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

Dark matter (DM) and modified Newtonian dynamics (MOND) models of rotationally supported galaxies lead to curves with different geometries in (gN, gtot)-space (g2-space). Here, gtot is the total acceleration and gN 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 ≥ rN (large radii) and r < rN (small radii) coincide, where rN is the radius where gN is greatest. In DM models with cored density profiles where gtot 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 ≥ rN and r < rN do not coincide. Finally in DM models with cuspy density profiles such as the NFW profile where gtot is formally non-zero at the galactic origin the curves are open, and again the curve segments at radii r ≥ rN and r < rN do not coincide. We develop a test of whether data at small and large radii coincide and investigate rotation curves from the SPARC data base 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.