Newtonian fractional-dimension gravity and disk galaxies

This paper continues previous work on a possible alternative model of gravity, based on the theory of fractional-dimension spaces applied to Newton’s law of gravitation. In particular, our Newtonian Fractional-Dimension Gravity (NFDG) is now applied to axially-symmetric stellar structures, such as thin/thick disk galaxies described by exponential, Kuzmin, or other similar mass distributions. As in the case of spherically-symmetric structures, which was studied in previous work on the subject, we examine a possible connection between NFDG and Modified Newtonian Dynamics (MOND), a leading alternative gravity model, which accounts for the observed properties of galaxies and other astrophysical structures without requiring the dark matter (DM) hypothesis. By relating the MOND acceleration constant a0 ' 1.2×10−10m s−2 to a natural scale length l0 in NFDG, namely a0 ≈ GM/l2 0 for a galaxy of mass M, and by using the empirical Radial Acceleration Relation (RAR), we are able to explain the connection between the observed radial acceleration gobs and the baryonic radial acceleration gbar in terms of a variable local dimension D. As an example of this methodology, we provide a detailed rotation curve fitting for the case of the field dwarf spiral galaxy NGC 6503.