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

Recent work indicates that star-forming early-type galaxies (ETGs) residing in the blue cloud migrate rapidly to the red sequence within around a Gyr, passing through several phases of increasingly strong AGN activity in the process (Schawinski et al. 2007, MNRAS, 382, 1415; S07 hereafter). We show that natural depletion of the 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 in S07. 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 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 timescale' and removes part of the 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 S07. We find that acceptable models have feedback timescales <0.2 Gyrs. The mass fraction in young stars in the remnants is <5% and the residual gas fractions are less than 0.6%, in good agreement with the recent literature. At least half of the initial gas reservoir is removed as the galaxies evolve from the blue cloud to the red sequence. If we restrict ourselves to feedback timescales similar to the typical duty cycles of local AGN (a few hundred Myrs) then a few tenths of a percent of the luminosity of an early-type Seyfert (10^11 LSun) must couple to the gas reservoir in order to produce migration times that are consistent with the observations.