Mass Calibration of the CODEX Cluster Sample using SPIDERS Spectroscopy
  -- I. The Richness-Mass Relation
  We use galaxy dynamical information to calibrate the richness-mass scaling
relation of a sample of 428 galaxy clusters that are members of the CODEX
sample with redshifts up to z~0.7. These clusters were X-ray selected using the
ROSAT All-Sky Survey (RASS), cross-matched to associated systems in the
redMaPPer catalog from the Sloan Digital Sky Survey. The spectroscopic sample
we analyze was obtained in the SPIDERS program and contains ~7800 red member
galaxies. Adopting NFW mass and galaxy density profiles and a broad range of
orbital anisotropy profiles, we use the Jeans equation to calculate halo
masses. Modeling the scaling relation as $\lambda \propto \text{A}_{\lambda}
{M_{\text{200c}}}^{\text{B}_{\lambda}} ({1+z})^{\gamma_{\lambda}}$, we find the
parameter constraints $\text{A}_{\lambda}=38.6^{+3.1}_{-4.1}\pm3.9$,
$\text{B}_{\lambda}=0.99^{+0.06}_{-0.07}\pm0.04$, and
$\gamma_{\lambda}=-1.13^{+0.32}_{-0.34}\pm0.49$. We find good agreement with
previously published mass trends with the exception of those from stacked weak
lensing analyses. We note that although the lensing analyses failed to account
for the Eddington bias, this is not enough to explain the differences. We
suggest that differences in the levels of contamination between pure redMaPPer
and RASS+redMaPPer samples could well contribute to these differences. The
redshift trend we measure is more negative than but statistically consistent
with previous results. We suggest that our measured redshift trend reflects a
change in the cluster galaxy red sequence fraction with redshift, noting that
the trend we measure is consistent with but somewhat stronger than an
independently measured redshift trend in the red sequence fraction. We also
examine the impact of a plausible model of correlated scatter in X-ray
luminosity and optical richness, showing it has negligible impact on our
results.
