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

Akram Hasani Zonoozi*, Patrick Lieberz, Indranil Banik, Hosein Haghi, Pavel Kroupa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)
8 Downloads (Pure)


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 ΣSFR ∝ Σgasn. 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 (ΣSFE) 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 ΣSFR ∝ Σgasn 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 ϵSFE = constant ≈ 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 ΣSFR by at most a factor of √2.

Original languageEnglish
Pages (from-to)5468-5478
Number of pages11
JournalMonthly Notices of the Royal Astronomical Society
Issue number4
Early online date20 Jul 2021
Publication statusPublished - Oct 2021


  • Galaxies: ISM
  • Galaxies: Star formation
  • Galaxies: Statistics
  • Galaxy: Disc
  • Gravitation
  • Instabilities


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