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Register a new userMass Calibration of the CODEX Cluster Sample using SPIDERS Spectroscopy -- I. The Richness-Mass Relation
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We use galaxy dynamical information to calibrate the richness-mass scaling relation of a sample of 428 galaxy clusters that are members of the CODEX sample with redshifts up to z~0.7. These clusters were X-ray selected using the ROSAT All-Sky Survey (RASS), cross-matched to associated systems in the redMaPPer catalog from the Sloan Digital Sky Survey. The spectroscopic sample we analyze was obtained in the SPIDERS program and contains ~7800 red member galaxies. Adopting NFW mass and galaxy density profiles and a broad range of orbital anisotropy profiles, we use the Jeans equation to calculate halo masses. Modeling the scaling relation as $lambda propto text{A}_{lambda} {M_{text{200c}}}^{text{B}_{lambda}} ({1+z})^{gamma_{lambda}}$, we find the parameter constraints $text{A}_{lambda}=38.6^{+3.1}_{-4.1}pm3.9$, $text{B}_{lambda}=0.99^{+0.06}_{-0.07}pm0.04$, and $gamma_{lambda}=-1.13^{+0.32}_{-0.34}pm0.49$. We find good agreement with previously published mass trends with the exception of those from stacked weak lensing analyses. We note that although the lensing analyses failed to account for the Eddington bias, this is not enough to explain the differences. We suggest that differences in the levels of contamination between pure redMaPPer and RASS+redMaPPer samples could well contribute to these differences. The redshift trend we measure is more negative than but statistically consistent with previous results. We suggest that our measured redshift trend reflects a change in the cluster galaxy red sequence fraction with redshift, noting that the trend we measure is consistent with but somewhat stronger than an independently measured redshift trend in the red sequence fraction. We also examine the impact of a plausible model of correlated scatter in X-ray luminosity and optical richness, showing it has negligible impact on our results.
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The COnstrain Dark Energy with X-ray clusters (CODEX) sample contains the largest flux limited sample of X-ray clusters at $0.35 < z < 0.65$. It was selected from ROSAT data in the 10,000 square degrees of overlap with BOSS, mapping a total number of 2770 high-z galaxy clusters. We present here the full results of the CFHT CODEX program on cluster mass measurement, including a reanalysis of CFHTLS Wide data, with 25 individual lensing-constrained cluster masses. We employ $lensfit$ shape measurement and perform a conservative colour-space selection and weighting of background galaxies. Using the combination of shape noise and an analytic covariance for intrinsic variations of cluster profiles at fixed mass due to large scale structure, miscentring, and variations in concentration and ellipticity, we determine the likelihood of the observed shear signal as a function of true mass for each cluster. We combine 25 individual cluster mass likelihoods in a Bayesian hierarchical scheme with the inclusion of optical and X-ray selection functions to derive constraints on the slope $alpha$, normalization $beta$, and scatter $sigma_{ln lambda | mu}$ of our richness-mass scaling relation model in log-space: $left<ln lambda | mu right> = alpha mu + beta$, with $mu = ln (M_{200c}/M_{mathrm{piv}})$, and $M_{mathrm{piv}} = 10^{14.81} M_{odot}$. We find a slope $alpha = 0.49^{+0.20}_{-0.15}$, normalization $ exp(beta) = 84.0^{+9.2}_{-14.8}$ and $sigma_{ln lambda | mu} = 0.17^{+0.13}_{-0.09}$ using CFHT richness estimates. In comparison to other weak lensing richness-mass relations, we find the normalization of the richness statistically agreeing with the normalization of other scaling relations from a broad redshift range ($0.0<z<0.65$) and with different cluster selection (X-ray, Sunyaev-Zeldovich, and optical).
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.
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 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.
Accurate measurement of galaxy cluster masses is an essential component not only in studies of cluster physics, but also for probes of cosmology. However, different mass measurement techniques frequently yield discrepant results. The SDSS MaxBCG catalogs mass-richness relation has previously been constrained using weak lensing shear, Sunyaev-Zeldovich (SZ), and X-ray measurements. The mass normalization of the clusters as measured by weak lensing shear is >~25% higher than that measured using SZ and X-ray methods, a difference much larger than the stated measurement errors in the analyses. We constrain the mass-richness relation of the MaxBCG galaxy cluster catalog by measuring the gravitational lensing magnification of type I quasars in the background of the clusters. The magnification is determined using the quasars variability and the correlation between quasars variability amplitude and intrinsic luminosity. The mass-richness relation determined through magnification is in agreement with that measured using shear, confirming that the lensing strength of the clusters implies a high mass normalization, and that the discrepancy with other methods is not due to a shear-related systematic measurement error. We study the dependence of the measured mass normalization on the cluster halo orientation. As expected, line-of-sight clusters yield a higher normalization; however, this minority of haloes does not significantly bias the average mass-richness relation of the catalog.
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