Stellar Mass to Halo Mass Scaling Relation for X-ray Selected Low Mass
  Galaxy Clusters and Groups out to Redshift $z\approx1$
  We present the stellar mass-halo mass scaling relation for 46 X-ray selected
low-mass clusters or groups detected in the XMM-BCS survey with masses
$2\times10^{13}M_{\odot}\lesssim M_{500}\lesssim2.5\times10^{14}M_{\odot}$ at
redshift $0.1\le z \le1.02$. The cluster binding masses $M_{500}$ are inferred
from the measured X-ray luminosities \Lx, while the stellar masses $M_{\star}$
of the galaxy populations are estimated using near-infrared imaging from the
SSDF survey and optical imaging from the BCS survey. With the measured \Lx\ and
stellar mass $M_{\star}$, we determine the best fit stellar mass-halo mass
relation, accounting for selection effects, measurement uncertainties and the
intrinsic scatter in the scaling relation. The resulting mass trend is
$M_{\star}\propto M_{500}^{0.69\pm0.15}$, the intrinsic (log-normal) scatter is
$\sigma_{\ln M_{\star}|M_{500}}=0.36^{+0.07}_{-0.06}$, and there is no
significant redshift trend $M_{\star}\propto (1+z)^{-0.04\pm0.47}$, although
the uncertainties are still large. We also examine $M_{\star}$ within a fixed
projected radius of $0.5$~Mpc, showing that it provides a cluster binding mass
proxy with intrinsic scatter of $\approx93\%$ (1$\sigma$ in $M_{500}$). We
compare our $M_{\star}=M_{\star}(M_{500}, z)$ scaling relation from the XMM-BCS
clusters with samples of massive, SZE-selected clusters
($M_{500}\approx6\times10^{14}M_{\odot}$) and low mass NIR-selected clusters
($M_{500}\approx10^{14}M_{\odot}$) at redshift $0.6\lesssim z \lesssim1.3$.
After correcting for the known mass measurement systematics in the compared
samples, we find that the scaling relation is in good agreement with the high
redshift samples, suggesting that for both groups and clusters the stellar
content of the galaxy populations within $R_{500}$ depends strongly on mass but
only weakly on redshift out to $z\approx1$.
