Exploring Milky Way rotation curves with Gaia DR3: a comparison between $Λ$CDM, MOND, and General Relativistic approaches

TL;DR

The paper analyzes Milky Way rotation curves using Gaia DR3 for 719,143 young disc stars to test MOND and ΛCDM with an Einasto halo against a classical NFW/MWC and a general-relativistic model. Employing a consistent baryonic component (bulge plus thin and thick discs) and Bayesian model comparison, it finds MOND, ΛCDM, and relativistic models provide statistically equivalent fits, with ΛCDM requiring more dark matter and a virial mass in the range $M_{200}=1.5\text{--}2.5\times10^{12}\,M_\odot$. Non-Newtonian/dark-matter contributions dominate beyond roughly $10$–$15$ kpc across all models. The study highlights a tension with some literature on the Milky Way’s mass scale and underscores the need for further work to reconcile GR effects, dark matter distributions, and alternative gravitational theories in shaping Galactic rotation curves.

Abstract

With the release of Gaia DR3, we extend the comparison between dynamical models for the Milky Way rotation curve initiated in the previous work. Utilising astrometric and spectro-photometric data for 719143 young disc stars within $|z|<1$ kpc and up to $R \simeq 19$ kpc, we investigate the accuracy of MOND and $Λ$CDM frameworks in addition to previously studied models, such as the classical one with a Navarro-Frenk-White dark matter halo and a general relativistic model. We find that all models, including MOND and $Λ$CDM, are statistically equivalent in representing the observed rotational velocities. However, $Λ$CDM, characterized by an Einasto density profile and cosmological constraints on its parameters, assigns more dark matter than the model featuring a Navarro-Frenk-White profile, with the virial mass estimated at $1.5\text{-}2.5 \times 10^{12} \, {\rm M}_{\odot}$ - a value significantly higher than recent literature estimates. Beyond $10\text{-}15$ kpc, non-Newtonian/non-baryonic contributions to the rotation curve are found to become dominant for all models consistently. Our results suggest the need for further exploration into the role of General Relativity, dark matter, and alternative theories of gravitational dynamics in shaping Milky Way's rotation curve.

Figures (7)

• Figure 1: Rotation curve for the full sample, compared with rotation curves from the recent literature jiaoDetectionKeplerianDecline2023wangMappingMilkyWay2023ouDarkMatterProfile2024labiniMassModelsMilky2023zhouCircularVelocityCurve2023. The 2D histogram of the full stellar sample in the $(R, V_\phi)$-space is plotted in the background beordoGeometrydrivenDarkmattersustainedMilky2024e.
• Figure 2: $\Lambda$CDM constraint relations, given by equations (\ref{['eq:SHM']}), (\ref{['eq:HMC']}), and (\ref{['eq:alpha']}). Coloured data points are the best parameter estimates for each stellar sample (see table \ref{['table:fit_params']}). The shaded gray regions represent the 1-,2-,3-$\sigma$ ranges around the mean relations.
• Figure 3: The azimuthal velocity profile of the MW as derived from the sample of disc tracers selected from Gaia DR3. For each dataset, the black starred symbols represent the median azimuthal velocity at the median distance from the galactic centre of the stellar population within each of the radial bins beordoGeometrydrivenDarkmattersustainedMilky2024e, where the RSE of the velocity distribution defines the corresponding error bar. The red, blue, green, and yellow curves show the best-fitting to the BG, MWC, MOND, and $\Lambda$CDM models, respectively. The filled areas represent the 68 per cent reliability intervals of each rotation curve; note that for $R \lesssim 4.5$ kpc both the classical and the relativistic curves are very uncertain because of the lack of data in that region.
• Figure 4: Density profiles of the MW at $z=0$ for the four models, with their corresponding 68 per cent confidence intervals; in each panel, the red, blue, green, and orange solid lines represent the baryonic matter contributions for the BG, MWC, MOND, and $\Lambda$CDM models respectively. The blue and orange dashed lines show the total matter for the MWC and $\Lambda$CDM models, while the dash-dotted lines are the corresponding dark matter contributions. The vertical grey dashed lines represent the values of $r_{\rm in}$ and $R_{\rm out}$ of the BG model, while the vertical grey band spans the radial range covered by the sample. Finally, the black dot represents the local mass density inferred at the Sun position, i.e. $\rho_{\rm bar}(R_{\odot}) = 0.084 \pm 0.012$ M$_\odot {\rm pc}^{-3}$ from mckeeSTARSGASDARK2015.
• Figure 5: Red, blue, green and yellow lines refer to the BG, MWC, MOND, and $\Lambda$CDM models, respectively. The dashed lines represent the Newtonian/baryonic counterparts to the rotation curves: $V_{\rm eN}^{\rm BG}$ is the relativistic effective Newtonian velocity for the BG model, $V_{\rm bar}^{\rm MWC}$ and $V_{\rm bar}^{\rm \Lambda CDM}$ are the velocities contributed by the baryonic matter for the MWC and $\Lambda$CDM models, and $V_{\rm bar}^{\rm MOND}$ is the Newtonian velocity contributed by the baryonic matter for the MOND model. The solid lines show the MWC and $\Lambda$CDM halo components alone, respectively $V_{\rm h}^{\rm MWC}$ and $V_{\rm h}^{\rm \Lambda CDM}$, the gravitational dragging contribution for the BG model, i.e. $V_{\rm drag}^{\rm BG}$, and the Mondian boost $V_{\rm acc}^{\rm MOND}$. In the bottom right corner of each panel, $z_{\rm eff}$ represents the effective vertical width of validity for the relativistic disc in the BG framework.