The Challenge to MOND from Ultra-faint Dwarf Galaxies

Modified Newtonian Dynamics (MOND) at low acceleration has been astonishingly powerful at explaining the flat rotation curve of galaxies and the relation between the baryonic content of the galaxies and their observed circular velocity, known as the Baryonic Tully-Fisher Relationship (BTFR). It is known that MOND fails at explaining the observed velocity dispersion of the ultra-faint dwarf galaxies (UFDs) with the justification that UFDs are more prone to tidal disruption in MOND compared to cold dark matter model. We show that: (i) the ratio of tidal to internal acceleration in UFDs is extremely low, (ii) there is no correlation between the deviation of UFDs from MOND's prediction as a function of tidal susceptibility, and (iii) recent constraints from Gaia proper motion analysis on the orbital parameters of the UFDs exacerbates the challenge to MOND. In particular, Gaia data indicates that Ursa Major I is experiencing a recent infall into the Milky Way's halo, and its inconsistency with MOND at 7-$\sigma$ level can not be attributed to being an early infall satellite. Moreover, the new data from Gaia DR2 shows Willman I to have the least eccentric orbit of all UFDs, and its deviation from MOND at 4-$\sigma$ level can not be attributed to a highly eccentric orbit as previously suggested. Finally, given that Tucana III is the only UFD observed to show tidal features, Reticulum II and Segue I are two other UFDs that potentially challenge MOND as they have comparable galactocentric distances to Tucana III while showing no tidal features. Whether wide binaries have inflated the velocity dispersion of the UFDs remains an open question to be addressed with future multi-epoch observations.