🔭 astrophysics

Galaxy rotation curve based on RGB stars from the Gaia DR3 catalogue

Using a sample of over 4.5 million RGB stars from the Gaia DR3 catalogue and the Jeans equation, this paper constructs a detailed, model-independent circular velocity curve of the Milky Way out to 20 kpc, yielding a solar circular velocity of $229.63 \pm 0.30$ km s $^{-1}$ and an average slope of $-2.29 \pm 0.05$ km s $^{-1}$ kpc $^{-1}$ between 6 and 20 kpc.

Original authors: P. N. Fedorov, A. M. Dmytrenko, V. S. Akhmetov, A. B. Velichko, V. P. Khramtsov, S. I. Denyshchenko, I. B. Vavilova, D. V. Dobrycheva, O. Sergijenko, A. A. Vasylenko, O. V. Kompaniiets

Published 2026-07-29

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CC BY 4.0

Original authors: P. N. Fedorov, A. M. Dmytrenko, V. S. Akhmetov, A. B. Velichko, V. P. Khramtsov, S. I. Denyshchenko, I. B. Vavilova, D. V. Dobrycheva, O. Sergijenko, A. A. Vasylenko, O. V. Kompaniiets

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Milky Way not as a static, silent island of stars, but as a giant, swirling cosmic carousel. For decades, astronomers have tried to figure out exactly how fast this carousel spins at different distances from the center. Why does this matter? Because the speed of the spin is the ultimate clue to how much "stuff" is inside the galaxy. If you know how fast a merry-go-round spins, you can guess how heavy the horses and the platform are. In our galaxy, this "stuff" includes the billions of visible stars we can see, but also a mysterious, invisible substance called dark matter that holds everything together. If we get the spin speed wrong, our map of the galaxy's mass is wrong, and we can't understand how our cosmic neighborhood is built or how it compares to other galaxies.

To solve this puzzle, scientists usually use a mathematical tool called the Jeans equation. Think of this equation as a cosmic speedometer that tries to calculate the "perfect" speed a star should have if it were orbiting in a perfect circle, like a planet around the sun. However, real stars are messy. They don't just orbit; they wobble, drift, and bump into each other, creating a "traffic jam" effect that throws off the speedometer. Furthermore, we are stuck inside the galaxy, trying to measure the spin of a giant wheel while standing on one of its spokes, looking out at a tiny slice of the rim. It's like trying to guess the speed of a whole highway by only watching cars in one lane, from a single spot, while the cars are changing lanes and speeding up or slowing down.

This is where a new study by P. N. Fedorov and their team comes in. They decided to take a fresh look at the Milky Way's spin using the most detailed star map humanity has ever created: the Gaia DR3 catalogue. Instead of relying on old models or guessing, they looked at nearly 4.5 million specific stars called Red Giant Branch (RGB) stars. These are old, bright, and easy to spot, acting like glowing lanterns scattered across the galaxy's disk. The team didn't just look at the average speed; they mapped the speed in tiny, 1-kilometer-wide (well, 1-kiloparsec, which is about 3,260 light-years) bubbles across a huge slice of the galaxy, from 150 to 210 degrees around the center.

Here is what they found. First, they confirmed that at our own neighborhood (the Sun's distance), the galaxy spins at about 229.63 kilometers per second. This matches what other scientists have guessed before, which is a good sign. But as they looked further out, between 6 and 20 kiloparsecs (about 19,000 to 65,000 light-years) from the center, they saw something interesting: the spin isn't perfectly flat. It's actually slowing down, dropping by about 2.29 kilometers per second for every kiloparsec you move away from the center.

The most exciting part of their discovery is that the spin speed isn't the same in every direction. If you look at the galaxy from one angle, it might spin slightly faster or slower than if you look from another angle. The authors found that this difference can be as much as 20 kilometers per second depending on where you look. They also spotted some "bumps" and "dips" in the speed curve, specifically around 13 and 18 kiloparsecs from the center. These aren't just measurement errors; the team checked their math and used different distance calculations, and the dips remained. This suggests that the galaxy's velocity field is more complex and "wobbly" in the outer regions than we thought, possibly influenced by the transition from the thin disk of stars to the thicker halo, or perhaps by waves rippling through the galaxy.

The authors are careful to say that while their map is incredibly detailed, it's still a local view. Because we can't see the whole galaxy at once, and because the outer edges are a bit chaotic, we can't just take their curve and assume it applies to the entire universe of the Milky Way. However, this detailed, model-free map gives us a much sharper tool to compare our galaxy with others. It tells us that the Milky Way isn't a simple, smooth spinning disk, but a dynamic, slightly uneven structure that changes its speed and behavior depending on where you stand and which way you look.

