Fermionic Dark Matter spikes: origin and growth of Black Hole seeds

TL;DR

This paper models the formation and structure of fermionic dark matter spikes around supermassive black holes using a general relativistic approach, revealing new density profiles and the importance of dark matter properties in galaxy dynamics.

Contribution

It introduces a self-consistent relativistic model of fermionic dark matter spikes around SMBHs, exploring different initial conditions and their impact on spike profiles and SMBH seed growth.

Findings

Dilute fermionic DM develops a $ ho \,\sim r^{-3/2}$ spike.

Semi-degenerate fermions form novel, particle-dependent spike profiles.

Fermionic spikes may be depleted by SMBHs, not just enhanced.

Abstract

We characterize the overdensity (spike) of fermionic dark matter (DM) particles around a supermassive black hole (SMBH) within a general relativistic analysis. The initial DM halo distribution is obtained by solving the equilibrium equations of a self-gravitating system of massive fermions at a finite temperature, according to the Ruffini-Arg\"uelles-Rueda (RAR) model. The final fermionic DM spike is calculated around a Schwarzschild SMBH. We explore two possible interpretations for the origin and evolution of the SMBH seed. One corresponds to the traditional scenario proposed by Gondolo & Silk (1999), where a small BH mass of baryonic origin sits at the halo's center and grows adiabatically. The other one, from DM origin, where the dense and degenerate fermion core predicted by the RAR model grows adiabatically by capturing baryons until its gravitational collapse, providing a heavy SMBH seed, whose specific value depends on the fermion mass. We study different initial fermionic DM profiles that the theory allows. We show that overall dilute (i.e., Boltzmannian) fermionic DM develops the well-known spike with density profile $\rho \sim r^{-3/2}$. Instead, for semi-degenerate fermions with a dense and compact core surrounded by a diluted halo, we find novel spike profiles that depend on the particle mass and nature. In the more general case, fermionic spikes do not develop a simple power-law profile. Furthermore, the SMBH does not always imply an enhancement of the surrounding DM density; it might also deplete it. Thus, the self-consistent inclusion of the DM candidate nature and mass in determining the structure and distribution of DM in galaxies, including the DM spikes around SMBHs, is essential for the specification of DM astrophysical probes such as BH mergers, gravitational waves, or stellar orbits.