The XXL Survey X: K-band luminosity - weak-lensing mass relation for
  groups and clusters of galaxies
  We present the K-band luminosity-halo mass relation, $L_{K,500}-M_{500,WL}$,
for a subsample of 20 of the 100 brightest clusters in the XXL Survey observed
with WIRCam at the Canada-France-Hawaii Telescope (CFHT). For the first time,
we have measured this relation via weak-lensing analysis down to $M_{500,WL}
=3.5 \times 10^{13}\,M_\odot$. This allows us to investigate whether the slope
of the $L_K-M$ relation is different for groups and clusters, as seen in other
works. The clusters in our sample span a wide range in mass, $M_{500,WL}
=0.35-12.10 \times 10^{14}\,M_\odot$, at $0<z<0.6$. The K-band luminosity
scales as $\log_{10}(L_{K,500}/10^{12}L_\odot) \propto \beta
log_{10}(M_{500,WL}/10^{14}M_\odot)$ with $\beta = 0.85^{+0.35}_{-0.27}$ and an
intrinsic scatter of $\sigma_{lnL_K|M} =0.37^{+0.19}_{-0.17}$. Combining our
sample with some clusters in the Local Cluster Substructure Survey (LoCuSS)
present in the literature, we obtain a slope of $1.05^{+0.16}_{-0.14}$ and an
intrinsic scatter of $0.14^{+0.09}_{-0.07}$. The flattening in the $L_K-M$ seen
in previous works is not seen here and might be a result of a bias in the mass
measurement due to assumptions on the dynamical state of the systems. We also
study the richness-mass relation and find that group-sized halos have more
galaxies per unit halo mass than massive clusters. However, the brightest
cluster galaxy (BCG) in low-mass systems contributes a greater fraction to the
total cluster light than BCGs do in massive clusters; the luminosity gap
between the two brightest galaxies is more prominent for group-sized halos.
This result is a natural outcome of the hierarchical growth of structures,
where massive galaxies form and gain mass within low-mass groups and are
ultimately accreted into more massive clusters to become either part of the BCG
or one of the brighter galaxies. [Abridged]
