  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.
