The Star Formation History and Dynamics of the Ultra-diffuse Galaxy
  Dragonfly 44 in MOND and MOG
  The observed line-of-sight velocity dispersion $\sigma_{los}$ of the ultra
diffuse galaxy Dragonfly 44 (DF44) requires a Newtonian dynamical mass-to-light
ratio of $M_{dyn}/L_I=26^{+7}_{-6}$ Solar units. This is well outside the
acceptable limits of our stellar population synthesis (SPS) models, which we
construct using the integrated galactic initial mass function (IGIMF) theory.
Assuming DF44 is in isolation and using Jeans analysis, we calculate
$\sigma_{los}$ profiles of DF44 in Milgromian dynamics (MOND) and modified
gravity (MOG) theories without invoking dark matter. Comparing with the
observed kinematics, the best-fitting MOND model has $M_{dyn}/L_I =
3.6_{-1.2}^{+1.6}$ and a constant orbital anisotropy of
$\beta=-0.5_{-1.6}^{+0.4}$. In MOG, we first fix its two theoretical parameters
$\alpha$ and $\mu$ based on previous fits to the observed rotation curve data
of The HI Nearby Galaxy Survey (THINGS). The DF44 $\sigma_{los}$ profile is
best fit with $M_{dyn}/L_I=7.4_{-1.4}^{+1.5}$, larger than plausible SPS
values. MOG produces a $\sigma_{los}$ profile for DF44 with acceptable
$M_{dyn}/L_I$ and isotropic orbits if $\alpha$ and $\mu$ are allowed to vary.
MOND with the canonical $a_0$ can explain DF44 at the $2.40 \sigma$ confidence
level (1.66\%) if considering both its observed kinematics and typical star
formation histories in an IGIMF context. However, MOG is ruled out at $5.49
\sigma$ ($P$-value of $4.07 \times 10^{-8}$) if its free parameters are fixed
at the highest values consistent with THINGS data.
