The Cusp/Core Problem in Galactic Halos: Long-Slit Spectra for a Large Dwarf Galaxy Sample

We derive inner dark matter halo density profiles for a sample of 165 low-mass galaxies using rotation curves obtained from high-quality, long-slit optical spectra assuming minimal disks and spherical symmetry. For $\rho(r) \sim r^{-\alpha}$ near the galaxy center we measure median inner slopes ranging from $\alpha_m = 0.22 \pm 0.08$ to $0.28 \pm 0.06$ for various subsamples of the data. This is similar to values found by other authors, and in stark contrast to the intrinsic cusps ($\alpha_{int}\sim1$) predicted by simulations of halo assembly in cold dark matter (CDM) cosmologies. To elucidate the relationship between $\alpha_m$ and $\alpha_{int}$ in our data, we simulate long-slit observations of model galaxies with halo shapes broadly consistent with the CDM paradigm. Simulations with $\alpha_{int}=1/2$ and 1 recover both the observed distribution of $\alpha_m$ and correlations between $\alpha_m$ and primary observational parameters such as distance and disk inclination, whereas those with $\alpha_{int}=5/4$ are marginally consistent with the data. Conversely, the hypothesis that low-mass galaxies have $\alpha_{int}=3/2$ is rejected. While the simulations do not imply that the data favor intrinsic cusps over cores, they demonstrate that the discrepancy between $\alpha_m$ and $\alpha_{int}\sim1$ for our sample does not necessarily imply a genuine conflict between our results and CDM predictions: rather, the apparent cusp/core problem may be reconciled by considering the impact of observing and data processing techniques on rotation curves derived from long-slit spectra.