Consequences of radially correlated rotation curves for galaxy mass models

ABSTRACT Consecutive points in rotation curve measurements are correlated with each other, but this is usually ignored when constructing galaxy mass models. We apply a recently proposed data-driven approach to include the characteristic amplitude and scale length of such correlations as ‘nuisance parameters’. We construct mass models for 134 galaxies from the SPARC (Spitzer Photometry and Accurate Rotation Curves) rotation curve compilation with Navarro–Frenk–White (NFW) and pseudo-isothermal sphere (pISO) models for the dark halo. Allowing for correlations in the rotation curves generally improves the goodness of fit for both halo models, often yielding a formally good fit ($\chi ^2_\mathrm{r}\approx 1$) and model uncertainties that seem more representative of the constraining power of the data. For both halo models, the inference on the typical correlation amplitude and scale length are very similar and physically plausible, $\sim 20\, \mathrm{km}\, \mathrm{s}^{-1}$ and $\sim 5\, \mathrm{kpc}$, respectively. The parametric form that we use to describe the correlations is intentionally simple, and our fitting approach makes the parameters describing possible correlations prone to ‘absorbing’ other systematic errors, so we regard these estimates as upper limits. Without allowing for correlations, we find a statistical preference for the pISO over the NFW model for 88/134 galaxies; this preference essentially disappears when correlations are allowed for. Accounting for correlations in rotation curves when constructing mass models fundamentally affects how they are interpreted, highlighting an important systematic uncertainty that affects evidence for cusps or cores in dark matter haloes.