Galactic rotation curves exhibit diverse behavior in the inner regions, while obeying an organizing principle, i.e., they can be approximately described by a radial acceleration relation or the Modified Newtonian Dynamics phenomenology. We analyze the rotation curve data from the SPARC sample, and explicitly demonstrate that both the diversity and uniformity are naturally reproduced in a hierarchical structure formation model with the addition of dark matter self-interactions. The required concentrations of the dark matter halos are fully consistent with the concentration-mass relation predicted by the Planck cosmological model. The inferred stellar massto-light (3.6 µm) ratios scatter around 0.5M /L , as expected from population synthesis models, leading to a tight radial acceleration relation and baryonic Tully-Fisher relation. The inferred stellar-halo mass relation is consistent with the expectations from abundance matching. These results indicate that the inner dark matter halos of galaxies are thermalized due to the self-interactions of dark matter particles.

We compare proposed solutions to the core vs cusp issue of spiral galaxies, which has also been framed as a diversity problem, and demonstrate that the cuspiness of dark matter halos is correlated with the stellar surface brightness. We compare the rotation curve fits to the SPARC sample from a self-interacting dark matter (SIDM) model, which self-consistently includes the impact of baryons on the halo profile, and hydrodynamical N-body simulations with cold dark matter (CDM) . The SIDM model predicts a strong correlation between the core size and the stellar surface density, and it provides the best global fit to the data. The CDM simulations without strong baryonic feedback effects fail to explain the large dark matter cores seen in low surface brightness galaxies. On the other hand, with strong feedback, CDM simulations do not produce galaxy analogs with high stellar and dark matter densities, and therefore they have trouble in explaining the rotation curves of high surface brightness galaxies. This implies that current feedback implementations need to be modified. We also explicitly show how the concentration-mass and stellar-to-halo mass relations together lead to a radial acceleration relation (RAR) in an averaged sense, and reiterate the point that the RAR does not capture the diversity of galaxy rotation curves in the inner regions. These results make a strong case for SIDM as the explanation for the cores and cusps of field galaxies.