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

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Dark Matter (DM) and Modified Newtonian Dynamics (MOND) models of rotationally supported galaxies lead to curves, $\mathcal{C}$, with different geometries in $(g_{\rm bar},g_{\rm tot})$-space ($g2$-space). Here $g_{\rm tot}$ is the total centripetal acceleration of matter in a rotationally supported galaxy and $g_{\rm bar}$ is that from the baryonic (visible) matter distribution assuming Newtonian gravity. Specifically, in models of the baryonic matter where $g_{\rm bar}$ is zero at the galactic origin, the MOND modified inertia curves in $g2$-space are closed with zero area $\mathcal{A}(\mathcal{C}_{\rm MOND})= 0$. In DM models with cored density profiles where $g_{\rm tot}$ is also zero at the galactic origin, the curves are again closed, but the area of the closed curves are in general non-zero, $\mathcal{A}(\mathcal{C}_{DM})\neq 0$. The geometry of galactic rotation curve data from the SPARC database is investigated in order to discriminate between different models.