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

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.

Automated summary

The Kennicutt-Schmidt law describes the relationship between star formation rate and gas density in disc galaxies, and using Milgromian dynamics reveals further insights about galaxy evolution. Enhanced disc self-gravity in MOND allows star formation to extend to larger galactocentric radii and the analytical derivation of the relationship between star formation rate and gas density can offer valuable information about cloud sizes and masses. Additionally, temperature affects star formation rate by a factor of root 2 at most, and empirically found corrections to the Kennicutt-Schmidt law are accounted for in the presented relations.