The Kennicutt–Schmidt Law and Gas Scale Height in Luminous and Ultraluminous Infrared Galaxies

A new analysis of high-resolution data from the Atacama Large Millimeter/submillimeter Array for five luminous or ultraluminous infrared galaxies gives a slope for the Kennicutt–Schmidt (KS) relation equal to for gas surface densities Σmol > 103 M⊙ pc−2 and an assumed constant CO-to-H2 conversion factor. The velocity dispersion of the CO line, σv, scales approximately as the inverse square root of Σmol, making the empirical gas scale height determined from nearly constant, 150–190 pc, over 1.5 orders of magnitude in Σmol. This constancy of H implies that the average midplane density, which is presumably dominated by CO-emitting gas for these extreme star-forming galaxies, scales linearly with the gas surface density, which in turn implies that the gas dynamical rate (the inverse of the freefall time) varies with , thereby explaining most of the super-linear slope in the KS relation. Consistent with these relations, we also find that the mean efficiency of star formation per freefall time is roughly constant, 5%–7%, and the gas depletion time decreases at high Σmol, reaching only ∼16 Myr at Σmol ∼ 104 M⊙ pc−2. The variation of σv with Σmol and the constancy of H are in tension with some feedback-driven models, which predict σv to be more constant and H to be more variable. However, these results are consistent with simulations in which large-scale gravity drives turbulence through a feedback process that maintains an approximately constant Toomre Q instability parameter.