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.