Mass–Richness Relations for X-Ray and SZE-selected Clusters at 0.4 < z < 2.0 as Seen by Spitzer at 4.5 μm

We study the mass–richness relation of 116 spectroscopically confirmed massive clusters at 0.4 < z < 2 by mining the Spitzer archive. We homogeneously measure the richness at 4.5 μm for our cluster sample within a fixed aperture of 2' radius and above a fixed brightness threshold, making appropriate corrections for both background galaxies and foreground stars. We have two subsamples, those which have (a) literature X-ray luminosities and (b) literature Sunyaev–Zel'dovich effect masses. For the X-ray subsample we re-derive masses adopting the most recent calibrations. We then calibrate an empirical mass–richness relation for the combined sample spanning more than one decade in cluster mass and find the associated uncertainties in mass at fixed richness to be ±0.25 dex. We study the dependence of the scatter of this relation with galaxy concentration, defined as the ratio between richness measured within an aperture radius of 1 and 2 arcmin. We find that at fixed aperture radius the scatter increases for clusters with higher concentrations. We study the dependence of our richness estimates with depth of the 4.5 μm imaging data and find that reaching a depth of at least [4.5] = 21 AB mag is sufficient to derive reasonable mass estimates. We discuss the possible extension of our method to the mid-infrared WISE All Sky Survey data and the application of our results to the Euclid mission. This technique makes richness-based cluster mass estimates available for large samples of clusters at very low observational cost.