  A long-standing problem for models of galaxy formation has been the mismatch
between the predicted shape of the mass function of dark matter halos and the
observed shape of the luminosity function of galaxies. The number of massive
halos is predicted to decrease as a power law (N proportional to M^-2) out to
very large masses, while the galaxy luminosity function cuts off exponentially
at luminosities above L*. This implies that the efficiency with which gas cools
onto massive systems is lower than expected. This letter investigates the role
of radio-loud active galactic nuclei (AGN) in continually re-heating the
cooling gas. By combining two observational results, the time-averaged energy
output associated with recurrent radio source activity is determined, as a
function of the black hole mass of the host galaxy: H = 10^21.4 (M_BH /
M_sun)^1.6 W. It is shown that for massive elliptical galaxies this
radio-source heating balances the radiative energy losses from the hot gas
surrounding the galaxy. The recurrent radio-loud AGN activity may therefore
provide a self-regulating feedback mechanism capable of controlling the rate of
growth of galaxies.
