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

doi:10.1093/mnras/stab2068

paper

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

arXiv:2109.00497 · doi:10.1093/mnras/stab2068

Abstract

The Kennicutt-Schmidt law is an empirical relation between the star formation rate surface density ( $Σ_{S F R}$ ) and the gas surface density ( $Σ_{g a s}$ ) in disc galaxies. The relation has a power-law form $Σ_{S F R} \propto Σ_{g a s}^{n}$ . Assuming that star formation results from gravitational collapse of the interstellar medium, $Σ_{S F R}$ can be determined by dividing $Σ_{g a s}$ by the local free-fall time $t_{f f}$ . The formulation of $t_{f f}$ yields the relation between $Σ_{S F R}$ and $Σ_{g a s}$ , assuming that a constant fraction ( $ε_{S F E}$ ) of gas is converted into stars every $t_{f f}$ . 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 $t_{f f}$ ) as a function of $Σ_{g a s}$ and the rotation curve. We analytically derive the relation $Σ_{S F R} \propto Σ_{g a s}^{n}$ 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 $Σ_{S F R}$ of up to 25\% using MOND in the central regions of dwarf galaxies. Due to the enhanced role of disk 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 $ε_{S F E} = constant \approx 1.1%$ . 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 $Σ_{S F R}$ by at most a factor of $2$ .

Accepted for publication in MNRAS. 12 pages, 10 figures

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

Abstract

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