A Simplified Treatment of Gravitational Interaction on Galactic Scales

I present a simple scheme for the treatment of gravitational interactions on galactic scales. In analogy to known mechanisms of quantum field theory, I assume ad hoc that gravitation is mediated by virtual exchange particles - gravitons - with very small but non-zero masses. The resulting density and mass profiles are proportional to the mass of the gravitating body. The mass profile scales with the centripetal acceleration experienced by a test particle orbiting the central mass; this comes at the cost of postulating a universal characteristic acceleration a0 = 4.3*10^{-12} m/s^2 (or 8*pi*a0 = 1.1*10^{-10} m/s^2). The scheme predicts the asymptotic flattening of galactic rotation curves, the Tully-Fisher/Faber-Jackson relations, the mass discrepancy-acceleration relation of galaxies, the surface brightness-acceleration relation of galaxies, the kinematics of galaxy clusters, and "Renzo's rule" correctly; additional (dark) mass components are not required. Given that it is based on various ad-hoc assumptions, and given further limitations, the scheme I present is not yet a consistent theory of gravitation; rather, it is a "toy model" providing a convenient scaling law that simplifies the description of gravity on galactic scales.