Annu. Rev. Astron. Astrophys. 1982. 20: 547-85 Copyright © 1982 by Annual Reviews. All rights reserved

2.2 A Description of the X-Ray Gas Distribution

The detail and sophistication of thermal bremsstrahlung models for the X-ray emission has grown with that of the observations. The first models assumed self-gravitating, isothermal spheres (e.g. Lea et al. 1973). Subsequently more realistic models were developed, including the hydrostatic-isothermal model (Lea 1975, Gull & Northover 1975, Yahil & Ostriker 1973, Bahcall & Sarazin 1977, Cavaliere & Fusco-Femiano 1976, 1981, Gorenstein et al. 1978). While this model is too simple to fully describe the X-ray gas, it provides a useful characterization of the cluster with a minimum number of parameters. This model assumes that both the X-ray-emitting gas and the optical galaxies are in hydrostatic equilibrium and that each is isothermal. It further requires that the galaxies be in equilibrium with the total gravitational mass. Zwicky (1957), Bahcall (1975), and Rood et al. (1972) found that the galaxy distribution in the cores of rich clusters can be described by a bounded isothermal Emden sphere. With the King (1972) approximation to the isothermal sphere, the X-ray surface brightness has a distribution

where a is the core radius of the galaxy distribution. The parameter is the ratio of the energy per unit mass in galaxies to the energy per unit mass in the gas and is given by

where µ is the mean molecular weight, m_H is the mass of the hydrogen atom, is the cluster velocity dispersion, k is Boltzmanns constant, and T_gas is the X-ray gas temperature. A value of equal to one implies that the galaxies and gas have equal scale heights, while smaller values of imply a more extended distribution for the gas than for the galaxies. In a well-studied system, one can compute directly from the observed velocity dispersion and measured X-ray temperature, and can check for self-consistency by independently determining its value from the X-ray surface brightness distribution.