A Method for Discriminating Between Dark Matter Models and MOND Modified Inertia via Galactic Rotation Curves

TL;DR

This paper proposes a geometric test in $g2$-space to distinguish between dark matter and MOND models of galactic rotation curves, analyzing SPARC data to demonstrate its potential despite uncertainties.

Contribution

It introduces a novel geometric method in $g2$-space to discriminate dark matter models from MOND modified inertia using rotation curve data.

Findings

The test can differentiate between DM and MOND models based on curve closure and area.

Analysis of SPARC data shows the method's potential despite systematic uncertainties.

The geometric approach highlights key differences in galactic rotation curve behaviors.

Abstract

Dark Matter (DM) and Modified Newtonian Dynamics (MOND) models of rotationally supported galaxies lead to curves with different geometries in $(g_{N},g_{tot})$-space ($g2$-space). Here $g_{tot}$ is the total acceleration and $g_{N}$ is the acceleration as obtained from the baryonic matter via Newtonian dynamics. In MOND modified inertia (MI) models the curves in $g2$-space are closed with zero area and so curve segments at radii $r\geq r_{N}$ (large radii) and $r< r_{N}$ (small radii) coincide, where $r_{N}$ is the radius where $g_N$ is greatest. In DM models with cored density profiles where $g_{tot}$ is also zero at the galactic centre, the curves are again closed, but the area of the closed curves are in general non-zero because the curve segments at radii $r\geq r_{N}$ and $r<r_{N}$ do not coincide. Finally in DM models with cuspy density profiles such as the NFW profile where $g_{tot}$ is formally non-zero at the galactic origin the curves are open, and again the curve segments at radii $r\geq r_{N}$ and $r< r_{N}$ do not coincide. We develop a test of whether data at small and large radii coincide and investigate rotation curves from the SPARC database in order to discriminate between the above geometries. Due to loosely quantified systematic uncertainties we do not underline the result of the test, but instead conclude that the test illustrates the relevance of this type of analysis and demonstrate the ability to discriminate between the considered DM and MI models in this way.