Cored DARKexp systems with finite size: numerical results

In the DARKexp framework for collisionless isotropic relaxation of self-gravitating matter, the central object is the differential energy distribution n(E), which takes a maximum-entropy form proportional to exp[−β(E − Φ(0))] − 1, Φ(0) being the depth of the potential well and β the standard Lagrange multiplier. Then the first and quite non-trivial problem consists in the determination of an ergodic phase-space distribution which reproduces this n(E). In this work we present a very extensive and accurate numerical solution of such DARKexp problem for systems with cored mass density and finite size. This solution holds throughout the energy interval Φ(0)≤ E≤ 0 and is double-valued for a certain interval of β. The size of the system represents a unique identifier for each member of this solution family and diverges as β approaches a specific value. In this limit, the tail of the mass density ρ(r) dies off as r⁻⁴, while at small radii it always starts off linearly in r, that is ρ(r)−ρ(0)$\propto$ r.