The velocity function of galaxies

We present a galaxy circular velocity function, Psi(log v), derived from existing luminosity functions and luminosity-velocity relations. Such a velocity function is desirable for several reasons. First, it enables an objective comparison of luminosity functions obtained in different bands and for different galaxy morphologies, with a statistical correction for dust extinction. In addition, the velocity function simplifies comparison of observations with predictions from high-resolution cosmological N-body simulations. We derive velocity functions from five different data sets and find rough agreement among them, but about a factor of 2 variation in amplitude. These velocity functions are then compared with N-body simulations of a ACDM model (corrected for baryonic infall) in order to demonstrate both the utility and the current limitations of this approach. The number density of dark matter halos and the slope of the velocity function near v(*), the circular velocity corresponding to an similar to L-* spiral galaxy, are found to be comparable to those of observed galaxies. The primary sources of uncertainty in construction of Psi(log v) from observations and N-body simulations are discussed, and explanations to account for discrepancies are suggested.