Investigating the properties of AGN feedback in hot atmospheres
  triggered by cooling-induced gravitational collapse
  Radiative cooling may plausibly cause hot gas in the centre of a massive
galaxy, or galaxy cluster, to become gravitationally unstable. The subsequent
collapse of this gas on a dynamical timescale can provide an abundant source of
fuel for AGN heating and star formation. Thus, this mechanism provides a way to
link the AGN accretion rate to the global properties of an ambient cooling
flow, but without the implicit assumption that the accreted material must have
flowed onto the black hole from 10s of kiloparsecs away. It is shown that a
fuelling mechanism of this sort naturally leads to a close balance between AGN
heating and the radiative cooling rate of the hot, X-ray emitting halo.
Furthermore, AGN powered by cooling-induced gravitational instability would
exhibit characteristic duty cycles (delta) which are redolent of recent
observational findings: delta is proportional to L_X/sigma_{*}^{3}, where L_X
is the X-ray luminosity of the hot atmosphere, and sigma_{*} is the central
stellar velocity dispersion of the host galaxy. Combining this result with
well-known scaling relations, we deduce a duty cycle for radio AGN in
elliptical galaxies that is approximately proportional to M_{BH}^{1.5}, where
M_{BH} is the central black hole mass. Outburst durations and Eddington ratios
are also given. Based on the results of this study, we conclude that
gravitational instability could provide an important mechanism for supplying
fuel to AGN in massive galaxies and clusters, and warrants further
investigation.
