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A clean measurement of the evolution of the galaxy cluster mass function cansignificantly improve our understanding of cosmology from the rapid growth ofcluster masses below z < 0.5. Here we examine the consistency of clustercatalogues selected from the SDSS by applying two independent gravity-basedmethods using all available spectroscopic redshifts from the DR10 release.First, we detect a gravitational redshift related signal for 20,119 and 13,128clusters with spectroscopic redshifts contained in the GMBCG and redMaPPercatalogues, respectively, at a level of $\sim - 10$ km s$^{-1}$. This we showis consistent with the magnitude expected using the richness-mass relationsprovided by the literature and after applying recently clarified relativisticand flux bias corrections. This signal is also consistent with the richestclusters in the larger catalogue of Wen et al. (2012), corresponding to$M_{200m} \gtrsim 2 \times 10^{14}\,\mathrm{M}_\odot\,h^{-1}$, however we findno significant detection of gravitational redshift signal for less richedclusters, which may be related to bulk motions from substructure and spuriouscluster detections. Second, we find all three catalogues generatemass-dependent levels of lensing magnification bias, which enhances the meanredshift of flux-selected background galaxies from the BOSS survey. Themagnitude of this lensing effect is generally consistent with the correspondingrichness-mass relations advocated for the surveys. We conclude that allcatalogues comprise a high proportion of reliable clusters, and that the GMBCGand redMaPPer cluster finder algorithms favor more relaxed clusters with ameaningful gravitational redshift signal, as anticipated by the red-sequencecolour selection of the GMBCG and redMaPPer samples.

Comparing gravitational redshifts of SDSS galaxy clusters with the magnification redshift enhancement of background BOSS galaxies