Dynamical delays between starburst and AGN activity in galaxy nuclei

Observations of active galactic nuclei (AGN) have suggested a possible delay between the peak of star formation (on some scale) and AGN activity. Inefficient fuelling (and/or feedback) from fast stellarwinds has been invoked to explain this, butwe argue this is unlikely in bright systems accreting primarily cold dense gas. We show that such a delay can arise even in bright quasars for purely dynamical reasons. If some large-scale process produces rapid inflow, smaller scales will quickly become gas dominated. As the gas density peaks, so does the star formation rate (SFR). However, gravitational torques which govern further inflow are relatively inefficient in gas-dominated systems; as more gas is turned into stars, the stars provide an efficient angular momentum sink allowing more rapid inflow. Moreover, the gas provided to the central regions in mergers or strong disc instabilities will typically be similar to 100 times larger than that needed to fuel the black hole (BH); the system is effectively in the 'infinite gas supply' limit. BH growth can therefore continue for some time while the gas supply exhausts, until it has significantly depleted to the point where the BH is finally 'starved'. Both of these effects act together with comparable magnitude, and mean that the peak of BH growth can lag the peak in the SFR measured at a given scale by a time-scale corresponding to the gas exhaustion time on that scale (similar to 10-100 local dynamical times). This predicts that the inferred delay will vary in a specific manner with the radius over which the SFR is measured. We discuss possible implications for the role of AGN feedback in suppressing star formation activity.