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, mH
is the mass of the hydrogen
atom, is the cluster velocity
dispersion, k is Boltzmanns constant,
and Tgas 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.