The Persistence of Universal Halo Profiles

Simple simulations suggest that the phase space structure of haloesidentified in cosmological calculations is invariant under the dynamics inducedby sinking substructure satellites -- the background expands so as to leave thetotal distribution unchanged. We use a Fokker-Planck formulation to show thatthis is the case. The solutions obtained are valid for any mass spectrum ofsubstructure, because the governing equation is linear in their mass weighedphase space distribution. If the clumps are considered solid, an exchange ofpoulations takes the form of an exponential instability, with characteristictimescale of the order of the dynamical friction time, leading to a low energycutoff in the distribution function of the background and a constant densitycore. We show that there are long lived solutions with such a cutoff. Theyapproximate a situation whereas the clumps are made of dense baryonic material.When stripping is important, as in the case of dissipationless substructure, itis likely that this situation is reversed -- the cutoff is now in the clumpdistribution function. A simple description suggests that this rendersequilibria even more long lived. The results of this paper suggest that haloprofiles similar to those found in dissipationless cosmological simulations areapproximately invariant under the interaction induced by the presence ofsubstructure satellites -- a necessary condition for the observed`universality'. In addition, the total profile, including baryons, should alsobe invariant; provided the latter are initially in the form of dense clumps,whose distribution follows that of the dark matter.