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.
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