Formation time-distribution of dark matter haloes: theories versus N-body simulations

In this paper we use numerical simulations to test the formation time distribution of dark matter haloes predicted by the analytical excursion set approaches. The formation time distribution is closely linked to the conditional mass function and this test is therefore an indirect probe of this distribution. The excursion set models tested are the extended Press-Schechter (EPS) model, the ellipsoidal collapse model, and the non-spherical collapse boundary model. Three sets of simulations (six realizations) have been used to investigate the halo formation time distribution for halo masses ranging from dwarf-galaxy-like haloes (M = 10(-3) M-*, where M-* is the characteristic non-linear mass scale) to massive haloes of M = 8.7M(*). None of the models can match the simulation results at both high and low redshift. In particular, dark matter haloes formed generally earlier in our simulations than predicted by the EPS model. This discrepancy might help explain why semi-analytical models of galaxy formation, based on EPS merger trees, underpredict the number of high redshift galaxies compared with recent observations