The persistence of the universal halo profiles

Abstract

Simple simulations suggest that the phase space structure of haloes identified in cosmological calculations is invariant under the dynamics induced by sinking substructure satellites -- the background expands so as to leave the total distribution unchanged. We use a Fokker-Planck formulation to show that this is the case. The solutions obtained are valid for any mass spectrum of substructure, because the governing equation is linear in their mass weighed phase space distribution. If the clumps are considered solid, an exchange of poulations takes the form of an exponential instability, with characteristic timescale of the order of the dynamical friction time, leading to a low energy cutoff in the distribution function of the background and a constant density core. We show that there are long lived solutions with such a cutoff. They approximate a situation whereas the clumps are made of dense baryonic material. When stripping is important, as in the case of dissipationless substructure, it is likely that this situation is reversed -- the cutoff is now in the clump distribution function. A simple description suggests that this renders equilibria even more long lived. The results of this paper suggest that halo profiles similar to those found in dissipationless cosmological simulations are approximately invariant under the interaction induced by the presence of substructure satellites -- a necessary condition for the observed `universality'. In addition, the total profile, including baryons, should also be invariant; provided the latter are initially in the form of dense clumps, whose distribution follows that of the dark matter.