  We use a semi-empirical model to investigate the radial acceleration relation
(RAR) in a cold dark matter (CDM) framework. Specifically, we build 80 model
galaxies covering the same parameter space as the observed galaxies in the
SPARC database, assigning them to dark matter halos using abundance matching
and halo mass-concentration relations. We consider several abundance matching
relations, finding some to be a better match to the kinematic data than others.
We compute the unavoidable gravitational interactions between baryons and their
dark matter halos, leading to an overall compression of the original NFW halos.
Before halo compression, high-mass galaxies approximately lie on the observed
RAR whereas low-mass galaxies display up-bending "hooks" at small radii due to
DM cusps, making them deviate systematically from the observed relation. After
halo compression, the initial NFW halos become more concentrated at small
radii, making larger contributions to rotation curves. This increases the total
accelerations, moving all model galaxies away from the observed relation. These
systematic deviations suggest that the CDM model with abundance matching alone
cannot explain the observed RAR. Further effects (e.g., feedback) would need to
counteract the compression with precisely the right amount of halo expansion,
even in high mass galaxies with deep potential wells where such effects are
generally predicted to be negligible.
