On the formation and stability of fermionic dark matter halos in a cosmological framework

TL;DR

This paper demonstrates that fermionic dark matter halos with core-halo structures are thermodynamically stable and can form naturally in a cosmological setting, with potential core collapse into black holes at high masses.

Contribution

It provides the first thermodynamic stability analysis of fermionic dark matter core-halo profiles within a cosmological framework, confirming their long-term stability and conditions for collapse.

Findings

Core-halo profiles are stable and long-lived.

A critical mass exists where cores collapse into black holes.

Collapse occurs for halos with mass >10^9 solar masses at high redshift.

Abstract

The formation and stability of collisionless self-gravitating systems are long standing problems, which date back to the work of D. Lynden-Bell on violent relaxation and extends to the issue of virialization of dark matter (DM) halos. An important prediction of such a relaxation process is that spherical equilibrium states can be described by a Fermi-Dirac phase-space distribution, when the extremization of a coarse-grained entropy is reached. In the case of DM fermions, the most general solution develops a degenerate compact core surrounded by a diluted halo. As shown recently, the latter is able to explain the galaxy rotation curves while the DM core can mimic the central black hole. A yet open problem is whether this kind of astrophysical core-halo configurations can form at all, and if they remain stable within cosmological timescales. We assess these issues by performing a thermodynamic stability analysis in the microcanonical ensemble for solutions with given particle number at halo virialization in a cosmological framework. For the first time we demonstrate that the above core-halo DM profiles are stable (i.e. maxima of entropy) and extremely long lived. We find the existence of a critical point at the onset of instability of the core-halo solutions, where the fermion-core collapses towards a supermassive black hole. For particle masses in the keV range, the core-collapse can only occur for $M_{\rm vir} \gtrsim 10^9 M_\odot$ starting at $z_{\rm vir}\approx 10$ in the given cosmological framework. Our results prove that DM halos with a core-halo morphology are a very plausible outcome within nonlinear stages of structure formation.