The evolution of substructure in galaxy, group and cluster haloes - II. Global properties

In a previous paper, we described a new method for including detailed information about substructure in semi-analytic models of dark matter halo formation based on merger trees. In this paper, we present the basic predictions of our full model of halo formation. We first describe the overall properties of substructure in galaxy, group or cluster haloes at the present day. We then discuss the evolution of substructure, and the effect of the mass-accretion history of an individual halo on the mass function and orbital grouping of its subhalo population. We show, in particular, that the shape of the subhalo mass function is strongly correlated with the formation epoch of the halo. In a third paper in this series, we will compare the results of our semi-analytic method with the results of self-consistent numerical simulations of halo formation.