Cored DARKexp systems with finite size: numerical results

TL;DR

This paper provides a detailed numerical analysis of DARKexp systems with finite size and cored density profiles, revealing their structural properties and behavior near critical parameters.

Contribution

It offers the first extensive numerical solutions for cored DARKexp systems with finite size, including their behavior across energy ranges and near critical parameters.

Findings

Mass density tail decays as r^{-4} at large radii.

Density starts linearly at small radii, i.e., proportional to r.

System size diverges as a specific parameter approaches a critical value.

Abstract

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 $\exp[-\beta(E - \Phi(0))] - 1$, $\Phi(0)$ being the depth of the potential well and $\beta$ 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 $\Phi(0)\le E\le 0$ and is double--valued for a certain interval of $\beta$. The size of the system represents a unique identifier for each member of this solution family and diverges as $\beta$ approaches a specific value. In this limit, the tail of the mass density $\rho(r)$ dies off as $r^{-4}$, while at small radii it always starts off linearly in $r$, that is $\rho(r)-\rho(0)\propto r$.