  Cosmological $N$-body simulations predict dark matter (DM) haloes with steep
central cusps (e.g. NFW, Navarro et al. 1996). This contradicts observations of
gas kinematics in low-mass galaxies that imply the existence of shallow DM
cores. Baryonic processes such as adiabatic contraction and gas outflows can,
in principle, alter the initial DM density profile, yet their relative
contributions to the halo transformation remain uncertain. Recent high
resolution, cosmological hydrodynamic simulations (Di Cintio et al. 2014, DC14)
predict that inner density profiles depend systematically on the ratio of
stellar to DM mass (M$_*$/M$_{\text{halo}}$). Using a Markov Chain Monte Carlo
approach, we test the NFW and the M$_*$/M$_{\text{halo}}$-dependent DC14 halo
models against a sample of 147 galaxy rotation curves from the new {\it
Spitzer} Photometry and Accurate Rotation Curves (SPARC) data set. These
galaxies all have extended H{\small I} rotation curves from radio
interferometry as well as accurate stellar mass density profiles from
near-infrared photometry. The DC14 halo profile provides markedly better fits
to the data compared to the NFW profile. Unlike NFW, the DC14 halo parameters
found in our rotation curve fits naturally fall within two standard deviations
of the mass-concentration relation predicted by $\Lambda$CDM and the stellar
mass-halo mass relation inferred from abundance matching with few outliers.
Halo profiles modified by baryonic processes are therefore more consistent with
expectations from $\Lambda$ cold dark matter ($\Lambda$CDM) cosmology and
provide better fits to galaxy rotation curves across a wide range of galaxy
properties than do halo models that neglect baryonic physics. Our results offer
a solution to the decade long cusp-core discrepancy.
