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 environmentsranging from normal galactic disks to starbursts and ULIRGs in terms of theobservables of those systems. Our calculation is based on three premises: (1)star formation occurs in virialized molecular clouds that are supersonicallyturbulent; (2) the density distribution within these clouds is lognormal, asexpected for supersonic isothermal turbulence; (3) stars form in any sub-regionof a cloud that is so overdense that its gravitational potential energy exceedsthe energy in turbulent motions. We show that a theory based on this model isconsistent with simulations and with the observed star formation rate in theMilky Way. We use our theory to derive the Kennicutt-Schmidt Law from firstprinciples, and make other predictions that can be tested by futureobservations. We also provide an algorithm for estimating the star formationrate that is suitable for inclusion in numerical simulations.Comment: 20 pages, 9 figures, emulateapj format, accepted for publication in Ap