Dark Matter Cores and Cusps in Spiral Galaxies and their Explanations
  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.
