Sub-Eddington star-forming regions are super-Eddington: Momentum-driven outflows from supersonic turbulence

We show that the turbulent gas in the star-forming regions of galaxies is unstable to wind formation via momentum deposition by radiation pressure or other momentum sources like supernova explosions, even if the system is below the average Eddington limit. This conclusion follows from the fact that the critical momentum injection rate per unit mass for unbinding gas from a self-gravitating system is proportional to the gas surface density and that a turbulent medium presents a broad distribution of column densities to the sources. For an average Eddington ratio of G≃ 0.1 and for turbulent Mach numbers ≳ 30, we find that ~1 per cent of the gas is ejected per dynamical time-scale at velocities larger than the local escape velocity. Because of the lognormal shape of the surface density distribution, the mass-loss rate is highly sensitive to the average Eddington ratio, reaching ~20-40 per cent of the gas mass per dynamical time for G≃ 1. Using this model we find a large scatter in the mass-loading factor for star-forming galaxies, ranging from ~10^-3-10, but with significant uncertainties. Implications for the efficiency of star formation in giant molecular clouds are highlighted. For radiation pressure feedback alone, we find an increasing star formation efficiency as a function of initial gas surface density. Uncertainties are discussed.