The star formation law in galactic disks

Measurements of the distribution of Hα emission in galaxies have been combined with published H I and CO data, in order to reassess the dependence of the massive star formation rate (SFR) on the density and dynamics of the interstellar gas. The disk-averaged Hα surface brightness is correlated with the mean atomic and total gas surface densities, but is only weakly correlated with the mean molecular gas density inferred from CO emission. Radial profiles of gas and Hα emission in 15 galaxies have been used to define the relationship between the SFR and gas surface density. In dense regions the SFR and total gas density are well represented by a Schmidt power-law relation (R = aSIGMANᵍ_), with index N = 1. 3 +/- 0. 3, and nearly the same value for the zero point a, at least for the galaxies in our sample. This Schmidt law breaks down, however, at densities below a critical threshold value. Massive star formation is completely suppressed at surface densities well below the threshold, while at densities near the the threshold value the slope of the SFR-density relation is much steeper than a normal Schmidt law. The observed threshold densities vary by an order of magnitude among the galaxies in our sample and appear to be largely independent of whether the predominant gas phase is atomic or molecular. The star formation threshold appears to be associated with the onset of large-scale gravitational instabilities in the gas disks. A simple single-fluid (Toomre) disk stability model predicts threshold densities and radii which are in excellent agreement with the observations. The same analysis demonstrates that the radial distribution of gas in late-type galaxies closely follows the threshold surface density, confirming a hypothesis originally proposed by Quirk, and indicating the importance of star formation thresholds in virtually all parts of the disk. The combination of a nearly linear star formation law at high densities with a strongly nonlinear SFR-density law near the threshold redresses many of the previous observational difficulties with the Schmidt law and may provide physical insights into such diverse phenomena as nuclear and disk starbursts, the suppression of star formation in gas-rich S0 galaxies and low surface brightness galaxies, star formation in spiral arms, the observation of radial cutoffs to stellar disks, and the star formation histories of disk galaxies.