The relation between velocity dispersion and central galaxy density in clusters of galaxies

A correlation between cluster velocity dispersion and average central galaxy density is reported. The correlation covers the range from rich clusters to small groups of galaxies, or, in terms of velocity dispersion, from vr approximately 1500 to approximately 100 km/s. This result is useful for estimating unknown velocity dispersions in clusters with the aid of the relatively easily determined 0.5 Mpc central galaxy density parameter. When combined with the virial theorem, the above relation also suggests that the mass-to-light ratio of galaxy systems increases with the system's velocity dispersion.