How Much Mass do Supermassive Black Holes Eat in their Old Age?
  We consider the distribution of local supermassive black hole Eddington ratios and accretion rates, accounting for the dependence of radiative efficiency and bolometric corrections on the accretion rate. We find that black hole mass growth, both of the integrated mass density and the masses of most individual objects, must be dominated by an earlier, radiatively efficient, high accretion rate stage, and not by the radiatively inefficient low accretion rate phase in which most local supermassive black holes are currently observed. This conclusion is particularly true of supermassive black holes in elliptical host galaxies, as expected if they have undergone merger activity in the past which would fuel quasar activity and rapid growth. We discuss models of the time evolution of accretion rates and show that they all predict significant mass growth in a prior radiatively efficient state. The only way to avoid this conclusion is through careful fine-tuning of the accretion/quasar timescale to a value that is inconsistent with observations. Our results agree with a wide range of observational inferences drawn from the quasar luminosity function and X-ray background synthesis models, but our approach has the virtue of being independent of the modeling of source populations. Models in which black holes spend the great majority of their time in low accretion rate phases are thus completely consistent both with observations implying mass gain in relatively short, high accretion rate phases and with the local distribution of accretion rates. 
Philip F. Hopkins, Ramesh Narayan, Lars Hernquist (Harvard-Smithsonian   Center for Astrophysics)