How Much Mass Do Supermassive Black Holes Eat in Their Old Age?

We consider the distribution of local supermassive black hole Eddingtonratios and accretion rates, accounting for the dependence of radiativeefficiency and bolometric corrections on the accretion rate. We find that blackhole mass growth, both of the integrated mass density and the masses of mostindividual objects, must be dominated by an earlier, radiatively efficient,high accretion rate stage, and not by the radiatively inefficient low accretionrate phase in which most local supermassive black holes are currently observed.This conclusion is particularly true of supermassive black holes in ellipticalhost galaxies, as expected if they have undergone merger activity in the pastwhich would fuel quasar activity and rapid growth. We discuss models of thetime evolution of accretion rates and show that they all predict significantmass growth in a prior radiatively efficient state. The only way to avoid thisconclusion is through careful fine-tuning of the accretion/quasar timescale toa value that is inconsistent with observations. Our results agree with a widerange of observational inferences drawn from the quasar luminosity function andX-ray background synthesis models, but our approach has the virtue of beingindependent of the modeling of source populations. Models in which black holesspend the great majority of their time in low accretion rate phases are thuscompletely consistent both with observations implying mass gain in relativelyshort, high accretion rate phases and with the local distribution of accretionrates.Comment: 11 pages, 4 figures, matches version accepted to Ap