Weak Lensing Analysis of CODEX Clusters using Dark Energy Camera Legacy
  Survey : Mass-Richness Relation
  We present the weak lensing analysis of 279 CODEX clusters using imaging data
from 4200 $\text{deg}^{2}$ of the DECam Legacy Survey (DECaLS) Data Release 3.
The cluster sample results from a joint selection in X-ray, optical richness in
the range $20 \leq \lambda < 110$, and redshift in the range $0.1 \leq z \leq
0.2$. We model the cluster mass ($M_{\rm 200c}$) and the richness relation with
the expression $\left\langle M_{\rm 200c} | \lambda \right\rangle \propto M_{0}
\, (\lambda / 40)^{F_{\lambda}}$. By measuring the CODEX cluster sample as an
individual cluster, we obtain the best-fit values, $M_{0} =
3.24^{+0.29}_{-0.27} \times 10^{14} \text{M}_{\odot}$, and $F_{\lambda} = 1.00
^{+0.22}_{-0.22}$ for the richness scaling index, consistent with a power law
relation. Moreover, we separate the cluster sample into three richness groups;
$\lambda = 20 - 30, 30 - 50$ and $50 - 110$, and measure the stacked excess
surface mass density profile in each group. The results show that both methods
are consistent. In addition, we find an excellent agreement between our weak
lensing based scaling relation and the relation obtained with dynamical masses
estimated from cluster member velocity dispersions measured by the
SDSS-IV/SPIDERS team. This suggests that the cluster dynamical equilibrium
assumption involved in the dynamical mass estimates is statistically robust for
a large sample of clusters.
