The build-up of haloes within Press-Schechter theory

Modelling the build-up of haloes is important for linking the formation of galaxies with cosmological models. A simple model of halo growth is provide d by Press-Schechter (PS) theory, where the initial field of density fluctu ations is smoothed using spherically symmetric filters centred on a given p osition to obtain information about the likelihood of later collapse on var ying scales. In this paper the predicted halo mass growth is compared for t hree filter shapes: Gaussian, top-hat and sharp k-space. Preliminary work i s also presented analysing the build-up of haloes within numerical simulati ons using a friends-of-friends group finder. The best-fit to the simulation mass function was obtained using PS theory with a top-hat filter. By compa ring both the backwards conditional mass function, which gives the distribu tion of halo progenitors, and the distribution of halo mergers in time, the build-up of haloes in the simulations is shown to be better fitted by PS t heory with a sharp k-space filter. This strengthens previous work, which al so found the build-up of haloes in simulations to be well matched to PS the ory with a sharp k-space filter by providing a direct comparison of differe nt filters and by extending the statistical tools used to analyse halo mass growth. The usefulness of this work is illustrated by showing that the cos mological evolution in the proportion of haloes that have undergone recent merger is predicted to be independent of mass and power spectrum and to onl y depend upon cosmology. Recent results from observations of field galaxies are shown to match the evolution expected, but are not sufficiently accura te to distinguish usefully between cosmological parameters.