Rotation Curve of the Milky Way

Abstract

We investigate the rotation curve of the Milky Way using a multi-component mass model including a stellar disk, a gaseous disk, a bulge/bar component, and a dark-matter halo. The stellar and gas contributions are calibrated using recent observational determinations of the Galactic surface-density distribution, while the dark-matter halo is modelled with standard spherical profiles. We compute the circular-velocity contributions of the different components using a combination of spherical mass reconstruction for the bulge and halo, and thin-disk Hankel-transform methods for the disk and gas components. We first fit the stellar surface-density profile to determine a fiducial bulge-disk decomposition and then use this calibration to predict the Galactic rotation curve. We find that, although the resulting stellar mass model reproduces the observed surface-density profile reasonably well, it does not provide a fully satisfactory description of the rotation-curve data, with the largest discrepancies arising in the inner Galaxy. We then consider an alternative RC-first calibration strategy, in which the bulge and disk parameters are adjusted to improve the kinematic fit. While this significantly improves the agreement with the observed rotation curve, the corresponding stellar surface-density profile becomes inconsistent with the independently inferred baryonic distribution. Our results highlight a tension between photometric and kinematic constraints within simplified axisymmetric models and indicate that a fully consistent description of the Milky Way mass distribution likely requires a more realistic treatment of the bulge/bar structure and of baryonic systematic uncertainties.

Figures (5)

• Figure 1: Adopted gas surface-density profiles used in the rotation-curve decomposition. The blue curve shows the adopted average surface-density profile $\Sigma(R)$, while the shaded band provides an indicative envelope capturing systematic uncertainty in the gas distribution. Black points show the reference data used for comparison. The HI profile exhibits a broad maximum at intermediate radii, and declines towards large radii. The H$_2$ profile is centrally concentrated, decreases with radius more steeply than HI. These gas profiles are used to compute the gaseous contribution to the circular speed through $V_{\rm gas}^2(R)=V_{\rm HI}^2(R)+V_{\rm H_2}^2(R)$ and are therefore a key input for separating baryonic and DM contributions in the RC-first calibration. The data are taken from MertschPhan2023 and MertschVittino2021 and references therein.
• Figure 2: Best-fit decomposition of the stellar surface-density profile. Figure \ref{['fig:sigma_disk_bulge_fit']} shows the stellar surface-density profile $\Sigma(R)$ extracted from Lian2025StellarMass (cyan) together with the best-fit two-component model. The dashed and dash-dotted curves indicate the disk and bulge contributions, respectively, and the solid curve is their sum. Overall, the model reproduces the radial trend of the extracted profile over most of the fitted range, providing the calibrated bulge--disk decomposition used in the subsequent rotation-curve prediction.
• Figure 3: Figure \ref{['fig:rc_linear']} compares the observed rotation-curve data (black points with error bars) with the model prediction (solid black line), decomposed into bulge, disk, gas (HI and ${\rm H}_2$), and DM contributions. This figure highlights the disagreement at small distances between the theoretical model calibrated with the surface brightness observation of disk and bulge stars (see Figure \ref{['fig:sigma_disk_bulge_fit']}) and the data. It shows also which component dominates at different radii: the bulge in the inner region, the stellar disk at intermediate radii, and the DM halo at large radii. The decomposition provides a physical interpretation of the observed kinematics in terms of the underlying mass components. To emphasize the inner-Galaxy behaviour, Figure \ref{['fig:rc_log']} shows the same rotation-curve decomposition as Figure \ref{['fig:rc_linear']} but on a logarithmic radial scale.
• Figure 4: RC-first rotation-curve decomposition of the Milky Way shown on complementary radial scales. Black points with error bars represent the observed circular velocity $V_{\rm obs}(R)$ as a function of Galactocentric radius $R$. The solid black curve shows the total model circular velocity, $V_{\rm model}^2 = V_{\rm bulge}^2 + V_{\rm disk}^2 + V_{\rm gas}^2 + V_{\rm DM}^2$, where $V_{\rm gas}^2 = V_{\rm HI}^2 + V_{\rm H_{2}}^2$. Colored curves indicate the contributions from the bulge (red), stellar disk (green), gas components (HI/${\rm H}_2$; blue/olive), and the NFW DM halo (yellow). Panel (a) shows the logarithmic radial scale and panel (b) the linear radial scale.
• Figure 5: Stellar surface-density profile reconstructed using the RC-calibrated parameter set, shown together with the extracted $\Sigma(R)$ data and the corresponding bulge, disk, and total model components. After tuning the bulge--disk parameters to match the rotation-curve data, we reconstruct the corresponding stellar surface-density profile $\Sigma(R)$ and compare it with the extracted surface-density dataset in Figure \ref{['fig:sigma_rc_calibrated']}. Although the reconstructed profile follows the broad radial decline, the agreement with the extracted $\Sigma(R)$ data is limited, with the most pronounced discrepancy occurring in the bulge-dominated inner region.