A general theory of turbulence-regulated star formation, from spirals to ultraluminous infrared galaxies

We derive an analytic prediction for the star formation rate in environments ranging from normal galactic disks to starbursts and ULIRGs in terms of the observables of those systems. Our calculation is based on three premises: ( 1) star formation occurs in virialized molecular clouds that are supersonically turbulent; ( 2) the density distribution within these clouds is lognormal, as expected for supersonic isothermal turbulence; and ( 3) stars form in any subregion of a cloud that is so overdense that its gravitational potential energy exceeds the energy in turbulent motions. We show that a theory based on this model is consistent with simulations and with the observed star formation rate in the Milky Way. We use our theory to derive the Kennicutt-Schmidt law from first principles and make other predictions that can be tested by future observations. We also provide an algorithm for estimating the star formation rate that is suitable for inclusion in numerical simulations.