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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 sigma_{ln L_X}^2=(0.86pm0.02)^2 to sigma_{ln L_X}^2=(0.69pm0.02)^2. Relative to the maxBCG richness estimate, it also removes the strong redshift dependence of the richness scaling relations, and is significantly more robust to photometric and redshift errors. These improvements are largely due to our more sophisticated 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 be easily generalized to other mass tracers.
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Gravitational lensing magnification is measured with a significance of 9.7 sigma on a large sample of galaxy clusters in the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). This survey covers ~154 deg^2 and contains over 18,000 cluster candidates at redshifts 0.2 <= z <= 0.9, detected using the 3D-Matched Filter cluster-finder of Milkeraitis et al. (2010). We fit composite-NFW models to the ensemble, accounting for cluster miscentering, source-lens redshift overlap, as well as nearby structure (the 2-halo term), and recover mass estimates of the cluster dark matter halos in range of ~10^13 M_sun to 2*10^14 M_sun. Cluster richness is measured for the entire sample, and we bin the clusters according to both richness and redshift. A mass-richness relation M_200 = M_0 (N_200 / 20)^beta is fit to the measurements. For two different cluster miscentering models we find consistent results for the normalization and slope, M_0 = (2.3 +/- 0.2)*10^13 M_sun, beta = 1.4 +/- 0.1 and M_0 = (2.2 +/- 0.2)*10^13 M_sun, beta = 1.5 +/- 0.1. We find that accounting for the full redshift distribution of lenses and sources is important, since any overlap can have an impact on mass estimates inferred from flux magnification.
We explore the use of a sufficient statistic based on the identified members that are obtained for samples that are selected under the $M_0$ capture-recapture closed population model (Schwarz and Seber, 1999). A Rao-Blackwellized version of the estimator based on a sufficient statistic is then presented. We explore the efficiency of the improved estimator via a simulation study. The R code for the simulation is provided in the appendix.
We explore the use of a sufficient statistic based on the data of samples that are selected under the M_0 capture-recapture closed population model (Schwarz and Seber, 1999). A Rao-Blackwellized version of the estimator based on a sufficient statistic is then presented. Though the improvements made on the preliminary capture-recapture estimates are likely to be negligible, this body of work is primarily intended to contribute to the theory around the capture-recapture models. The code for a simulation is provided in the appendix.
Identifying galaxy clusters through overdensities of galaxies in photometric surveys is the oldest and arguably the most economic and mass-sensitive detection method, compared to X-ray and Sunyaev-Zeldovich Effect surveys that detect the hot intracluster medium. However, a perennial problem has been the mapping of optical richness measurements on to total cluster mass. Emitted at a conformal distance of 14 Gpc, the cosmic microwave background acts as a backlight to all intervening mass in the Universe, and therefore has been gravitationally lensed. Here we present a calibration of cluster optical richness at the 10 per cent level by measuring the average cosmic microwave background lensing convergence measured by Planck towards the positions of large numbers of optically-selected clusters, detecting the deflection of photons by haloes of total mass of the order 10**14 solar masses. Although mainly aimed at the study of larger-scale structures, the Planck lensing reconstruction can yield nearly unbiased results for stacked clusters on arcminute scales. The lensing convergence only depends on the redshift integral of the fractional overdensity of matter, so this approach offers a clean measure of cluster mass over most of cosmic history, largely independent of baryon physics.
The cluster correlation function and its richness dependence are determined from 1108 clusters of galaxies -- the largest sample of clusters studied so far -- found in 379 deg^2 of Sloan Digital Sky Survey early data. The results are compared with previous samples of optically and X-ray selected clusters. The richness-dependent correlation function increases monotonically from an average correlation scale of ~ 12 h^{-1} Mpc for poor clusters to ~ 25 h^{-1} Mpc for the richer, more massive clusters with a mean separation of ~ 90 h^{-1} Mpc. X-ray selected clusters suggest slightly stronger correlations than optically selected clusters (~ 2-sigma). The results are compared with large-scale cosmological simulations. The observed richness-dependent cluster correlation function is well represented by the standard flat LCDM model (Omega_m ~= 0.3, h ~= 0.7), and is inconsistent with the considerably weaker correlations predicted by Omega_m = 1 models. An analytic relation for the correlation scale versus cluster mean separation, r_0 - d, that best describes the observations and the LCDM prediction is r_0 ~= 2.6 sqrt{d} (for d ~= 20 - 90 h^{-1} Mpc). Data from the complete Sloan Digital Sky Survey, when available, will greatly enhance the accuracy of the results and allow a more precise determination of cosmological parameters.
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