Evaluating Semi-Analytic Halo Merging Histories

We evaluate the accuracy of semi-analytic merger-trees by comparing them with the merging histories of dark-matter halos in N-body simulations, focusing on the joint distribution of the number of progenitors and their masses. We first confirm that the halo mass function as predicted directly by the Press-Schechter (PS) model deviates from the simulations by up to 50% depending on the mass scale and redshift, while the means of the projected distributions of progenitor number and mass for a halo of a given mass are more accurately predicted by the Extended PS model. We then use the full merger trees to study the joint distribution as a function of redshift and parent-halo mass. We find that while the deviation of the mean quantities due to the inaccuracy of the Extended PS model partly propagates into the higher moments of the distribution, the merger-tree procedure does not introduce a significant additional source of error. In particular, certain properties of the merging history such as the mass ratio of the progenitors and the total accretion rate are reproduced quite accurately for galaxy sized halos ($\sim 10^{12}\msun$), and less so for larger masses. We conclude that although there could be $\sim 50%$ deviations in the absolute numbers and masses of progenitors and in the higher order moment of these distributions, the relative properties of progenitors for a given halo are reproduced fairly well by the merger trees. They can thus provide a useful framework for modelling galaxy formation once the above-mentioned limitations are taken into account.