The maximum flux of star-forming galaxies

The importance of radiation pressure feedback in galaxy formation has been extensively debated over the last decade. The regime of greatest uncertainty is in the most actively starforming galaxies,where large dust columns can potentially produce a dust-reprocessed infrared radiation field with enough pressure to drive turbulence or eject material. Here, we derive the conditions under which a self-gravitating mixed gas-star disc can remain hydrostatic despite trapped radiation pressure. Consistently, taking into account the self-gravity of the medium, the star- and dust-to-gas ratios, and the effects of turbulent motions not driven by radiation, we show that galaxies can achieve a maximum Eddington-limited star formation rate per unit area Σ_*,crit ~ 10³M_⊙ pc^-2 Myr^-1, corresponding to a critical flux of F_*,crit ~ 10¹³ L_⊙ kpc^-2 similar to previous estimates; higher fluxes eject mass in bulk, halting further star formation. Conversely, we show that in galaxies below this limit, our 1D models imply simple vertical hydrostatic equilibrium and that radiation pressure is ineffective at driving turbulence or ejecting matter. Because the vast majority of star-forming galaxies lie below the maximum limit for typical dust-to-gas ratios, we conclude that infrared radiation pressure is likely unimportant for all but the most extreme systems on galaxy-wide scales. Thus, while radiation pressure does not explain the Kennicutt-Schmidt relation, it does impose an upper truncation on it. Our predicted truncation is in good agreement with the highest observed gas and star formation rate surface densities found both locally and at high redshift.