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