Effects of Intracluster Gas and Duct upon the Virial Theorem.

In the present paper the application of the virial theorem to clusters of galaxies (or stars) is reezamined for the case in which a significant fraction of the total mass of the cluster exists in the form of intracluster gas. A modified form for the expression of the virial theorem in this case is obtained in terms of the mean-square velocity of the galaxies, the total mass of the galaxies, the total mass of the gas, the radius of the cluster, a coefficient depending upon the spatial distribution of the galaxies, and a second coefficient depending upon both the spatial distribution of the galaxies and the spatial distribution of the gas-the two distributions being different in general. The two coefficients are evaluated and tabulated for those cases in which the two distributions can be approximated by the polytropic distributions with integral indices. It is shown how the coefficients corresponding to more general distributions can be approximated by means of the tabulated coefficients.