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Merging History Trees of Dark Matter Haloes: a Tool for Exploring Galaxy Formation Models

A method of deriving and using merging history trees of dark matter galaxy haloes directly from pure gravity N-body simulations is presented. This combines the full non-linearity of N-body simulations with the flexibility of the semi-analytical approach. Merging history trees derived from power-law initial perturbation spectrum simulations (for indices $n=-2$ and $n=0$) by Warren et al. (1992) are shown. As an example of a galaxy formation model, these are combined with evolutionary stellar population synthesis, via simple scaling laws for star formation rates, showing that if most star formation occurs during merger-induced bursts, then a nearly flat faint-end slope of the galaxy luminosity function may be obtained in certain cases. Interesting properties of hierarchical halo formation are noted: (1) In a given model, merger rates may vary widely between individual haloes, and typically 20%-30% of a halo's mass may be due to infall of uncollapsed material. (2) Small mass haloes continue to form at recent times: as expected, the existence of young, low redshift, low metallicity galaxies (e.g., Izotov et al. 1997) is consistent with hierarchical galaxy formation models. (3) For $n=-2,$ the halo spatial correlation function can have a very high initial bias due to the high power on large scales.