The Galaxy Cluster Concentration-Mass Scaling Relation
  Scaling relations of clusters have made them particularly important
cosmological probes of structure formation. In this work, we present a
comprehensive study of the relation between two profile observables,
concentration ($\mathrm{c_{vir}}$) and mass ($\mathrm{M_{vir}}$). We have
collected the largest known sample of measurements from the literature which
make use of one or more of the following reconstruction techniques: Weak
gravitational lensing (WL), strong gravitational lensing (SL), Weak+Strong
Lensing (WL+SL), the Caustic Method (CM), Line-of-sight Velocity Dispersion
(LOSVD), and X-ray. We find that the concentration-mass (c-M) relation is
highly variable depending upon the reconstruction technique used. We also find
concentrations derived from dark matter only simulations (at approximately
$\mathrm{M_{vir} \sim 10^{14} M_{\odot}}$) to be inconsistent with the WL and
WL+SL relations at the $\mathrm{1\sigma}$ level, even after the projection of
triaxial halos is taken into account. However, to fully determine consistency
between simulations and observations, a volume-limited sample of clusters is
required, as selection effects become increasingly more important in answering
this. Interestingly, we also find evidence for a steeper WL+SL relation as
compared to WL alone, a result which could perhaps be caused by the varying
shape of cluster isodensities, though most likely reflects differences in
selection effects caused by these two techniques. Lastly, we compare
concentration and mass measurements of individual clusters made using more than
one technique, highlighting the magnitude of the potential bias which could
exist in such observational samples.
