VELOCITY FUNCTIONS OF GALAXIES AND CLUSTERS OF GALAXIES

We construct velocity functions of field galaxies and clusters of galaxies which are number densities as functions of the circular velocities of the systems. The circular velocities are obtained from data of H I 21 cm line width and/or stellar velocity dispersion for galaxies, and from an X-ray temperature function for clusters of galaxies. It is found that elliptical and S0 galaxies dominate at the high-velocity end of the galaxy velocity function in contrast to the field luminosity function in which spiral galaxies dominate at the high-luminosity end. The galaxy and cluster velocity functions almost form a single, continuous function, but for a small gap at the boundary. This may imply that galaxies and clusters of galaxies consist of a single population, in a dynamical sense. A cold dark matter model with OMEGA0 = 1 and a high bias agrees well with the observed velocity functions, while OMEGA0 < 1 models are inconsistent.