On the law of star formation in disk galaxies

The observational relationship between the stellar surface brightness and the surface brightness in Hα 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, σ_T, and the gas surface density, σ_g; d_σ*/ dt = ∈σ_T ⁿ σ_g ^m, we find that the observations constrain (n + m) > 1, and that the best fit is obtained for 1.5 < (n + m) < 2.5. Both a Schmidt Law of the form dσ*/dt = ∈σ_g, and a star-formation law of the form dσ*/dt = ∈Ωσ_g, where Ω is the angular velocity at the radial point considered, seem to be excluded by observations. The observed scatter in the stellar surface brightness versus Hα surface brightness 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 = 1/3 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 model explicitly includes the secular evolution of the vertical structure of the gaseous and stellar components of galactic disks, and the effect of the galaxian potential.