  Recent studies in different types of galaxies reveal that the product of the
central density and the core radius ($\rho_cr_c$) is a constant. However, some
empirical studies involving galaxy clusters suggest that the product
$\rho_cr_c$ depends weakly on the total dark halo mass. In this article, we
re-analyse the hot gas data from 106 clusters and obtain a surprisingly tight
scaling relation: $\rho_c \propto r_c^{-1.46 \pm 0.16}$. This result generally
agrees with the claims that $\rho_cr_c$ is not a constant for all scales of
structure. Moreover, this relation does not support the velocity-dependent
cross section of dark matter if the core formation is due to the
self-interaction of dark matter.
