2019ApJ...882....5W

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 1.74_–0.07^+0.09 for gas surface densities Σ_mol > 10³ M_☉ pc^–2 and an assumed constant CO-to-H₂ conversion factor. The velocity dispersion of the CO line, σ_v, scales approximately as the inverse square root of Σ_mol, making the empirical gas scale height determined from H∼0.5σ ²/(πGΣ_mol) nearly constant, 150-190 pc, over 1.5 orders of magnitude in Σ_mol. 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 Σ_mol^1/2, 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 Σ_mol, reaching only ∼16 Myr at Σ_mol ∼ 10⁴ M_☉ pc^–2. The variation of σ_v with Σ_mol and the constancy of H are in tension with some feedback-driven models, which predict σ_v 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.