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.
