A tight scaling relation of dark matter in galaxy clusters

Recent studies in different types of galaxies reveal that the product of the central density and the core radius (${\rho }_c{r}_c$) is a constant. However, some empirical studies involving galaxy clusters suggest that the product ${\rho }_c{r}_c$ 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 ${\rho }_c{r}_c$ 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.