Cored density profiles in the DARKexp model

Abstract

The DARKexp model represents a novel and promising attempt to solve a long standing problem of statistical mechanics, that of explaining from first principles the quasistationary states at the end of the collisionless gravitational collapse. The model, which yields good fits to observation and simulation data on several scales, was originally conceived to provide a theoretical basis for the 1/r cusp of the Navarro-Frenk-White profile. In this note we show that it also allows for cored density profiles that, when viewed in three dimensions, in the r → 0 limit have the conical shape characteristic of the Burkert profile. It remains to be established whether both cusps and cores, or only one of the two types, are allowed beyond the asymptotic analysis of this work.

Cored DARKexp systems with finite size: numerical results

“…We have found here a novel family of ergodic systems with finite size, mass and energy and with a cored density profile. They match very well the analytic results of [47] and have interesting physical properties summarized in Figs. 14 and 15.…”

“…In fact, ergodic phase-space distributions have by themselves a limited applicability to the outcome of real collapses, where angular momentum plays a crucial role also in case of perfect spherical symmetry. Our goal in this work, as in the preceding one [47], was to develop a framework, both analytic and numeric, for a trustworthy and accurate solution of the DARKexp problem, since we regard the DARKexp model as a well founded first-principle approach to the quasi-equilibrium of collisionless self-gravitating matter, which moreover happens to be compatible with observations and N −body simulations. We have found here a novel family of ergodic systems with finite size, mass and energy and with a cored density profile.…”

“…(2.14) and (2.21). Some analytical results were obtained in [47] concerning the next-to-leading asymptotics near s = 0 of F (s), ν(s), G(s), and x(s).…”

“…In other words, we obtain the profiles for f (E) and ρ(r) at many different values of β with no limitations on the range of E or r. In particular, this means that our numerical solutions confirm the behavior of ρ(r) near r = 0 reported in eq. 7.2 of [47], namely…”

“…Our numerical approach is described in detail in section 4. It is based on the precise dimensionless formulation of the DARKexp problem put forward in [47] and repeated here in section 2 for completeness. This formulation lends itself very naturally to the use of the Chebyshev approximation as central numerical tool.…”