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 $a_c{\lesssim}10^{-10}ms^{-2}$. 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 aM. 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 $a_M=(1.06{\pm}0.05){\times}10^{-10}ms^{-2}$. 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 nor 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.