Correlations in the matter distribution in CLASH galaxy clusters
  We study the total and dark matter (DM) density profiles as well as their
correlations for a sample of 15 high-mass galaxy clusters by extending our
previous work on several clusters from Newman et al. Our analysis focuses on 15
CLASH X-ray-selected clusters that have high-quality weak- and strong-lensing
measurements from combined Subaru and {\em Hubble Space Telescope}
observations. The total density profiles derived from lensing are interpreted
based on the two-phase scenario of cluster formation. In this context, the
brightest cluster galaxy (BCG) forms in the first dissipative phase, followed
by a dissipationless phase where baryonic physics flattens the inner DM
distribution. This results in the formation of clusters with modified DM
distribution and several correlations between characteristic quantities of the
clusters. We find that the central DM density profiles of the clusters are
strongly influenced by baryonic physics as found in our earlier work. The inner
slope of the DM density for the CLASH clusters is found to be flatter than the
Navarro--Frenk--White profile, ranging from $\alpha=0.30$ to $0.79$. We examine
correlations of the DM density slope $\alpha$ with the effective radius
$R_\mathrm{e}$ and stellar mass $M_\mathrm{e}$ of the BCG, finding that these
quantities are anti-correlated with a Spearman correlation coefficient of $\sim
-0.6$. We also study the correlation between $R_\mathrm{e}$ and the cluster
halo mass $M_{500}$, and the correlation between the total masses inside 5\,kpc
and 100\,kpc. We find that these quantities are correlated with Spearman
coefficients of $0.68$ and $0.64$, respectively. These observed correlations
are in support of the physical picture proposed by Newman et al.
