Abstract
The Kennicutt-Schmidt law is an empirical relation between the star formation rate surface density (Sigma(SFR)) and the gas surface density (Sigma(gas)) in disc galaxies. The relation has a power-law form Sigma(SFR) proportional to Sigma(n)(gas).
Assuming that star formation results from gravitational collapse of the interstellar medium, Sigma(SFR) can be determined by dividing Sigma(gas) by the local free-fall time t(ff). The formulation of t(ff) yields the relation between Sigma(SFR) and Sigma(gas), assuming that a constant fraction (epsilon(SFE)) of gas is converted into stars every t(ff).
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 t(ff)) as a function of Sigma(gas) and the rotation curve. We analytically derive the relation Sigma(SFR) proportional to Sigma(n)(gas) 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 Sigma(SFR) of up to 25 percent 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(SFE) = constant approximate to 1.1 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 Sigma(SFR) by at most a factor of root 2.