How stellar feedback simultaneously regulates star formation and drives outflows

We present an analytic model for how momentum deposition from stellar feedback simultaneously regulates star formation and drives outflows in a turbulent interstellar medium (ISM). Because the ISM is turbulent, a given patch of ISM exhibits sub-patches with a range of surface densities. The high-density patches are 'pushed' by feedback, thereby driving turbulence and self-regulating local star formation. Sufficiently low-density patches, however, are accelerated to above the escape velocity before the region can self-adjust and are thus vented as outflows. When the gas fraction is ≳ 0.3, the ratio of the turbulent velocity dispersion to the circular velocity is sufficiently high that at any given time, of the order of half of the ISM has surface density less than the critical value and thus can be blown out on a dynamical time. The resulting outflows have a mass-loading factor (η ≡ dot{M}_{out}/M_{star }) that is inversely proportional to the gas fraction times the circular velocity. At low gas fractions, the star formation rate needed for local self-regulation, and corresponding turbulent Mach number, declines rapidly; the ISM is 'smoother', and it is actually more difficult to drive winds with large mass-loading factors. Crucially, our model predicts that stellar-feedback-driven outflows should be suppressed at z ≲ 1 in M_⋆ ≳ 10¹⁰ M_⊙ galaxies. This mechanism allows massive galaxies to exhibit violent outflows at high redshifts and then 'shut down' those outflows at late times, thereby enabling the formation of a smooth, extended thin stellar disc. We provide simple fitting functions for η that should be useful for sub-resolution and semi-analytic models.