The Kennicutt-Schmidt Law and Gas Scale Height in Luminous and Ultra-Luminous Infrared Galaxies

Abstract

A new analysis of high-resolution data from the Atacama Large Millimeter/submillimeter Array (ALMA) for 5 luminous or ultra-luminous infrared galaxies gives a slope for the Kennicutt-Schmidt (KS) relation equal to $1.74_{-0.07}^{+0.09}$ for gas surface densities ${\Sigma }_{\mathrm{mol}}>10^3{M}_{\odot }$ pc${}^{-2}$ and an assumed constant CO-to-H${}_2$ conversion factor. The velocity dispersion of the CO line, ${\sigma }_v$, scales approximately as the inverse square root of ${\Sigma }_{\mathrm{mol}}$, making the empirical gas scale height determined from $H\sim 0.5{\sigma }^2/(\pi G{\Sigma }_{\mathrm{mol}})$ nearly constant, 150-190 pc, over 1.5 orders of magnitude in ${\Sigma }_{\mathrm{mol}}$. 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 free-fall time) varies with ${\Sigma }_{\mathrm{mol}}^{1/2}$, 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 free-fall time is roughly constant, 5%-7%, and the gas depletion time decreases at high ${\Sigma }_{\mathrm{mol}}$, reaching only $\sim 16$ Myr at ${\Sigma }_{\mathrm{mol}}\sim 10^4{M}_{\odot }$ pc${}^{-2}$. The variation of ${\sigma }_v$ with ${\Sigma }_{\mathrm{mol}}$ and the constancy of $H$ are in tension with some feedback-driven models, which predict ${\sigma }_v$ 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.

Accepted to ApJ. 13 pages, 3 figures, 1 table. Supplementary data table used to generate the plots is included