Dark and visible matter distribution in Coma cluster: theory vs observations

We investigate dark and visible matter distribution in the Coma cluster in the case of the Navarro-Frenk-White (NFW) profile. A toy model where all galaxies in the cluster are concentrated inside a sphere of an effective radius $R_{\mathrm{eff}}$ is considered. It enables us to obtain the mean velocity dispersion as a function of $R_{\mathrm{eff}}$. We show that, within the observation accuracy of the NFW parameters, the calculated value of $R_{\mathrm{eff}}$ can be rather close to the observable cutoff of the galaxy distribution. Moreover, the comparison of our toy model with the observable data and simulations leads to the following preferable NFW parameters for the Coma cluster: $R_{200} \approx 1.77\,h^{-1} \, \mathrm{Mpc} = 2.61\, \mathrm{Mpc}$, $c=3\div 4$ and $M_{200}= 1.29h^{-1}\times10^{15}M_{\odot}$. In the Coma cluster the most of galaxies are concentrated inside a sphere of the effective radius $R_{\mathrm{eff}}\sim 3.7$ Mpc and the line-of-sight velocity dispersion is $1004\, \mathrm{km}\, \mathrm{s}^{-1}$.