Newtonian Fractional-Dimension Gravity and Rotationally Supported Galaxies

TL;DR

This paper extends Newtonian gravity to fractional dimensions and applies it to galaxy rotation curves, showing potential connections to MOND and explaining observed acceleration relations without dark matter.

Contribution

It introduces a fractional-dimensional gravity model that fits galaxy rotation curves and relates to MOND, offering an alternative explanation to dark matter.

Findings

Model fits rotation curves of three galaxies.

Relates MOND acceleration constant to fractional dimension scale.

Explains Radial Acceleration Relation via variable local dimension.

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.