A Weak Lensing Study of X-ray Groups in the COSMOS survey: Form and
  Evolution of the Mass-Luminosity Relation
  Measurements of X-ray scaling laws are critical for improving cosmological
constraints derived with the halo mass function and for understanding the
physical processes that govern the heating and cooling of the intracluster
medium. In this paper, we use a sample of 206 X-ray selected galaxy groups to
investigate the scaling relation between X-ray luminosity (Lx) and halo mass
(M00) where M200 is derived via stacked weak gravitational lensing. This work
draws upon a broad array of multi-wavelength COSMOS observations including 1.64
square degrees of contiguous imaging with the Advanced Camera for Surveys (ACS)
and deep XMM-Newton/Chandra imaging. The combined depth of these two data-sets
allows us to probe the lensing signals of X-ray detected structures at both
higher redshifts and lower masses than previously explored. Weak lensing
profiles and halo masses are derived for nine sub-samples, narrowly binned in
luminosity and redshift. The COSMOS data alone are well fit by a power law,
M200 ~ Lx^a, with a slope of a=0.66+-0.14. These results significantly extend
the dynamic range for which the halo masses of X-ray selected structures have
been measured with weak gravitational lensing. As a result, tight constraints
are obtained for the slope of the M-Lx relation. The combination of our group
data with previously published cluster data demonstrates that the M-Lx relation
is well described by a single power law, a=0.64+-0.03, over two decades in
mass, 10^13.5-10^15.5 h72^-1 Msun. These results are inconsistent at the 3.7
level with the self-similar prediction of a=0.75. We examine the redshift
dependence of the M-Lx relation and find little evidence for evolution beyond
the rate predicted by self-similarity from z ~ 0.25 to z ~ 0.8.
