AGN outflows trigger starbursts in gas-rich galaxies

Recent well resolved numerical simulations of AGN feedback have shown that its effects on the host galaxy may be not only negative but also positive. In the late gas poor phase, AGN feedback blows the gas away and terminates star formation. However, in the gas-rich phase(s), AGN outflows trigger star formation by over-compressing cold dense gas and thus provide positive feedback on their hosts. In this paper we study this AGN-triggered starburst effect. We show that star formation rate in the burst increases until the star formation feedback counteracts locally the AGN outflow compression. Globally, this predicts a strong nearly linear statistical correlation between the AGN and starburst bolometric luminosities in disc galaxies, L_* \propto L_{AGN}^{5/6}. The correlation is statistical only because AGN activity may fluctuate on short time scales (as short as tens of years), and because AGN may turn off but its effects on the host may continue to last until the AGN-driven outflow leaves the host, which may be up to 10 times longer than the duration of the AGN activity. The coefficient in front of this relation depends on the clumpiness and morphology of the cold gas in the galaxy. A "maximum starburst" takes place in am azimuthally uniform gas disc, for which we derive an upper limit of L_* \sim 50 times larger than L_{AGN} for typical quasars. For more clumpy and/or compact cold gas distributions, the starburst luminosity decreases. We also suggest that similar AGN-triggerred starbursts are possible in hosts of all geometries, including during galaxy mergers, provided the AGN is activated. Finally, we note that due to the short duration of the AGN activity phase the accelerating influence of AGN on starbursts may be much more common than observations of simultaneous AGN and starbursts would suggest.