  We calculate the rate at which dark matter halos merge to form higher mass systems. Two complementary derivations using Press-Schechter theory are given, both of which result in the same equation for the formation rate. First, a derivation using the properties of the Brownian random walks within the framework of Press-Schechter theory is presented. We then use Bayes' theorem to obtain the same result from the standard Press-Schechter mass function. The rate obtained is shown to be in good agreement with results from Monte-Carlo and N-body simulations. We illustrate the usefulness of this formula by calculating the expected cosmological evolution in the rate of star formation that is due to short-lived, merger-induced starbursts. The calculated evolution is well-matched to the observed evolution in ultraviolet luminosity density, in contrast to the lower rates of evolution that are derived from semi-analytic models that do not include a dominant contribution from starbursts. Hence we suggest that the bulk of the observed ultraviolet starlight at z > 1 arises from short-lived, merger-induced starbursts. Finally, we show that a simple merging-halo model can also account for the bulk of the observed evolution in the comoving quasar space density. 
Cosmological Evolution & Hierarchical Galaxy Formation