© CAMBRIDGE UNIVERSITY PRESS 1999

2.7. Central Density and Core Size

Central number density of galaxies in rich compact clusters (Bahcall 1975, 1977; Dressler 1978) is (for galaxies in the brightest 3 magnitude range)

(17)

The central density reaches ~ 10⁴h³ galaxies Mpc^-3 for the richest compact clusters. The typical central mass density in rich compact clusters, determined from cluster dynamics is

(18)

where _r,c is the radial (line-of-sight) central cluster velocity dispersion (in km s^-1) and R_c is the cluster core radius (in Mpc).

Core radii of typical rich compact clusters, determined from the galaxy distribution (Bahcall 1975; Dressler 1978; Sarazin 1986) are in the range

(19)

Core radii of the X-ray emitting intracluster gas (Section 3) are

(20)

The core radius of the mass distribution determined from gravitational lensing observations of some clusters may be smaller, R_c 50 kpc, than determined by the galaxy and gas distribution.

The typical central density of the hot intracluster gas in rich clusters (Section 3) is

(21)