Scaling relations for dark matter core density and radius from Chandra
  X-ray cluster sample
  A large number of studies have found that the dark matter surface density,
given by the product of the dark matter core radius ($r_c$) and core density
($\rho_c$) is approximately constant for a wide range of galaxy systems.
However, there has been only one systematic study of this {\it ansatz} for
galaxy clusters by Chan (arXiv:1403.4352), who found that the surface density
for clusters is not constant and $\rho_c \sim r_c^{-1.46}$. We carry out this
test for an X-ray sample of 12 relaxed clusters from Chandra observations,
implementing the same procedure as Chan, but also accounting for the gas and
star mass. We find that $\rho_c \propto r_c^{-1.08 \pm 0.055}$, with an
intrinsic scatter of about 18%. Therefore, the dark matter surface density for
our cluster data shows deviations from a constant value at only about
1.4$\sigma$.
