Preventing Star Formation in Early-Type Galaxies with Late-Time Stellar
  Heating
  We revisit previous suggestions that the heating provided by the winds of
dying low-mass stars plays an important role in preventing star formation in
quiescent galaxies. At the end of their asymptotic giant branch phase,
intermediate and low-mass stars eject their envelopes rapidly in a super-wind
phase, usually giving rise to planetary nebulae. In spheroidal galaxies with
high stellar velocity dispersions, the interaction of these ejected envelopes
with the ambient diffuse gas can lead to significant, isotropic and
steady-state heating that scales as $\dot{M}_\ast\sigma_\ast^2$. We show that
cooling of the central regions of the hot diffuse halo gas can be delayed for a
Hubble time for halos more massive than $\sim10^{12.5}M_{\odot}$ at $0<z<2$,
although stellar heating alone is unlikely to forestall cooling in the most
massive clusters at $z=0$. This mechanism provides a natural explanation for
the strong trend of galaxy quiescence with stellar surface density and velocity
dispersion. In addition, since the ejected material will thermalize to
$kT\sim\sigma_\ast^2$, this mechanism provides an explanation for the observed
similarity between the central temperature of the hot diffuse gas and
$\sigma_\ast^2$, a result which is not trivial in light of the short inferred
cooling times of the hot gas. The main uncertainty in this analysis is the
ultimate fate of the stellar ejecta. Preventing accumulation of the ejecta in
the central regions may require energy input from another source, such as Type
Ia supernovae. Detailed simulations of the interaction of the stellar wind with
the ambient gas are required to better quantify the net effect of AGB heating.
