The Circular Velocity Curve of the Milky Way from 5 to 25 kpc
Open accessAbstract
We measure the circular velocity curve v c(R) of the Milky Way with the highest precision to date across Galactocentric distances of 5 ≤ R ≤ 25 kpc. Our analysis draws on the six-dimensional phase-space coordinates of ≳23,000 luminous red giant stars, for which we previously determined precise parallaxes using a data-driven model that combines spectral data from APOGEE with photometric information from WISE, 2MASS, and Gaia. We derive the circular velocity curve with the Jeans equation assuming an axisymmetric gravitational potential. At the location of the Sun we determine the circular velocity with its formal uncertainty to be = with systematic uncertainties at the ∼2%–5% level. We find that the velocity curve is gently but significantly declining at (−1.7 ± 0.1) km s−1 kpc−1, with a systematic uncertainty of 0.46 km s−1 kpc−1, beyond the inner 5 kpc. We exclude the inner 5 kpc from our analysis due to the presence of the Galactic bar, which strongly influences the kinematic structure and requires modeling in a nonaxisymmetric potential. Combining our results with external measurements of the mass distribution for the baryonic components of the Milky Way from other studies, we estimate the Galaxy’s dark halo mass within the virial radius to be = and a local dark matter density of = .
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The Eilers et al. (2019) rotation curve shows a dip at R > 20 kpc that is a few sigma away from the best-fitting global model.
“In that region, the Eilers et al. (2019) rotation curve shows a dip that is a few sigma away from the best fitting global model.”
From The milky way total mass profile as inferred from Gaia DR2 (2020) · cites this paper as Eilers et al. (2019)
The Summary and Discussion reports a mild but significant deviation of about 15 km/s from the steadily declining curve at R ≈ 19–21 kpc, which supports the claim of a feature near 20 kpc. It does not describe that feature as a dip specifically at R > 20 kpc or quantify its distance from the best-fitting global model as a few sigma; its nearby sigma statements concern other comparisons. (LLM, conf=0.85)
Experimental — accuracy not yet measuredThe Eilers et al. (2019) rotation curve errors grow from 2 percent for R < 15 kpc to ∼10 percent for R > 20 kpc.
“with Eilers et al. showing that these errors grow from 2 percent for R < 15 kpc to ∼ 10 percent for R > 20 kpc .”
From The milky way total mass profile as inferred from Gaia DR2 (2020) · cites this paper as Eilers et al. (2019)
Section 5.2 (page unavailable) says the rotation-curve systematic uncertainties are 2%–5% out to about 20 kpc and rise beyond 20 kpc. It does not give approximately 10% beyond 20 kpc, or specify 2% for all radii below 15 kpc. (LLM, conf=0.84)
Experimental — accuracy not yet measuredThe Eilers et al. (2019) analysis found a gentle decline of slope -1.7 ± 0.1 km s^-1 kpc^-1 over 5-25 kpc and inferred a virial mass of Mvir = (7.25 ± 0.26) × 10^11 M⊙ from an NFW fit.
“The early Eilers et al. (2019) analysis, using ∼ 23 000 red giant branch (RGB) stars with APOGEE spectroscopy and spectrophotometric distances, found a gentle decline of slope -1 . 7 ± 0 . 1 km s -1 kpc -1 over 5-25 kpc (with a reported systematic slope uncertainty of 0 . 46 km s -1 kpc -1 ) and inferred a virial mass of M vir = (7 . 25 ± 0 . 26) × 10 11 M ⊙ from an NFW fit, where the quoted mass”
From The rotation curve of the Milky Way: State of the art, the Keplerian decline debate, and implications for dark matter (2026) · cites this paper as Eilers et al., 2019
Section 5.1 reports a gentle decline of −1.7 ± 0.1 km s⁻¹ kpc⁻¹ across 5–25 kpc, and the Summary and Discussion reports an NFW-based virial mass of 7.25 × 10¹¹ M⊙. The quoted mass uncertainty does not match our copy: the Summary and Discussion gives ±0.25 × 10¹¹ M⊙, not ±0.26 × 10¹¹ M⊙. (LLM, conf=0.90)
Experimental — accuracy not yet measuredThe NFW virial mass of Eilers et al. (2019) was derived by fitting equation (32) to the RC; its quoted uncertainty is formal, while the authors estimated a 2-5% systematic uncertainty in the circular-speed normalisation.
“The NFW virial mass was derived by fitting equation (32) to the RC; its quoted uncertainty is formal, while the authors estimated a 2-5% systematic uncertainty in the circular-speed normalisation.”
From The rotation curve of the Milky Way: State of the art, the Keplerian decline debate, and implications for dark matter (2026) · cites this paper as Eilers et al. (2019)
Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measuredThe outermost Eilers et al. bins at R ≳ 18 kpc lie below their own NFW fit and are consistent, within their larger error bars, with the DR3 determinations.
“The outermost Eilers et al. bins at R ≳ 18 kpc lie below their own NFW fit and are consistent, within their larger error bars, with the DR3 determinations.”
From The rotation curve of the Milky Way: State of the art, the Keplerian decline debate, and implications for dark matter (2026) · cites this paper as Eilers et al. (2019)
The Summary and Discussion (page not available) reports outer-radius velocity measurements, a deviation around 19–21 kpc, and an NFW halo fit; Table 1 there shows larger uncertainties in several of the outermost bins. Our copy does not establish that the outermost bins as a group lie below the NFW fit, and it makes no comparison with DR3 determinations. (LLM, conf=0.85)
Experimental — accuracy not yet measured
The main constraining power of our model comes from the Eilers et al. (2019) circular velocity data.
