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 SDSS 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 GMBCG and redMaPPer catalogues , respectively , at a level of \sim -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 et al .
( 2012 ) , corresponding to M _ { 200 m } \gtrsim 2 \times 10 ^ { 14 } \mathrm { M } _ { \odot } h ^ { -1 } , however we find no significant detection of gravitational redshift signal for less riched clusters , which may be related to bulk motions from substructure and spurious cluster detections .
Second , 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 BOSS 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 favor more relaxed clusters with a meaningful gravitational redshift signal , as anticipated by the red-sequence colour selection of the GMBCG and redMaPPer samples .