A comparison between observed and analytical velocity dispersion profiles of 20 nearby galaxy clusters

We derive analytical expression for the velocity dispersion of galaxy clusters, using the statistical mechanical approach. We compare the observed velocity dispersion profiles for 20 nearby (z≤0.1) galaxy clusters with the analytical ones. It is interesting to find that the analytical results closely match with the observed velocity dispersion profiles only if the presence of the diffuse matter in clusters is taken into consideration. This takes us to introduce a new approach to detect the ratio of diffuse mass, M _diff , within a galaxy cluster. For the present sample, the ratio f=M _diff /M, where M the cluster’s total mass is found to has an average value of 45±12 %. This leads us to the result that nearly 45 % of the cluster mass is impeded outside the galaxies, while around 55 % of the cluster mass is settled in the galaxies.