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Cluster Lensing Profiles Derived from a Redshift Enhancement of Magnified BOSS-Survey Galaxies

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 samples 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.