Regulation of star formation by large-scale gravitoturbulence

Abstract

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