Technical Summary: Galaxy Rotation Curve Based on RGB Stars from the Gaia DR3 Catalogue

Problem Statement
The determination of the Milky Way's circular velocity curve, $V_c(R)$ , is fundamental to understanding the Galaxy's mass distribution and dynamics. However, classical approaches relying on the axisymmetric Jeans equation face significant challenges. These include the assumption of dynamical equilibrium and axial symmetry, which are known to be violated in the Milky Way due to asymmetries and non-stationarity. Furthermore, existing estimates of the Galactic mass vary by more than a factor of three, a discrepancy attributed not to experimental error but to incomplete data and model-dependent assumptions. A critical obstacle in extending rotation curves to large radii ( $R > 15$ kpc) is the rapid deterioration of parallax-based distance precision and the systematic bias introduced by asymmetric drift in tracer populations, particularly Red Giant Branch (RGB) stars.

Methodology
The authors construct a detailed circular velocity curve out to $\sim 20$ kpc using only Gaia DR3 data, aiming to minimize reliance on model data and external assumptions.

Sample Selection: The study utilizes a sample of 4,547,980 RGB stars with measured spatial velocities. Selection criteria include stellar parameters ( $\log g < 3.0$ , $3000 \text{ K} < T_{\text{eff}} < 5200 \text{ K}$ ) and strict quality cuts: $RUWE < 1.4$, parallax significance $\varpi/\sigma_\varpi > 5$ , and exclusion of high-velocity halo stars ( $|V_Z| > 100 \text{ km s}^{-1}$ ).
Data Corrections: Systematic errors are addressed through:
- Parallax bias correction using the $Z_5$ and $Z_6$ terms from Lindegren et al. (2021).
- Proper motion corrections for stars with absolute magnitudes $9 < M_G < 13$ (Cantat-Gaudin & Brandt 2021).
- Magnitude-dependent radial velocity corrections based on Gaia DR3 documentation.
Spatial Binning: The analysis is performed in spherical bins of radius 1 kpc, centered on a grid in the Galactic mid-plane ( $Z=0$ ) and at heights $Z = \pm 0.5, \pm 1.0$ kpc. Grid spacing is 100 pc.
Kinematic Analysis:
- Centroid velocities and the full kinematic tensor are derived using the Ogorodnikov–Milne model within each bin to account for local velocity gradients.
- To isolate intrinsic velocity dispersion from measurement noise, the authors compute the covariance matrix of propagated astrometric errors for each star and subtract the mean error contribution from the observed dispersion tensor.
- Jeans Equation: The radial component of the Jeans equation in cylindrical coordinates is solved to derive $V_c(R)$ . The authors explicitly calculate the asymmetric drift correction and the cross-term contributions using the second-order moments of the velocity distribution ( $\langle v_R^2 \rangle, \langle v_\Theta^2 \rangle, \langle v_R v_Z \rangle$ ) and the tracer density gradient.
- Distance Estimation: Distances are derived directly from corrected parallaxes ( $d = 1/\varpi_{\text{corr}}$ ) rather than photogeometric priors or spectrophotometric models, to maintain independence from Galactic models.

Key Results

Solar Neighborhood: At the Sun's distance ( $R_0 = 8.122$ kpc), the derived circular velocity is $V_c(R_0) = 229.63 \pm 0.30 \text{ km s}^{-1}$ , consistent with many previous estimates.
Rotation Curve Slope: In the range $R = 6$ to $20$ kpc and azimuth $\Theta = 150^\circ$ to $210^\circ$ , the average slope of the circular velocity is $(-2.29 \pm 0.05) \text{ km s}^{-1} \text{ kpc}^{-1}$ .
Azimuthal Dependence: The study reveals that $V_c$ is not a global constant but exhibits dependence on azimuth $\Theta$ . Differences between curves at different azimuths can reach $\sim 20 \text{ km s}^{-1}$ , particularly at large radii ( $R > 15$ kpc).
Structural Features: The derived curve shows specific peculiarities (dips/changes in slope) near $R \sim 13$ kpc and $R \sim 18$ kpc. These features persist even when using alternative distance estimates (photogeometric distances from Bailer-Jones et al. 2021), suggesting they reflect a complex velocity field rather than parallax inaccuracies.
Comparison with Eilers et al. (2019): The authors' curve up to 15 kpc closely matches the values of Eilers et al. (2019), though the current study provides significantly higher spatial detail. However, beyond 16 kpc, the slope of the current curve is steeper than that reported by Eilers et al. (2019).

Significance and Claims
The paper claims to provide a highly detailed, model-independent rotation curve constructed solely from Gaia DR3 data. By minimizing assumptions regarding the tracer population and distance priors, the authors argue that their results offer a more robust local characteristic of the Galaxy's dynamics.

The study emphasizes that the circular velocity curve should be viewed as a local characteristic dependent on azimuth, rather than a global property applicable to the entire Galaxy. Consequently, the authors caution against using a single azimuthally averaged $V_c(R)$ to infer the total Galactic mass, as the lack of data over a wider range of $\Theta$ and the non-stationary nature of the outer disk introduce significant uncertainties.

The authors conclude that while their results do not contradict previous findings, the observed features (such as the velocity dips at 13 and 18 kpc) and the azimuthal variations suggest a more complex velocity field in the outer Galaxy than previously resolved. They propose that detailed $V_c$ and $V_\Theta$ maps, combined with morphological and compositional indicators, may serve as effective tools for identifying Milky Way analogues, rather than relying solely on global mass estimates.

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