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.
