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

6. THE VIRIAL MASS DISTRIBUTION

From X-ray images one can infer the total gravitational mass as a function of radius. If the radial X-ray temperature profile is measured, then the cluster mass distribution can be more precisely determined from the X-ray gas distribution than from the virial theorem, which requires an uncertain correction from line-of-sight to total velocity dispersion.

Fabricant et al. (1980) used the X-ray surface brightness distribution to demonstrate the existence of a dark halo surrounding M87 (see Section 4.2.1). Their analysis can be applied to an entire cluster or subcluster (see Section 3.2), the only condition being that the X-ray gas be in hydrostatic equilibrium. This criterion is valid in the evolved clusters with no dominant galaxies where there is no evidence for cooling, and also in the outer regions of clusters with dominant galaxies away from central cooling cores. In the absence of spatially resolved spectral data, an assumption must be made regarding the cluster temperature profile. In a relaxed cluster atmosphere away from any central galaxy and in the absence of a hot intercluster medium, we would expect an outward decrease in temperature. Hence the assumption of a constant temperature gives a minimum mass.

With this additional assumption, it remains only to determine _gas (r) from the observed surface brightness distribution projected on the sky. The numerical inversion described by Fabricant et al. (1980) was performed by Blair et al. (1980) and Bechtold et al. (1980) for representative evolved clusters with and without central, dominant galaxies. In addition, these authors computed the mass of X-ray-emitting gas. Table 4 lists their results, which show that the X-ray-determined cluster masses are comparable to the virial estimates (scaled to 0.5 Mpc) and also that the X-ray-emitting gas represents only ~ 10% of the total gravitational mass.

Table 4. Cluster masses

		Total mass	Gas mass
	Temperature	within 0.5 Mpc	within 0.5 Mpc
Cluster	(keV)	(x 1014 M)	(x 1013 M)
Abell 0085	6.8 ± .5 a	2.0	3.4
Abell 1795	5.8 ± 1.0 a	2.3	3.6
Abell 2255	3.8 - 10. b	3.3	3.5
Abell 2256	7.0 ± 1.0 a	6.3	4.1
a Mushotzky & Smith 1980
b Einstein IPC and MPC