Why do black holes trace bulges (& central surface densities), instead of galaxies as a whole?

Abstract

ABSTRACT Previous studies of fueling black holes in galactic nuclei have argued (on scales ${\sim}0.01{-}1000\,$pc) accretion is dynamical with inflow rates $\dot{M}\sim \eta \, M_{\rm gas}/t_{\rm dyn}$ in terms of gas mass Mgas, dynamical time tdyn, and some η. 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 fwind = Mejected/Mtotal 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 $\bar{a}_{\rm grav}\equiv G\, M_{\rm tot}(\lt r)/r^{2}$ 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 the slope and normalization of the MBH − σ and MBH − Mbulge relation, LAGN −SFR relations, and explanations for outliers in compact Es. Most strikingly, because star formation simulations show expulsion is efficient (fwind ∼ 1) below total-mass surface density $M_{\rm tot}/\pi \, r^{2}\lt \Sigma _{\rm crit}\sim 3\times 10^{9}\, \mathrm{M}_{\odot }\, {\rm kpc^{-2}}$ (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 Σcrit (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 (e.g. $\Sigma _{1\, {\rm kpc}}$), not ‘total’ galaxy properties.