Force-feeding Black Holes
  We propose that the growth of supermassive black holes is associated mainly
with brief episodes of highly super-Eddington infall of gas ("hyperaccretion").
This gas is not swallowed in real time, but forms an envelope of matter around
the black hole that can be swallowed gradually, over a much longer timescale.
However, only a small fraction of the black hole mass can be stored in the
envelope at any one time. We argue that any infalling matter above a few per
cent of the hole's mass is ejected as a result of the plunge in opacity at
temperatures below a few thousand degrees K, corresponding to the Hayashi
track. The speed of ejection of this matter, compared to the velocity
dispersion (sigma) of the host galaxy's core, determines whether the ejected
matter is lost forever or returns eventually to rejoin the envelope, from which
it can be ultimately accreted. The threshold between matter recycling and
permanent loss defines a relationship between the maximum black hole mass and
sigma that resembles the empirical M_BH-sigma relation.
