Collapsed and extended cold dark matter halos in softened n-body gravity

Abstract

The statistical mechanics of N cold dark matter (CDM) particles interacting via a softened gravitational potential is reviewed in the microcanonical ensemble and mean field limit. A phase diagram for the system is computed as a function of the total energy E and gravitational softening length ε. For softened systems, two stable phases exist: a collapsed phase, whose radial density profile ρ(r) is a central Dirac cusp, and an extended phase, for which ρ(r) has a central core and ρ(r) ∼ r-2.2 at large r. It is shown that many N-body simulations of CDM halos in the literature inadvertently sample the collapsed phase only, even though this phase is unstable when there is zero softening. Conseque..