The Kennicutt–Schmidt law and the main sequence of galaxies in Newtonian and milgromian dynamics

Abstract

ABSTRACT The Kennicutt–Schmidt law is an empirical relation between the star formation rate surface density (ΣSFR) and the gas surface density (Σgas) in disc galaxies. The relation has a power-law form $\Sigma _{\text{SFR}} \propto \Sigma _{\text{gas}}^{n}$. Assuming that star formation results from gravitational collapse of the interstellar medium, ΣSFR can be determined by dividing Σgas by the local free-fall time tff. The formulation of tff yields the relation between ΣSFR and Σgas, assuming that a constant fraction (εSFE) of gas is converted into stars every tff. This is done here for the first time using Milgromian dynamics (MOND). Using linear stability analysis of a uniformly rotating thin disc, it is possible to determine the size of a collapsing perturbation within it. This lets us evaluate the sizes and masses of clouds (and their tff) as a function of Σgas and the rotation curve. We analytically derive the relation $\Sigma _{\text{SFR}} \propto \Sigma _{\text{gas}}^{n}$ both in Newtonian and Milgromian dynamics, finding that n = 1.4. The difference between the two cases is a change only to the constant pre-factor, resulting in increased ΣSFR of up to 25 per cent using MOND in the central regions of dwarf galaxies. Due to the enhanced role of disc self-gravity, star formation extends out to larger galactocentric radii than in Newtonian gravity, with the clouds being larger. In MOND, a nearly exact representation of the present-day main sequence of galaxies is obtained if $\epsilon _{\text{SFE}} = \text{constant} \approx 1.1{{\ \rm per\ cent}}$. We also show that empirically found correction terms to the Kennicutt–Schmidt law are included in the here presented relations. Furthermore, we determine that if star formation is possible, then the temperature only affects ΣSFR by at most a factor of $\sqrt{2}$.