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 .