Hydrostatic Structure of a Hot Plasma in a Cluster of Galaxies

Hydrostatic equilibrium solutions for the hot gas in a cluster of galaxies have been studied assuming the polytropic relation. The final equilibrium state is related to the initial state of the gas in the cluster using the mass and energy conservation laws between the above two states. Results are applied to the X-ray source in Coma cluster. We have obtained the central temperature, the central density and the mass of the intracluster gas such as 1.8X10' OK, 2.8X10- 27 gm/cm' and 5.7X10"1'vf0, respectively. As for the X-ray emission mechanism of these sources, inverse compton and thermal bremsstrahlung theories have been proposed. However, recent spectral analyses of soft X-ray data2l tend to show a strong preference for the thermal model. Moreover, tailed radio sources3l and the excess of SO galaxies4l found in these clusters may be well interpreted, if hot intracluster gases exist. Concerning the thermal model, a wind model, sl infall models6l, 7) and static modelsn,sl have been studied. Lea8l has calculated the hydrostatic equilibrium solu tion for a polytropic gas in a cluster of galaxies under the boundary condition that the temperature of the gas approaches to zero at infinity. By comparing that solution with observations for the Coma cluster, she shows that the intracluster gas is distributed more widely than the galaxies by a factor of about 2"--'2.5 and the temperature of the gas given from a best-fit model is 1.5 X 108 oK. Takahara et al. 9l have investigated the dynamical collapse of gas in a cluster of galaxies. As a result of numerical calculations, they find that a hot plasma is formed after the bounce and it attains an equilibrium state. In § 2 the hydrostatic equilibrium solution for a polytropic gas in a cluster of galaxies is derived. In § 3 the hydrostatic equilibrium state which is attained after the dynamical collapse is discussed using the energy and mass conservation laws which relate the final state of the gas to the initial state. In § 4 the central temperature, the central density and the mass of the intracluster gas are obtained