The sub-Eddington boundary for the quasar mass-luminosity plane: A
  theoretical perspective
  By exploring more than sixty thousand quasars from the Sloan Digital Sky
Survey Data Release 5, Steinhardt & Elvis discovered a sub-Eddington boundary
and a redshift-dependent drop-off at higher black hole mass, possible clues to
the growth history of massive black holes. Our contribution to this special
issue of Universe amounts to an application of a model for black hole accretion
and jet formation to these observations. For illustrative purposes we include
about 100,000 data points from the Sloan Digital Sky Survey Data Release 7
where the sub-Eddington boundary is also visible, and propose a theoretical
picture that explains these features. By appealing to thin disk theory and both
the lower accretion efficiency and the time evolution of jetted quasars
compared to non-jetted quasars in our 'gap paradigm', we explain two features
of the sub-Eddington boundary. First, we show that a drop-off on the quasar
mass-luminosity plane for larger black hole mass occurs at all redshifts. But
the fraction of jetted quasars is directly related to the merger function in
this paradigm, which means the jetted quasar fraction drops with decrease in
redshift, which allows us to explain a second feature of the sub-Eddington
boundary, namely a redshift dependence of the slope of the quasar
mass-luminosity boundary at high black hole mass stemming from a change in
radiative efficiency with time. We are able to reproduce the mass dependence
of, as well as the oscillating behavior in, the slope of the sub-Eddington
boundary as a function of time. The basic physical idea involves retrograde
accretion occurring only for a subset of the more massive black holes which
implies that most spinning black holes in our model are prograde accretors. In
short, this paper amounts to a qualitative overview of how a sub-Eddington
boundary naturally emerges in the gap paradigm.
