The merging history of dark matter haloes in a hierarchical universe

We have developed a algorithm to investigate the merging history of present-day dark matter haloes in a universe where structure is built up hierarchically. The algorithm constructs merging history trees which can be used to trace the merging path of every halo mass element through all the progenitor haloes from which the present object formed. These trees follow merging histories from high redshift until z = 0 and so can be used to study the formation and merging of galaxies within the material which constitutes a single present-day group or cluster of galaxies. We have tested our results against those derived from numerical simulations of gravitational clustering and find that our algorithm correctly reproduces the mass distribution of the two largest halo progenitors at a series of redshifts. Applying our methods to the question of the survival of galaxy discs, we confirm that merging rates in a Ω = 1 cold dark matter universe may be too high to allow the observed predominace of spiral galaxies in the field. Low-density models have no such problem. An analysis of the frequency of substructure in galaxy clusters is unable to produce a reliable estimate of Ω because of the uncertainty in how long such substructure can last.