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. 
Zhankui Lu and H.J. Mo
astro-ph.GA