confirm these results. We begin by assembling a sample of 618 relatively isolated host galaxies, surrounded by a total of 1225 substantially fainter satellites. We observe the mean dynamical effect of these hosts on the motions of their satellites by assembling velocity difference histograms. Dividing the sample by host properties, we find significant variations in satellite velocity dispersion with host luminosity. We quantify these variations using a simple dynamical model, measuring \mtsd a dynamical mass within 260 \hinv kpc. The appropriateness of this mass reconstruction is checked by conducting a similar analysis within an N-body simulation. Comparison between the dynamical and lensing mass-to-light scalings shows reasonable agreement, providing some quantitative confirmation for the lensing results.Comment: 7 pages, 3 figures, accepted for publication in ApJ Letter

SDSS-RASS: Next Generation of Cluster-Finding Algorithms

We outline here the next generation of cluster-finding algorithms. We show how advances in Computer Science and Statistics have helped develop robust, fast algorithms for finding clusters of galaxies in large multi-dimensional astronomical databases like the Sloan Digital Sky Survey (SDSS). Specifically, this paper presents four new advances: (1) A new semi-parametric algorithm - nicknamed ``C4'' - for jointly finding clusters of galaxies in the SDSS and ROSAT All-Sky Survey databases; (2) The introduction of the False Discovery Rate into Astronomy; (3) The role of kernel shape in optimizing cluster detection; (4) A new determination of the X-ray Cluster Luminosity Function which has bearing on the existence of a ``deficit'' of high redshift, high luminosity clusters. This research is part of our ``Computational AstroStatistics'' collaboration (see Nichol et al. 2000) and the algorithms and techniques discussed herein will form part of the ``Virtual Observatory'' analysis toolkit.Comment: To appear in Proceedings of MPA/MPE/ESO Conference "Mining the Sky", July 31 - August 4, 2000, Garching, German

The galaxy-mass correlation function measured from weak lensing in the Sloan Digital Sky Survey

We present galaxy-galaxy lensing measurements over scales 0.025 to 10 h(-1) Mpc in the Sloan Digital Sky Survey (SDSS). Using a flux-limited sample of 127,001 lens galaxies with spectroscopic redshifts and mean luminosity [L] similar to L-* and 9,020,388 source galaxies with photometric redshifts, we invert the lensing signal to obtain the galaxy-mass correlation function xi(gm). We find xi(gm) is consistent with a power law, xi(gm) (r = r(0))(-gamma), with best-fit parameters gamma = 1.79 +/- 0.06 and r(0) (5.4 +/- 0.7) (0.27/Omega(m))(1/gamma) h(-1) Mpc. At fixed separation, the ratio xi(gg)/xi(gm) = b/r, where b is the bias and r is the correlation coefficient. Comparing with the galaxy autocorrelation function for a similarly selected sample of SDSS galaxies, we find that b/r is approximately scale-independent over scales 0.2 - 6.7 h(-1) Mpc, with mean [b/r] = (1.3 +/- 0.2) (Omega(m)/0.27). We also find no scale dependence in b/r for a volume-limited sample of luminous galaxies (-23.0 < M-r < -21.5). The mean b/r for this sample is [b/r](Vlim) = (2.0 +/- 0.7) (Omega(m)/0.27). We split the lens galaxy sample into subsets based on luminosity, color, spectral type, and velocity dispersion and see clear trends of the lensing signal with each of these parameters. The amplitude and logarithmic slope of xi(gm) increase with galaxy luminosity. For high luminosities (L similar to 5 L-*), xi(gm) deviates significantly from a power law. These trends with luminosity also appear in the subsample of red galaxies, which are more strongly clustered than blue galaxies

Robust Optical Richness Estimation with Reduced Scatter

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. (2009), 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 sigma_lnLX|lambda=0.63+/-0.02 for clusters with M_500c >~ 1.6e14 h_70^-1 M_sun. The corresponding scatter in mass at fixed richness is sigma_lnM|lambda ~ 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 4000 A 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 1 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 lambda richness measured for each cluster.Comment: Submitted to ApJ. 20 pages in emulateapj forma

A Gravitationally Lensed Quasar with Quadruple Images Separated by 14.62 Arcseconds

Gravitational lensing is a powerful tool for the study of the distribution of dark matter in the Universe. The cold-dark-matter model of the formation of large-scale structures predicts the existence of quasars gravitationally lensed by concentrations of dark matter so massive that the quasar images would be split by over 7 arcsec. Numerous searches for large-separation lensed quasars have, however, been unsuccessful. All of the roughly 70 lensed quasars known, including the first lensed quasar discovered, have smaller separations that can be explained in terms of galaxy-scale concentrations of baryonic matter. Although gravitationally lensed galaxies with large separations are known, quasars are more useful cosmological probes because of the simplicity of the resulting lens systems. Here we report the discovery of a lensed quasar, SDSS J1004+4112, which has a maximum separation between the components of 14.62 arcsec. Such a large separation means that the lensing object must be dominated by dark matter. Our results are fully consistent with theoretical expectations based on the cold-dark-matter model.Comment: 10 pages, 3 figures, to appear in the 18th&25th Dec issue of Nature (Letters to Nature