Classical bulges, supermassive blackholes and AGN feedback: Extension to
  low-mass galaxies
  The empirical model of Lu et al. 2014a for the relation between star
formation rate and halo mass growth is adopted to predict the classical bulge
mass ($M_{\rm cb}$) - total stellar mass ($M_\star$) relation for central
galaxies. The assumption that the supermassive black hole (SMBH) mass ($M_{\rm
BH}$) is directly proportional to the classical bulge mass, with the
proportionality given by that for massive galaxies, predicts a $M_{\rm BH}$ -
$M_\star$ relation that matches well the observed relation for different types
of galaxies. In particular, the model reproduces the strong transition at
$M_\star=10^{10.5}$ - $10^{11}M_{\odot}$, below which $M_{\rm BH}$ drops
rapidly with decreasing $M_\star$. Our model predicts a new sequence at
$M_\star <10^{10.5}M_{\odot}$, where $M_{\rm BH} \propto M_\star$ but the
amplitude is a factor of $\sim 50$ lower than the amplitude of the sequence at
$M_\star>10^{11}M_{\odot}$. If all SMBH grow through similar quasar modes with
a feedback efficiency of a few percent, the energy produced in low-mass
galaxies at redshift $z\gtrsim 2$ can heat the circum-galactic medium up to a
specific entropy level that is required to prevent excessive star formation in
low-mass dark matter halos.
