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 ansatz for galaxy clusters by Chan et al. (2015), 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, studied by Vikhlinin et al. (2006), implementing the same procedure as in Ref. Chan et al. (2015), 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$\sigma$.

大量研究发现，暗物质表面密度是由暗物质核心半径（${\mathrm{[R}}_C$）和芯密度（${\rho }_C$）对于广泛的星系系统大约是常数。然而，Chan等人仅对该星系团的ansatz进行过系统的研究。（2015），他发现簇的表面密度不是恒定的，并且${\rho }_C〜{\mathrm{[R}}_C^{-\mathrm{1个}。46}$。我们对Vikhlinin等人研究的Chandra观测到的12个松弛星团的X射线样本进行了这项测试。（2006年），执行与参考文献中相同的程序。Chan等。（2015年），但也考虑了气体和恒星质量。我们发现${\rho }_C\propto {\mathrm{[R}}_C^{-\mathrm{1个}。08\pm 0。055}$，其固有散射约为18％。因此，我们的聚类数据的暗物质表面密度显示仅在约1.4时偏离恒定值$\sigma$。