The scenario consistent with a wealth of observations for the missing mass problem is that of
weakly interacting dark matter particles. However, arguments or proposals for a Newtonian or
relativistic modified gravity scenario continue to be made. A distinguishing characteristic between
the two scenarios is that dark matter particles can produce a gravitational effect, in principle,
without the need of baryons while this is not the case for the modified gravity scenario where such
an effect must be correlated with the amount of baryonic matter. We consider here ultra-faint dwarf
(UFD) galaxies as a promising arena to test the two scenarios based on the above assertion. We
compare the correlation of the luminosity with the velocity dispersion between samples of UFD and
non-UFD galaxies, finding a trend of loss of correlation for the UFD galaxies. For example, we find
for 28 non-UFD galaxies a strong correlation coefficient of −0.688 which drops to −0.077 for the 23
UFD galaxies. Incoming and future data will determine whether the observed stochasticity for UFD
galaxies is physical or due to systematics in the data. Such a loss of correlation (if it is to persist)
is possible and consistent with the dark matter scenario for UFD galaxies but would constitute a
new challenge for the modified gravity scenario.
