Consequences of radially correlated rotation curves for galaxy mass models

TL;DR

This work investigates how radial correlations between rotation-curve data points affect galaxy mass-model inferences. Using a data-driven Gaussian-process covariance approach, it adds a simple per-galaxy correlation with amplitude $a_k$ and scale $s_k$ to mass-model fits for 134 SPARC galaxies under both NFW and pISO halos. The key finding is that accounting for these correlations generally improves fit quality and yields similar, physically plausible correlation parameters across halo models, thereby removing a statistical preference for cuspy versus cored halos and bringing halo properties closer to ΛCDM expectations. The study highlights radial correlations as a significant systematic in rotation-curve modeling and provides a framework and public supplementary resources to incorporate these effects in future analyses.

Abstract

Consecutive points in rotation curve measurements are correlated with each other, but this is usually ignored when constructing galaxy mass models. We apply the data-driven approach proposed by Posti (2022) to include the characteristic amplitude and scale length of such correlations as `nuisance parameters'. We construct mass models for $134$ galaxies from the SPARC 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 ($χ^2_\mathrm{r}\approx 1$) 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.

Figures (9)

• Figure 1: Mass models of DDO 154 for four cases. Upper left: NFW halo without GP model for correlations in rotation curve. Upper right: pISO halo without GP model. Lower left: NFW halo with GP model. Lower right: pISO halo with GP model. In all panels rotation curve measurements from the SPARC database are shown as points with error bars. The mass models show the gas (green line), stars (yellow line with shaded band) and halo (pink line with shaded band) components, along with the total model rotation curve (blue line with shaded band). The shaded bands show the $16^\mathrm{th}$-$84^\mathrm{th}$ percentile range of MCMC model evaluations at each radius. For both models, our view is that the GP case provides a more realistic description of models compatible with the data. Similar figures showing mass models for all $134$ galaxies in our sample are available as Supplementary Material.
• Figure 2: Goodness of fit and correlation amplitudes & scale lengths for DDO 154. Left panel: Reduced chi-squared $\chi^2_\mathrm{r}$ for each combination of halo model (NFW, solid lines; pISO, dashed lines) and Gaussian process model for radial correlations in the rotation curve (GP, red; nGP, black). In the nGP case there is a clear preference for the pISO halo model (lower typical $\chi^2_\mathrm{r}$), although neither model is a good fit ($\chi^2_\mathrm{r}\gg 1$). This preference vanishes when the GP model is used. Middle panel: Marginalized posterior probability distribution for the amplitude of radial correlations, $a_k$, in the rotation curve. Lines are as in left panel. Right panel: Marginalized posterior probability distribution for the scale length, $s_k$, of radial correlations in the rotation curve. Lines as in the left panel. The $a_k$ and $s_k$ distributions for the two models are nearly identical. All distributions are smoothed using Gaussian kernel density estimation (KDE).
• Figure 3: Comparison of the $\chi^2_\mathrm{r}$ values for the pISO (abscissa) and NFW (ordinate) halo models when constant uncertainties of $0.05\max(v_\mathrm{rot})$ are assumed on the rotation curve measurements. The points mark the median of the distribution across the MCMC samples with the $16^\mathrm{th}$-$84^\mathrm{th}$ percentile intervals shown by the error bars. The dashed red line shows the $1$:$1$ relation. A majority of the points lie above this line, indicating a preference for the pISO halo model. We select all galaxies whose rotation curve shapes can be well captured by at least one of the two halo models -- where at least one achieves a median $\chi^2_\mathrm{r} < 2$, shown as the shaded region.
• Figure 4: Upper left: Comparison of the $\chi^2_\mathrm{r}$ values for the pISO (abscissa) and NFW (ordinate) halo models with (red) and without (black) the GP model for radial correlations in the rotation curves. The points mark the median of the distribution across the MCMC samples with the $16^\mathrm{th}-84^\mathrm{th}$ percentile intervals shown by the error bars. The dashed red line shows the $1$:$1$ relation. The values are tabulated in Table \ref{['tab:all-chi2']}. Upper right: as upper left but cropped to the $\chi^2_\mathrm{r} < 3$ region. In the nGP case most points lie above the $1$:$1$ line indicating a preference for the pISO model, while in the GP case the points are evenly distributed around it, indicating no preference for either model. Lower left: distribution of $\chi^2_\mathrm{r}$ summed across all sampled galaxies, smoothed with Gaussian KDE. The same slight preference for the pISO model in the nGP case as noted in the description of the upper left panel is visible here as a slightly sharper peak near $\chi^2_\mathrm{r}=1$. In the GP case the distributions for the two halo models are almost identical and much more sharply peaked near $\chi^2_\mathrm{r}=1$ than their nGP counterparts. Lower right: The distribution of the fractional difference between the median $\chi^2_\mathrm{r}$ values for each galaxy. The distribution for the nGP case is slightly offset towards $\chi^2_\mathrm{r,pISO}<\chi^2_\mathrm{r,NFW}$, again indicating a slight preference for the pISO halo model. This confirms that the preference seen in the other panels is not driven only by a very strong preference for the pISO model in a small number of galaxies. In the GP case the distribution is centred about $0$, indicating no preference for one halo model over the other.
• Figure 5: Posterior probability distributions for $a_k$ (upper panel) and $s_k$ (lower panel) summed across all $134$ galaxies in our sample. Distributions are smoothed using Gaussian KDE. Both halo models show very similar distributions for correlation amplitude and scale length; the pISO model has a preference for very slightly stronger and further-reaching correlations.