Regulation of star formation by large scale gravito-turbulence

A simple model for star formation based on supernova (SN) feedback and gravitational heating via the collapse of perturbations in gravitationally unstable disks reproduces the Schmidt-Kennicutt relation between the star formation rate (SFR) per unit area, $\Sigma_{SFR}$, and the gas surface density, $\Sigma_g$, remarkably well. The gas velocity dispersion, $\sigma_g$, is derived self-consistently in conjunction with $\Sigma_{SFR}$ and is found to match the observations. Gravitational instability triggers {"gravito-turbulence"} at the scale of the least stable perturbation mode, boosting $\sigma_g$ at $\Sigma_g> \, \Sigma_g^\textrm{thr}=50\, {\rm M}_\odot\, {\rm pc}^{-2}$, and contributing to the pressure needed to carry the disk weight vertically. $\Sigma_{SFR}$ is reduced to the observed level at $ \Sigma_g > \Sigma_g^\textrm{thr}$, whereas at lower surface densities, SN feedback is the prevailing energy source. Our proposed star formation recipes require efficiencies of order 1\%, and the Toomre parameter, $Q$, for the joint gaseous and stellar disk is predicted to be close to the critical value for marginal stability for $\Sigma_g< \, \Sigma_g^\textrm{thr}$, spreading to lower values and larger gas velocity dispersion at higher $\Sigma_g$.