A SIMPLIFIED TREATMENT OF GRAVITATIONAL INTERACTION ON GALACTIC SCALES

I present a simple scheme for the treatment of gravitational interactions on galactic scales. In anal- ogy with 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 den- sity 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, but this comes at the cost of postulating a universal characteristic acceleration $a_0{\approx}4.3{\times}10^{-12}msec^{-2}$ (or $8{\pi}a_0{\approx}1.1{\times}10^{-10}msec^{-2}$). 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.