Richness-mass relation self-calibration for galaxy clusters

Abstract

This work attains a threefold objective: first, we derived the richness-mass scaling in the local Universe from data of 53 clusters with individual measurements of mass. We found a 0.46 ± 0.12 slope and a 0.25 ± 0.03 dex scatter measuring richness with a previously developed method. Second, we showed on a real sample of 250 0.06 < z < 0.9 clusters, most of which are at z < 0.3, with spectroscopic redshift that the colour of the red sequence allows us to measure the clusters' redshift to better than Δz = 0.02. Third, we computed the predicted prior of the richness-mass scaling to forecast the capabilities of future wide-field-area surveys of galaxy clusters to constrain cosmological parameters. To this aim, we generated a simulated universe obeying the richness-mass scaling that we found. We observed it with a PanStarrs 1+Euclid-like survey, allowing for intrinsic scatter between mass and richness, for errors on mass, on richness, and for photometric redshift errors. We fitted the observations with an evolving five-parameter richness-mass scaling with parameters to be determined. Input parameters were recovered, but only if the cluster mass function and the weak-lensing redshift-dependent selection function were accounted for in the fitting of the mass-richness scaling. This emphasizes the limitations of often adopted simplifying assumptions, such as having a mass-complete redshift-independent sample. We derived the uncertainty and the covariance matrix of the (evolving) richness-mass scaling, which are the input ingredients of cosmological forecasts using cluster counts. We find that the richness-mass scaling parameters can be determined 10 5 times better than estimated in previous works that did not use weak-lensing mass estimates, although we emphasize that this high factor was derived with scaling relations with different parameterizations. The better knowledge of the scaling parameters likely has a strong impact on the relative importance of the different probes used to constrain cosmological parameters. The fitting code used for computing the predicted prior, including the treatment of the mass function and of the weak-lensing selection function, is provided in Appendix A. It can be re-used, for example, to derive the predicted prior of other observable-mass scalings, such as the L X -mass relation.

Galaxy clusters and groups in the ALHAMBRA survey

“…This dispersion becomes comparable to what has been found in other optical broad-band surveys down to 2-3 orders of magnitude higher mass limits and to other non-optical mass estimators such as X-ray luminosity or Y SZ . (Rozo et al 2009;Hilbert & White 2010;Andreon & Bergé 2012). In addition, this value is comparable to the precision that other non-optical proxies, such as X-ray luminosity or the total integrated SZ signal over the cluster, YSZ, are obtaining for a more extended mass range (e.g Rozo et al 2014 and references herein).…”

Evolution of the cluster optical galaxy luminosity function in the CFHTLS: breaking the degeneracy between mass and redshift

“…This arises from the intrinsic scatter (σ int ) that exists between halo mass and cluster richness. This scatter is found to be of the order 0.3 dex in the local Universe (Andreon & Bergé 2012). This means a halo with mass ∼ 3σ int below the 10 14 M threshold could have the same richness as a halo of 10 14 M .…”

The insignificant evolution of the richness-mass relation of galaxy clusters

“…In contrast to these previous studies, we allow a possible log-normal scatter around the mean relation (the scatter is obvious in the Lin et al 2004 sample), and we prefer to zero-point quantities at z = 0.25 (the median redshift of our sample) instead of at z = 0. We also need to account for the mass function and for the selection function because the Malmquist-Eddington correction (the difference between latent and observed value) depends on the shape of the product of these two functions, see Andreon & Bergé (2012). We therefore take the mass function and its evolution from the Multidark simulation (Sect.…”

“…To fit the data, we used an updated version of the Bayesian estimation model in Andreon & Bergé (2012), which already accounts for the presence of a redshift term γ (Eq. (1)), for the cluster mass and selection function, and for the possible presence of an intrinsic scatter.…”

“…(1)), for the cluster mass and selection function, and for the possible presence of an intrinsic scatter. The Andreon & Bergé (2012) model adopts a Gaussian likelihood for richnesses and perfectly measured errors for masses. We therefore replace that part of the model by a more appropriate model, introduced in Andreon & Hurn (2010), which accounts for the non-Gaussian (Poisson) nature of galaxy counts, for the background, and also for the noisiness of the mass errors.…”