Mass-richness relations for X-ray and SZE clusters

We homogeneously measure the richness at 4.5um 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 +/-0.25dex. 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'.