Implications of a contracted dark matter halo for the Milky Way's inferred virial mass

Abstract

We investigate how reliably the global properties of Milky Way-mass dark matter haloes can be recovered from dynamical data over a limited radial range, particularly $\lesssim 30~\mathrm{kpc}$ where observations are most sensitive but baryonic processes modify the halo structure. Using the ARTEMIS simulations, which produce varying degrees of baryon-induced contraction, we fit dark matter profiles over restricted radial ranges using commonly adopted parametric models. Assuming negligible observational uncertainties allows the systematic errors from these choices to be isolated. When fits are confined to inner radii, an NFW profile underestimates the virial mass by a factor of $\approx 2$ on average ($\approx 4$ for some systems), and the concentration by a factor of $\approx 2$. Einasto and generalised-NFW models provide excellent local fits but retain similar global biases. In contrast, the contracted halo prescription from Cautun et al. (2020) yields stable extrapolations and recovers unbiased halo mass estimates over all radii. The inferred mass improves systematically with increasing radial coverage, and tracers beyond $\gtrsim 50~\mathrm{kpc}$ largely eliminate the mean bias for all models. The local dark matter density at the Solar radius is recovered to within $\lesssim 5\%$ for all profiles other than NFW. These biases are sufficient to reconcile recent low Milky Way mass estimates derived from inner rotation-curve analyses with the canonical $\approx 10^{12}~\mathrm{M}_\odot$. We additionally find a halo-to-halo scatter of $\gtrsim 0.1$ dex ($\approx 25\%$) persists even under idealised conditions, setting a likely lower limit for the precision of halo mass estimates.

Figures (6)

• Figure 1: Fractional difference in virial mass, $(M_{200\mathrm{c}} - M_{200\mathrm{c},\mathrm{DMO}})/M_{200\mathrm{c},\mathrm{DMO}}$, between the hydrodynamical and DMO counterparts of each ARTEMIS central halo. Colours denote the definition of $M_{200\mathrm{c}}$: dark blue for the standard total enclosed mass definition (Equation \ref{['eq:virial_condition']}), and dark red for the dark matter–rescaled definition which scales the enclosed DM mass by the cosmic mean baryon fraction (Equation \ref{['eq:mass_def_scaled']}). Left panel: Fractional mass differences as a function of the DMO virial mass; each circle corresponds to a single central halo. Right panel: Distribution of these fractional differences. In both panels, the dashed black line marks perfect agreement between hydrodynamical and DMO masses, while the grey dotted lines indicate $\pm 10~\%$ deviations. Applying the DM-rescaled definition greatly suppresses the systematic offset, showing that the dominant contribution to the total mass mismatch arises from baryons displaced from the halo rather than from any substantial loss of dark matter.
• Figure 2: Spherically averaged dark matter density profiles for three representative ARTEMIS central haloes (G40, G18, and G14). Solid lines show the hydrodynamical profiles after rescaling the enclosed dark matter mass by the cosmic mean baryon fraction; dashed lines of the same colours denote their DMO counterparts. Colours differentiate the individual haloes as indicated in the legend. The impact of baryons is most pronounced at radii $r \lesssim 20~\mathrm{kpc}$, where the hydrodynamical profiles depart markedly from the corresponding DMO profiles.
• Figure 3: Relation between the enclosed dark matter mass ratio, $\eta_{\mathrm{DM}}$, and the enclosed total mass ratio, $\chi_{\mathrm{tot}}$, for all central ARTEMIS haloes. Ratios are computed from the spherically averaged cumulative mass profiles in the hydrodynamical and DMO versions of each halo. Top panel:$\eta_{\mathrm{DM}}$–$\chi_{\mathrm{tot}}$ relation for individual haloes (dark red curves). The solid black line shows the Cautun_2020 best-fit power law, and the dashed grey line shows our best-fit to the ARTEMIS sample. Bottom panel: Fractional deviation of each halo from the Cautun_2020 prediction. The ARTEMIS haloes follow the same deterministic power law relation to within a few per cent, with both median offset and sample scatter within the Cautun_2020 model quoted bounds, confirming that their contraction formalism remains accurate in an independent simulation suite.
• Figure 4: Comparison of NFW, Contracted NFW (CNFW), gNFW, and Einasto fits when constrained to truncated radial ranges of simulated ARTEMIS haloes. Fits are applied to the DM circular velocity profiles of the DM-rescaled hydrodynamical runs. Top row of each panel: Circular velocity profiles, $V_{c}(r)$, of a representative halo (solid black) and its DMO analogue (dashed black), together with best fits obtained when the outer fitting radius is limited to 21 kpc (blue), 64 kpc (orange), and 214 kpc (green). Coloured arrows indicate the radial interval used for each fit, following the same colour scheme. Bottom rows of each panel: Logarithmic deviations (in dex) between the fitted, $V_c^{\rm fit}$, and simulated hydrodynamical, $V_c^{\rm sim}$, profiles. Thin curves show individual haloes, the thick curve the sample mean, and shaded regions the $1\sigma$ halo-to-halo scatter. The solid black line denotes zero deviation. In each sub-panel, the coloured vertical dash–dotted line marks the corresponding outer fitting radius. In all panels the vertical dash-dotted line marks the fixed inner fitting radius (i.e., $3~\mathrm{kpc}$). Across all profile families, restricted radial coverage increases systematic deviations in the extrapolated profile, with the magnitude and character of the bias strongly dependent on the chosen functional form.
• Figure 5: Model–dependent biases in extrapolated halo properties as a function of the maximum fitted radius, $r_{\rm max,fit}$. For each ARTEMIS halo we plot the logarithmic offset between the fitted parameter and its true/reference value. Top panel: Logarithmic offset between virial masses -- $\log M_{200\mathrm{c}}^{\rm fit} - \log M_{200\mathrm{c}}^{\rm sim}$ -- against the logarithm of the maximum fitting radius. Bottom panel: Same as the top panel but focusing on the concentration parameter. Hence showing deviations in the recovered concentration relative to that of the corresponding DMO halo -- $\log c^{\rm fit} - \log c^{\rm full~fit}_{\rm DMO}$. Thin coloured curves show individual haloes, thick curves the sample median, and shaded regions the $16^{\rm th}$–$84^{\rm th}$ percentile range. Columns, as well as colours, correspond to the four fitted models (NFW, CNFW, gNFW and Einasto, from left to right). In both panels, the grey shaded band indicates the typical observational range of the outermost radius probed by the Milky Way rotation curve. The figure demonstrates that restricting the fitted domain to small radii induces systematic, model-dependent biases in both halo mass and concentration, despite excellent local fits within the constrained region.