Newtonian fractional-dimension gravity and rotationally supported galaxies

Abstract

ABSTRACT We continue our analysis of Newtonian fractional-dimension gravity, an extension of the standard laws of Newtonian gravity to lower dimensional spaces, including those with fractional (i.e. non-integer) dimension. We apply our model to three rotationally supported galaxies: NGC 7814 (bulge-dominated spiral), NGC 6503 (disc-dominated spiral), and NGC 3741 (gas-dominated dwarf). As was done in the general cases of spherically symmetric and axially symmetric structures, which were studied in previous work on the subject, we examine a possible connection between our model and modified Newtonian dynamics, a leading alternative gravity model that explains the observed properties of these galaxies without requiring the dark matter hypothesis. In our model, the modified Newtonian dynamics acceleration constant $a_{0} \simeq 1.2 \times 10^{ -10}\,\mbox{m}\, \mbox{s}^{ -2}$ can be related to a natural scale length l0, namely $a_{0} \approx GM/l_{0}^{2}$ for a galaxy of mass M. Also, the empirical radial acceleration relation, connecting the observed radial acceleration gobs with the baryonic one gbar, can be explained in terms of a variable local dimension D. As an example of this methodology, we provide detailed rotation curve fits for the three galaxies mentioned above.