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 fr
om 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 $M_{200m} gtrsim 2 times 10^{14},mathrm{M}_odot,h^{-1}$, 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.
Galaxy-galaxy weak lensing is a direct probe of the mean matter distribution around galaxies. The depth and sky coverage of the CFHT Legacy Survey yield statistically significant galaxy halo mass measurements over a much wider range of stellar masses
($10^{8.75}$ to $10^{11.3} M_{odot}$) and redshifts ($0.2 < z < 0.8$) than previous weak lensing studies. At redshift $z sim 0.5$, the stellar-to-halo mass ratio (SHMR) reaches a maximum of $4.0pm0.2$ percent as a function of halo mass at $sim 10^{12.25} M_{odot}$. We find, for the first time from weak lensing alone, evidence for significant evolution in the SHMR: the peak ratio falls as a function of cosmic time from $4.5 pm 0.3$ percent at $z sim 0.7$ to $3.4 pm 0.2$ percent at $z sim 0.3$, and shifts to lower stellar mass haloes. These evolutionary trends are dominated by red galaxies, and are consistent with a model in which the stellar mass above which star formation is quenched downsizes with cosmic time. In contrast, the SHMR of blue, star-forming galaxies is well-fit by a power law that does not evolve with time. This suggests that blue galaxies form stars at a rate that is balanced with their dark matter accretion in such a way that they evolve along the SHMR locus. The redshift dependence of the SHMR can be used to constrain the evolution of the galaxy population over cosmic time.
We report the first detection of a redshift-depth enhancement of background galaxies magnified by foreground clusters. Using 300,000 BOSS-Survey galaxies with accurate spectroscopic redshifts, we measure their mean redshift depth behind four large sa
mples of optically selected clusters from the SDSS surveys, totalling 5,000-15,000 clusters. A clear trend of increasing mean redshift towards the cluster centers is found, averaged over each of the four cluster samples. In addition we find similar but noisier behaviour for an independent X-ray sample of 158 clusters lying in the foreground of the current BOSS sky area. By adopting the mass-richness relationships appropriate for each survey we compare our results with theoretical predictions for each of the four SDSS cluster catalogs. The radial form of this redshift enhancement is well fitted by a richness-to-mass weighted composite Navarro-Frenk-White profile with an effective mass ranging between M_200 ~ 1.4-1.8 10^14 M_sun for the optically detected cluster samples, and M_200 ~ 5.0 10^14 M_sun for the X-ray sample. This lensing detection helps to establish the credibility of these SDSS cluster surveys, and provides a normalization for their respective mass-richness relations. In the context of the upcoming bigBOSS, Subaru-PFS, and EUCLID-NISP spectroscopic surveys, this method represents an independent means of deriving the masses of cluster samples for examining the cosmological evolution, and provides a relatively clean consistency check of weak-lensing measurements, free from the systematic limitations of shear calibration.
