Dark halo microphysics and massive black hole scaling relations in galaxies

TL;DR

This paper models black hole-galaxy relations through dark matter microphysics, linking black hole mass to dark matter properties and galaxy velocity dispersions, providing new insights into dark matter physics and galaxy evolution.

Contribution

It introduces a self-gravitating dark matter model with specific microphysics that naturally explains black hole scaling relations and constrains dark matter properties from observations.

Findings

Black hole mass scales with dark matter velocity dispersion as m_bh ∝ σ^{F/2}.

Empirical m_bh-σ relations suggest dark matter degrees of freedom 7<F<10.

Dark matter microphysics influences galaxy core structures and globular cluster dynamics.

Abstract

We investigate the black hole (BH) scaling relation in galaxies using a model in which the galaxy halo and central BH are a self-gravitating sphere of dark matter (DM) with an isotropic, adiabatic equation of state. The equipotential where the escape velocity approaches the speed of light defines the horizon of the BH. We find that the BH mass ($m_\bullet$) depends on the DM entropy, when the effective thermal degrees of freedom ($F$) are specified. Relations between BH and galaxy properties arise naturally, with the BH mass and DM velocity dispersion following $m_\bullet\propto\sigma^{F/2}$ (for global mean density set by external cosmogony). Imposing observationally derived constraints on $F$ provides insight into the microphysics of DM. Given that DM velocities and stellar velocities are comparable, the empirical correlation between $m_\bullet$ and stellar velocity dispersions $\sigma_\star$ implies that $7<F<10$. A link between $m_\bullet$ and globular cluster properties also arises because the halo potential binds the globular cluster swarm at large radii. Interestingly, for $F>6$ the dense dark envelope surrounding the BH approaches the mean density of the BH itself, while the outer halo can show a nearly uniform kpc-scale core resembling those observed in galaxies.