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$\sigma$.