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.
