Richness-mass relation self-calibration for galaxy clusters ^⋆

¹ INAF – Osservatorio Astronomico di Brera, via Brera 28, Milano, Italy
² ETH Zurich, Department of Physics, Wolfgang Pauli Strasse 27, 8093 Zurich, Switzerland
e-mail: stefano.andreon@brera.inaf.it

Received: 27 July 2012
Accepted: 20 September 2012

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 10⁵ 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.