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 $\dot{M}$_*σ_*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 $\sim {10}^{12.5}{M}_{\odot }$ 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 that 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.