redMaPPer III: A Detailed Comparison of the Planck 2013 and SDSS DR8
  RedMaPPer Cluster Catalogs
  We compare the Planck Sunyaev-Zeldovich (SZ) cluster sample (PSZ1) to the
Sloan Digital Sky Survey (SDSS) redMaPPer catalog, finding that all Planck
clusters within the redMaPPer mask and within the redshift range probed by
redMaPPer are contained in the redMaPPer cluster catalog. These common clusters
define a tight scaling relation in the richness-SZ mass ($\lambda$--$M_{SZ}$)
plane, with an intrinsic scatter in richness of $\sigma_{\lambda|M_{SZ}} =
0.266 \pm 0.017$. The corresponding intrinsic scatter in true cluster halo mass
at fixed richness is $\approx 21\%$. The regularity of this scaling relation is
used to identify failures in both the redMaPPer and Planck cluster catalogs. Of
the 245 galaxy clusters in common, we identify three failures in redMaPPer and
36 failures in the PSZ1. Of these, at least 12 are due to clusters whose
optical counterpart was correctly identified in the PSZ1, but where the quoted
redshift for the optical counterpart in the external data base used in the PSZ1
was incorrect. The failure rates for redMaPPer and the PSZ1 are $1.2\%$ and
$14.7\%$ respectively, or 9.8% in the PSZ1 after subtracting the external data
base errors. We have further identified 5 PSZ1 sources that suffer from
projection effects (multiple rich systems along the line-of-sight of the SZ
detection) and 17 new high redshift ($z\gtrsim 0.6$) cluster candidates of
varying degrees of confidence. Should all of the high-redshift cluster
candidates identified here be confirmed, we will have tripled the number of
high redshift Planck clusters in the SDSS region. Our results highlight the
power of multi-wavelength observations to identify and characterize systematic
errors in galaxy cluster data sets, and clearly establish photometric data both
as a robust cluster finding method, and as an important part of defining clean
galaxy cluster samples.
