A simple model for AGN feedback in nearby early-type galaxies

Recent work (Schawinski et al.) indicates that star-forming early-type galaxies residing in the blue cloud migrate rapidly to the red sequence within around a Gyr, passing through several phases of increasingly strong active galactic nucleus (AGN) activity in the process. We show that natural depletion of the cold gas reservoir through star formation (i.e. in the absence of any feedback from the AGN) induces a blue-to-red reddening rate that is several factors lower than that observed by Schawinski et al. This is because the gas depletion rate due to star formation alone is too slow, implying that another process needs to be invoked to remove cold gas from the system and accelerate the reddening rate. We develop a simple phenomenological model, in which a fraction of the AGN's luminosity couples to the gas reservoir over a certain 'feedback time-scale' and removes part of the cold gas mass from the galaxy, while the remaining gas continues to contribute to star formation. We use the model to investigate scenarios which yield migration times consistent with the results of Schawinski et al. We find that acceptable models have feedback time-scales 0.2 Gyr. The mass fraction in young stars in the remnants is 5 percent and the residual cold gas fractions are less than 0.6 per cent, in good agreement with the recent literature. At least half of the initial cold gas reservoir is removed as the galaxies evolve from the blue cloud to the red sequence. If we restrict ourselves to feedback time-scales similar to the typical duty cycles of local AGN (a few hundred Myr) then a few tenths of a per cent of the luminosity of an early-type Seyfert (~1011 ) must couple to the cold gas reservoir in order to produce migration times that are consistent with the observations.