  We consider a model for quasar formation in which massive black holes are
formed and fuelled largely by the accretion of hot gas during the process of
galaxy formation. In standard hierarchical collapse models, objects about the
size of normal galaxies and larger form a dense hot atmosphere when they
collapse. We show that if such an atmosphere forms a nearly "maximal" cooling
flow, then a central black hole can accrete at close to its Eddington limit.
This leads to exponential growth of a seed black hole, resulting in a quasar in
some cases. In this model, the first quasars form soon after the first
collapses to produce hot gas. The hot gas is depleted as time progresses,
mostly by cooling, so that the accretion rate eventually falls below the
threshold for advection-dominated accretion, at which stage radiative
efficiency plummets and any quasar turns off. A simple implementation of this
model, incorporated into a semi-analytical model for galaxy formation,
over-produces quasars when compared with observed luminosity functions, but is
consistent with models of the X-ray Background which indicate that most
accretion is obscured. It produces few quasars at high redshift due to the lack
of time needed to grow massive black holes. Quasar fuelling by hot gas provides
a minimum level, sufficient to power most quasars at redshifts between one and
two, to which other sources of fuel can be added. The results are sensitive to
feedback effects, such as might be due to radio jets and other outflows.
