Can Massive Gravity Explain the Mass Discrepancy - Acceleration Relation
  of Disk Galaxies?
  The empirical mass discrepancy-acceleration (MDA) relation of disk galaxies
provides a key test for models of galactic dynamics. In terms of modified laws
of gravity and/or inertia, the MDA relation quantifies the transition from
Newtonian to modified dynamics at low centripetal accelerations a_c < 10^-10
m/s^2. As yet, neither dynamical models based on dark matter nor proposed
modifications of the laws of gravity/inertia have predicted the functional form
of the MDA relation. In this work, I revisit the MDA data and compare them to
four different theoretical scaling laws. Three of these scaling laws are
entirely empirical, the fourth one - the "simple mu" function of Modified
Newtonian Dynamics - derives from a toy model of gravity based on massive
gravitons (the "graviton picture"). All theoretical MDA relations comprise one
free parameter of the dimension of an acceleration, Milgrom's constant a_M. I
find that the "simple mu" function provides a good fit to the data free of
notable systematic residuals and provides the best fit among the four scaling
laws tested. The best-fit value of Milgrom's constant is a_M = (1.06 +/-
0.05)*10^-10 m/s^2. Given the successful prediction of the functional form of
the MDA relation, plus an overall agreement with the observed kinematics of
stellar systems spanning eight orders of magnitude in size and 14 orders of
magnitude in mass, I conclude that the "graviton picture" is sufficient (albeit
probably not a necessary or unique approach) to describe galactic dynamics on
all scales well beyond the scale of the solar system. This suggests that, at
least on galactic scales, gravity behaves as if it was mediated by massive
particles.
