A theory of galactic mass and rotation curves

Abstract

The goal of this paper is to account for the complete observed rotation curves of disk galaxies without dark matter. To attain that goal, use is made of a conservation law from stability theory of linear waves, leading to a vector-based theory of gravitation. In the theory, galactic centers are sites of strong gravitational fields. The new theory predicts extra matter at the center of disk galaxies, which is well-known to be consistent with intergalactic dynamics. For given disk radiusr0 and edge tangential speedv, the greater the deviation of a rotation curve from linear (solid disk rotation), the greater the mass of the galaxy as a multiple of Newtonian massr0v2/G, up to a factor of about 1000. In an approximate calculation it turns out that disk density δ(r) (in kg m−2) is proportional to 1/r for typical rotation curves. Rotation is characterized by two constants which in turn are determined by the edge speed and mass distribution. Not just any curve shape can be so obtained; in fact, the theoretically possible curves correspond to observed curves.