An Accurate Comprehensive Approach to Substructure: IV. Dynamical Friction

In three previous Papers we analysed the origin of the properties of halo substructure found in simulations. This was achieved by deriving them analytically in the peak model of structure formation, using the statistics of nested peaks (with no free parameter) plus a realistic model of subhalo stripping and shock-heating (with only one parameter). However, to simplify the treatment we neglected dynamical friction (DF). Here, we revisit that work by accounting for DF. That is also done in a fully analytic manner that avoids the numerical integration of the subhalo orbital motion. We obtain very simple expressions for the abundance and radial distribution of subhaloes of different masses that disentangle the effects of DF from those of tidal stripping and shock-heating. These analytic expressions reproduce and explain the results of simulations and allow one to extend them to haloes of any mass, redshift and formation times in any desired cosmology.