On the law of star formation in disk galaxies

Abstract

The observational relationship between the stellar surface brightness and the surface brightness in H-alpha in galactic disks is shown to be determined by the law of star formation in disk galaxies. Assuming the rate of star formation to take a generalized Schmidt power-law form dependent on both the total local matter surface density, sigmag; d sigma*/dt = epsilon sigmaTn, we find that the observations constrain (n + m is greater than 1), and that the best fit is obtained for 1.5 is less than (n + m) is less than 2.5. Both a Schmidt Law of the form d sigma*/dt = epsilon sigmag, and a star-formation law of the form d sigma*/dt = epsilon Omega sigmag, where Omega is the angular velocity at the radial point considered, seem to be excluded by observations. The observed scatter in the stellar surface brightness versus H-alpha surface brigtness versus H-alpha surface relationship can be interpreted as a scatter in the ratio of galaxian age to star-formation efficiency; younger galaxies being more gas-rich, and currently more active in forming stars. Finally, we discuss particular forms of the Schmidt Law given by theory. We show that a model having n =⅓ and m = 5/3, which gives a particularly good fit to the observations, follows as a consequence of stochastic self-regulating star formation moderated by cloud-cloud interactions in the disk potential, and by the energetic processes associated with the formation of massive stars. This models explicitly includes the secular evolution of the vertical structure of the gaseous and stellar components of galactic disks, and the effect ofthe galaxian potential.