2020MNRAS.496.1077P

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 >= 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 >= 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 >= r_N and r < r_N do not coincide.