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
$\Sigma_{SFR} \propto \Sigma_{gas}^n$. 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 ($\varepsilon_{SFE}$) 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 $\Sigma_{SFR} \propto
\Sigma_{gas}^{n}$ 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 $\Sigma_{SFR}$ 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
$\epsilon_{SFE} = \text{constant} \approx 1.1\%$. 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 $\Sigma_{SFR}$ by at most a factor
of $\sqrt{2}$.
