The dark-matter cusp-core gap may live in the error bars: correlated noise erases the preference for cored halos across five SPARC galaxies
Synopsis
Galaxy rotation curves have long favored cored dark-matter halos over the steeply rising cusps predicted by cold dark matter simulations. Fitting five SPARC galaxies with Bayesian inference while modeling correlated errors between neighboring radii largely closes that gap. In DDO 154 the reduced chi-square moves from 2.40 versus 9.41 to 0.94 versus 1.04, leaving one-dimensional rotation curves unable to separate the two halo shapes.
Interpretation
Under the standard independent-error assumption, cored halo models outperform the cuspy NFW profile across most of the SPARC sample, most clearly in gas-dominated dwarfs. Cold dark matter simulations default to an NFW cusp whose density rises as r to the minus one, while observed inner rotation curves rise more gently, the two-decade-old cusp-core discrepancy. Among five benchmark galaxies, DDO 154 gives a reduced chi-square of 2.40 for the cored ISO profile and 9.41 for NFW under standard fitting, while NGC 2403, NGC 3198 and UGC 128 slightly favor NFW, with disk-halo degeneracy growing in more massive systems.
When correlated errors between neighboring radii are sampled jointly with halo parameters as a Gaussian process term, the two halo shapes fit comparably well. Standard fitting treats each radius as statistically independent, yet beam smearing, non-circular gas motion and tilted-ring smoothing all correlate adjacent points. With the Gaussian process covariance, reduced chi-square values are 0.94 for ISO and 1.04 for NFW in DDO 154, 0.65 and 0.97 in NGC 2403, 0.42 and 0.47 in NGC 3198, 0.98 and 1.03 in UGC 128, and 0.37 and 0.43 in NGC 2841.
The narrowing of the cored-versus-cuspy gap appears in all five galaxies, with DDO 154 dropping from 7.01 to 0.10. Single-galaxy one-dimensional fits previously treated the reduced chi-square difference as the main evidence separating core from cusp. The gap falls from 0.26 to 0.05 in NGC 3198, from 0.53 to 0.05 in UGC 128, and from 1.16 to 0.06 in NGC 2841, while NGC 2403 shrinks by about 87 percent, from 2.54 to 0.32.
Perspective
The conclusions rest on five benchmark galaxies from the SPARC database, spanning dwarf irregulars, ordinary spirals and a massive low-surface-brightness spiral; DDO 154 has only 12 radial data points and UGC 128 has 22. For the massive, bulge-dominated NGC 2841 both models fit poorly and results are sensitive to the assumed stellar mass-to-light ratio. The source proposes next steps: reducing beam smearing with the Square Kilometre Array and its pathfinders, calibrating mass-to-light ratios independently from stellar velocity dispersion, and three-dimensional forward modeling of interferometric data cubes.
The cusp-core problem is not settled, and current data precision cannot rule out a central cusp hidden by correlated noise. The ISO reduced chi-square of 2.40 for DDO 154 disagrees with the 6.7 reported by a separate study of 134 galaxies, which the source attributes to differences in mass-to-light priors and bulge treatment. Self-interacting dark matter, fuzzy dark matter and MOND remain viable alternatives, and whether MOND's constant a0 varies across galaxy types is unresolved.