The observed line-of-sight velocity dispersion σ 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 σ 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 +1.6 −1.2 and a constant orbital anisotropy of β = −0.5 +0.4 −1.6 . In MOG, we first fix its two theoretical parameters α and µ based on previous fits to the observed rotation curve data of The HI Nearby Galaxy Survey (THINGS). The DF44 σ los profile is best fit with M dyn /L I = 7.4 +1.5 −1.4 , larger than plausible SPS values. MOG produces a σ los profile for DF44 with acceptable M dyn /L I and isotropic orbits if α and µ are allowed to vary. MOND with the canonical a 0 can explain DF44 at the 2.40σ 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 5.49σ (P -value of 4.07 × 10 −8 ) if its free parameters are fixed at the highest values consistent with THINGS data.

The observed velocity dispersion of the classical dwarf spheroidal (dSph) galaxies of the Milky Way (MW) requires the Newtonian stellar mass-to-light (M * /L) ratios in the range of about 10 to more than 100 solar units that are well outside the acceptable limit predicted by stellar population synthesis models. Using Jeans analysis, we calculate the line-of-sight velocity dispersion (σ los ) of stars in eight MW dSphs in the context of the modified gravity (MOG) theory of Moffat, assuming a constant M * /L ratio without invoking the exotic cold dark matter. First, we use the weak field approximation of MOG and assume the two parameters α and µ of the theory to be constant as has already been inferred from fitting to the observed rotational data of The HI Nearby Galaxy Survey catalogue of galaxies. We find that the derived M * /L ratios for almost all dSphs are too large to be explained by the stellar population values. In order to fit the line-of-sight velocity dispersions of the dSph with reasonable M * /L values, we must vary α and µ on a case by case basis. A common pair of values cannot be found for all dSphs. Comparing with the values found from rotation curve fitting, it appears that µ correlates strongly with galaxy luminosity, shedding doubt on it as a universal constant.