Why do Black Holes Trace Bulges (& Central Surface Densities), Instead of Galaxies as a Whole?

TL;DR

This paper proposes a model where stellar feedback-driven gas expulsion, dependent on surface density, explains why black hole masses correlate with bulge properties rather than entire galaxies.

Contribution

It introduces a correction to accretion models incorporating stellar feedback effects, explaining the observed correlation of black hole mass with bulge surface density.

Findings

Black hole mass correlates with bulge surface density above a critical threshold.

Stellar feedback efficiency depends on gravitational acceleration and surface density.

The model explains why black holes trace bulge properties instead of whole galaxies.

Abstract

Previous studies of fueling black holes (BHs) in galactic nuclei have argued (on scales ~0.01-1000pc) accretion is dynamical with inflow rates $\dot{M}\sim\eta\,M_{\rm gas}/t_{\rm dyn}$ in terms of gas mass $M_{\rm gas}$, dynamical time $t_{\rm dyn}$, and some $\eta$. But these models generally neglected expulsion of gas by stellar feedback, or considered extremely high densities where expulsion is inefficient. Studies of star formation, however, have shown on sub-kpc scales the expulsion efficiency $f_{\rm wind}=M_{\rm ejected}/M_{\rm total}$ scales with the gravitational acceleration as $(1-f_{\rm wind})/f_{\rm wind}\sim\bar{a}_{\rm grav}/\langle\dot{p}/m_{\ast}\rangle\sim \Sigma_{\rm eff}/\Sigma_{\rm crit}$ where $\bar{a}_{\rm grav}\equiv G\,M_{\rm tot}(<r)/r^{2}$ and $\langle\dot{p}/m_{\ast}\rangle$ is the momentum injection rate from young stars. Adopting this as the simplest correction for stellar feedback, $\eta \rightarrow \eta\,(1-f_{\rm wind})$, we show this provides a more accurate description of simulations with stellar feedback at low densities. This has immediate consequences, predicting e.g. the slope and normalization of the $M-\sigma$ and $M-M_{\rm bulge}$ relation, $L_{\rm AGN}-$SFR relations, and explanations for outliers in compact Es. Most strikingly, because star formation simulations show expulsion is efficient ($f_{\rm wind}\sim1$) below total-mass surface density $M_{\rm tot}/\pi\,r^{2}<\Sigma_{\rm crit}\sim3\times10^{9}\,M_{\odot}\,{\rm kpc^{-2}}$ (where $\Sigma_{\rm crit}=\langle\dot{p}/m_{\ast}\rangle/(\pi\,G)$), BH mass is predicted to specifically trace host galaxy properties above a critical surface brightness $\Sigma_{\rm crit}$ (B-band $\mu_{\rm B}^{\rm crit}\sim 19\,{\rm mag\,arcsec^{-2}}$). This naturally explains why BH masses preferentially reflect bulge properties or central surface-densities ($\Sigma_{1\,{\rm kpc}}$), not 'total' galaxy properties.