Planck/SDSS Cluster Mass and Gas Scaling Relations for a Volume-Complete
  redMaPPer Sample
  Using Planck satellite data, we construct SZ gas pressure profiles for a
large, volume-complete sample of optically selected clusters. We have defined a
sample of over 8,000 redMaPPer clusters from the Sloan Digital Sky Survey
(SDSS), within the volume-complete redshift region 0.100 < z < 0.325, for which
we construct Sunyaev-Zel'dovich (SZ) effect maps by stacking Planck data over
the full range of richness. Dividing the sample into richness bins we
simultaneously solve for the mean cluster mass in each bin together with the
corresponding radial pressure profile parameters, employing an MCMC analysis.
These profiles are well detected over a much wider range of cluster mass and
radius than previous work, showing a clear trend towards larger break radius
with increasing cluster mass. Our SZ-based masses fall ~24% below the
mass-richness relations from weak lensing, in a similar fashion as the
"hydrostatic bias" related with X-ray derived masses. We correct for this bias
to derive an optimal mass-richness relation finding a slope 1.22 +/- 0.04 and a
pivot mass log(M_500/M_0)= 14.432 +/- 0.041, evaluated at a richness lambda=60.
Finally, we derive a tight Y_500-M_500 relation over a wide range of cluster
mass, with a power law slope equal to 1.72 +/- 0.07, that agrees well with the
independent slope obtained by the Planck team with an SZ-selected cluster
sample, but extends to lower masses with higher precision.
