The rotation curve of the Milky Way measured by Classical Cepheids from Gaia DR3

TL;DR

The paper delivers a precise Milky Way rotation curve in the 6–18 kpc range based on ~1,000 classical Cepheids with Gaia DR3 kinematics, leveraging Period-Wesenheit distances to minimize extinction effects. By applying Jeans-equation–based asymmetric drift corrections—even for young Cepheids—and careful sample selection, the RC shows a modest decline with radius and a localized dip–bump feature around 10–11 and 13–14 kpc. An averaged RC combining their measurements with prior work enables robust constraints on the local dark matter density and the halo mass within 18 kpc, with results consistent across multiple baryonic models and in agreement with previous RC studies. The findings reinforce the validity of standard RC analyses while underscoring the need for complementary outer-halo probes to refine the DM profile further.

Abstract

We determine the rotation curve (RC) of the Milky Way in the range 6 < R < 18 kpc using a sample of 903 carefully selected classical Cepheids with precise proper motions and high-quality radial velocities from \emph{Gaia} DR3. Their distances can be accurately measured from the well-known Period-Wesenheit relations. The RC is computed from the three-dimensional velocity components of these Cepheids. Generally, the RC shows a slight decline with distance from the Galactic center. On top of this general trend, the newly constructed RC shows a dip around R ~ 10-11 kpc, followed by a bump around R ~ 13-14 kpc. This feature has also been reported in other RC measurements, mostly in RCs traced by young tracers like Cepheids. To better constrain the Milky Way mass, an averaged RC is then constructed by combining measurements from this work and previous efforts. Due to the ambiguous nature of the dip-and-bump feature, this averaged RC is constructed only within the radial range where the RC appears to be less influenced by this feature. By using this averaged RC, we determine the circular velocity at solar position and also build a parameterized mass model of our Milky Way. The result for the circular velocity at the solar position is $V_c(R_0) = 236.8 \pm 0.8\ \mathrm{km\,s^{-1}}$, which is in good agreement with previous measurements. The local dark matter density and the enclosed dark matter halo mass within 18 kpc are estimated from the averaged RC under different baryonic models, yielding a series of consistent results: a local density of $0.33-0.40\ \mathrm{GeV\,cm^{-3}}$ and an enclosed mass of $1.19-1.45 \times 10^{11}\ M_\odot$.

Figures (8)

• Figure 1: Left panel: The $X-Y$ distribution of the final adopted sample. The black star denotes the position of the Galactic center. Right panel: the $R-Z$ distribution of the final adopted sample. The position of the Sun is marked by the red dot in both panels.
• Figure 2: Radial profiles of the radial velocity tensor $\sqrt{\langle V_{R}^2 \rangle}$. Grey dots indicate measurements for individual stars. The black dots represent the square root of the $\langle V_{R}^2 \rangle$ in each bin, with uncertainties calculated via bootstrapping with 100 resamples. The red line represents the best-fit exponential function to our sample’s $\sqrt{\langle V_{R}^2 \rangle}$, while the orange dashed line corresponds to the best-fit exponential model for $\sqrt{\langle V_{R}^2 \rangle}$ from ZH23. Overall, our derived $\sqrt{\langle V_{R}^2 \rangle}$ values are much lower than those reported in ZH23 across the radial range.
• Figure 3: The gray dots denote the rotation velocity $V_{\phi}$ of the sample stars. The blue dots represent the azimuthal velocity tensor, $\sqrt{\langle V_{\phi}^2 \rangle}$, calculated in radial bins. The magenta dots indicate the RC derived from Equation 2, which includes corrections for asymmetric drift. Uncertainties for both quantities (blue and magenta points) are estimated using bootstrapping with 100 resamples. The sky-blue region indicates the 1$\sigma$ uncertainty arising from the variations in $R_{0}$ and the proper motion of Sgr A* (see Section 3.3). The magenta dashed line illustrates the overall declining trend of the RC with Galactocentric radius, while localized fluctuations are superimposed on this trend.
• Figure 4: The relative systematic uncertainties are quantified as $(V_{\mathrm{c}}^{*}- V_{\mathrm{c}})/V_{\mathrm{c}}$, where $V_{\mathrm{c}}^{*}$ represents the RC derived after accounting for different systematic effects, and $V_{\mathrm{c}}$ denotes the original measurement. The upper panel shows the systematic uncertainties in the RC arising from variations in the adopted solar velocities, whereas the lower panel illustrates those associated with different choices of azimuthal wedges.
• Figure 5: The combined RC are denoted by the navy color hexagon points, covering only the range of $6<R<10$ kpc and $R>16$ kpc. The error bars for other points are given by the mean values of the uncertainties of the $V_{\mathrm{c}}$ given by the four measurements in each bin. The measurements by our Cepheids sample, as well as the results from previous works are also shown here by colored symbols.