The mass function of galaxies based on correlated velocity structure

This paper introduces a new approach to the calculation of the galactic mass multiplicity function based on the probability of correlated velocity structures existing on a given spatial scale. The correlations are supposed to have developed during a protogalactic era of virialized structures, before which time the density evolution had already become non-linear. We determine the density index empirically in this paper, although it may eventually be related to a spectrum of initial fluctuations. The subsequent non-linear dynamics are dealt with explicitly using a continuum model with tidal interactions simulated by an effective shear viscosity. Our predictions for the (unnormalized) mass function and for the large-scale velocity correlations between galaxies are deduced relatively directly from the ‘cosmic von Karman-Howarth’ equation implicit in our basic model. Our predictions are in good agreement with existing data. The first part of our paper offers a summary and a critique of alternative methods.