Origin of the Correlations Between Supermassive Black Holes and Their Host Galaxies

TL;DR

This paper investigates the origins of the tight correlations between supermassive black holes and their host galaxies, proposing that different physical processes underlie the $ ext{M}_ ext{BH}-\sigma$ and $ ext{M}_ ext{BH}- ext{M}_ ext{host}$ relations, supported by observational data.

Contribution

The study provides empirical evidence supporting a model where galaxy relaxation explains the $ ext{M}_ ext{BH}-\sigma$ relation, and self-regulation accounts for the $ ext{M}_ ext{BH}- ext{M}_ ext{host}$ relation.

Findings

Galaxies with the $ ext{M}_ ext{BH}-\sigma$ relation are near virial equilibrium.

The ratio of black hole accretion rate to star formation rate remains nearly constant at $ ext{BHAR}/ ext{SFR} \\sim 10^{-3}$ from redshift 0 to 3.

Different origins for the two correlations are supported: galaxy relaxation for $ ext{M}_ ext{BH}-\sigma$ and self-regulation for $ ext{M}_ ext{BH}- ext{M}_ ext{host}$.

Abstract

Observations have shown that supermassive black holes in nearby elliptical galaxies correlate tightly with the stellar velocity dispersion (the $\MBH - \sigma$ relation) and the stellar mass (the $\MBH - \Mhost$ relation) of their host spheroids. However, the origin of these correlations remains ambiguous. In a previous paper by Zhu et al., we proposed a model which links the M-$\sigma$ relation to the the dynamical state of the system and the $\MBH - \Mhost$ relation to the self-regulation of galaxy growth. To test this model, we compile a sample of observed galaxies with different properties and examine the dependence of the above correlations on these parameters. We find that galaxies that satisfy the the $\MBH - \sigma$ correlation appear to have reached virial equilibrium, as indicated by the ratio between kinetic energy and gravitational potential, 2K/U $\sim$ 1. Furthermore, the ratio of black hole accretion rate to star formation rate remains nearly constant, BHAR /SFR $\sim$ $10^{-3}$, in active galaxies over a wide range of mass in the redshift range z=0 - 3. These results confirm our theoretical model that the observed correlations have different origins: the $\MBH - \sigma$ relation may result from galaxy relaxation, while the $\MBH$ - $\Mhost$ relation may be due to self-regulated black hole accretion and star formation in galaxies.