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 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 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, but this comes at the cost of postulating a universal characteristic acceleration ao approximate to 4.3 x 10(-12) m sec(-2) (or 8 pi a(0) approximate to 1.1 x 10(-10) m sec(-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.