A clean measurement of the evolution of the galaxy cluster mass function can significantly improve our understanding of cosmology from the rapid growth of cluster masses below z<0.5. Here, we examine the consistency of cluster catalogues selected from the Sloan Digital Sky Survey by applying two independent gravity-based methods using all available spectroscopic redshifts from the DR10 release. First, we detect a gravitational redshift related signal for 20,119 and 13,128 clusters with spectroscopic redshifts contained in the Gaussian Mixture Brightest Cluster Galaxy (GMBCG) and red-sequence Matched-filter Probabilistic Percolation (redMaPPer) catalogues, respectively, at a level of∼−10 km s−1. This we show is consistent with the magnitude expected using the richness-mass relations provided by the literature and after applying recently clarified relativistic and flux bias corrections. This signal is also consistent with the richest clusters in the larger catalogue of Wen etal., corresponding to M200m≳2×1014 M⊙ h−1; however, we find no significant detection of a gravitational redshift signal for lower richness clusters, which may be related to bulk motions from substructure and spurious cluster detections. Secondly, we find all three catalogues generate mass-dependent levels of lensing magnification bias, which enhances the mean redshift of flux-selected background galaxies from the Baryon Oscillation Spectroscopic Survey survey. The magnitude of this lensing effect is generally consistent with the corresponding richness-mass relations advocated for the surveys. We conclude that all catalogues comprise a high proportion of reliable clusters, and that the GMBCG and redMaPPer cluster finder algorithms favour more relaxed clusters with a meaningful gravitational redshift signal, as anticipated by the red-sequence colour selection of the GMBCG and redMaPPer sample
