Newtonian Fractional-Dimension Gravity and Rotationally Supported Galaxies

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 (Disk-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 which explains the observed properties of these galaxies without requiring the Dark Matter hypothesis. In our model, the MOND acceleration constant $a_{0} \simeq 1.2 \times 10^{-10}\mbox{m}\thinspace \mbox{s}^{ -2}$ can be related to a natural scale length $l_{0}$, 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 $g_{obs}$ with the baryonic one $g_{bar}$, 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.