“The main constraining power of our model comes from the Eilers et al. (2019) circular velocity data”
From The milky way total mass profile as inferred from Gaia DR2 (2020) · cites this paper as Eilers et al. 2019
Most of the constraining power comes from the Eilers et al. (2019) circular velocity data.
“We note that most of the constraining power comes from the Eilers et al. (2019) circular velocity data.”
From The milky way total mass profile as inferred from Gaia DR2 (2020) · cites this paper as Eilers et al. 2019
The Eilers et al. (2019) data are inferred from axisymmetric Jeans modelling of the six-dimensional phase space distribution of more than 23,000 red giant stars with precise parallax measurements.
“These data are inferred from axisymmetric Jeans modelling of the six-dimensional phase space distribution of more than 23,000 red giant stars with precise parallax measurements.”
From The milky way total mass profile as inferred from Gaia DR2 (2020) · cites this paper as Eilers et al. 2019
The contracted NFW halo model matches well the Eilers et al. (2019) and Callingham et al. (2019) measurements used for fitting.
“Figure 10 shows that the contracted NFW halo model matches well the Eilers et al. (2019) and Callingham et al. (2019) measurements, which were the ones used for the fitting procedure.”
From The milky way total mass profile as inferred from Gaia DR2 (2020) · cites this paper as Eilers et al. (2019)
The default analysis adds in quadrature an uncertainty of 0.21 σ_sys to the Eilers et al. rotation curve errors.
“ii) by adding in quadrature an uncertainty of 0 . 21 σ sys (black curve; this is the default approach used in our analysis)”
From The milky way total mass profile as inferred from Gaia DR2 (2020) · cites this paper as Eilers et al. (2019)
In the absence of model uncertainties, using only the Eilers et al. (2019) observational errors, the best-fit model has a reduced χ2 ≃ 2.
“In this case, the best fit model has a reduced χ 2 ≃ 2 .”
From The milky way total mass profile as inferred from Gaia DR2 (2020) · cites this paper as Eilers et al. (2019)
Eilers et al. (2019) results apply over R = 5-25 kpc.
“These results apply over R = 5-25 kpc.”
From The rotation curve of the Milky Way: State of the art, the Keplerian decline debate, and implications for dark matter (2026) · cites this paper as Eilers et al. (2019)
Eilers et al. (2019) established the pre-DR3 benchmark using 23 000 RGB stars with APOGEE spectroscopy.
“Eilers et al. (2019) established the pre-DR3 benchmark using 23 000 RGB stars with APOGEE spectroscopy.”
From The rotation curve of the Milky Way: State of the art, the Keplerian decline debate, and implications for dark matter (2026) · cites this paper as Eilers et al. (2019)
The Msph,30 cannot be ranked directly against NFW virial-mass estimates of (5-8) × 10^11 solar masses because those refer to a different radius and depend on halo extrapolation.
“It cannot be ranked directly against NFW virial-mass estimates of (5-8) × 10 11 M ⊙ (Eilers et al., 2019; Ou et al., 2024), because those refer to a different radius and depend on halo extrapolation.”
From The rotation curve of the Milky Way: State of the art, the Keplerian decline debate, and implications for dark matter (2026) · cites this paper as Eilers et al. (2019)
The inferred inner-plateau velocity is somewhat below the canonical vc(R0) approximately 229 km/s of Eilers et al. (2019).
“somewhat below the canonical vc ( R 0 ) ≈ 229 km s -1 of Eilers et al. (2019);”
From The rotation curve of the Milky Way: State of the art, the Keplerian decline debate, and implications for dark matter (2026) · cites this paper as Eilers et al. (2019)
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References 44 · Cited by 404
Research works printed but not linked: 5
- Binney, J., & Tremaine, S. 2008, Galactic Dynamics (2nd ed.; Princeton, NJ: Princeton Univ. Press)
- Eadie, G., & Jurić, M. 2018, arXiv:1810.10036 · arXiv
- Hogg, D. W., Eilers, A.-C., & Rix, H.-W. 2018, arXiv:1810.09468 · arXiv
- Watkins, L. L., van der Marel, R. P., Sohn, S. T., & Evans, N. W. 2018, arXiv:1804.11348 · arXiv
- Wegg, C., Gerhard, O., & Bieth, M. 2018, arXiv:1806.09635 · arXiv
- Authors
- Eilers, A.-C., Hogg, D. W., Rix, H.-W., & Ness, M. K.
- Affiliations
- Heidelberg University (DE)
- Max Planck Institute for Astronomy (DE)
- Flatiron Institute (US)
- Corresponding author
- Eilers, Anna-Christina
- Venue
- The Astrophysical Journal
- Publisher
- American Astronomical Society
- Published
- 2019-01-20
- Volume
- 871
- Issue
- 1
- Pages
- 120
- ISSN
- 0004-637X (ISSN-L)
- 1538-4357
- OpenAlex
- W2896737565
- Cited by
- 404
- References
- 44
- Citations by year
- 2026: 41 · 2025: 74 · 2024: 64 · 2023: 51 · 2022: 47 · 2021: 55 · 2020: 50 · 2019: 22
- FWCI
- 23.22
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- The Astrophysical Journal (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- National Aeronautics and Space Administration
- California Institute of Technology
- European Space Agency
- Flatiron Health
- Max-Planck-Institut für Astronomie
- Jet Propulsion Laboratory
- University of California, Los Angeles
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Stellar, planetary, and galactic studies
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Galaxies: Formation, Evolution, Phenomena
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Keywords
- Milky Way, circular velocity curves, dark matter halos, red giants, Jeans equation, galactic bars, dark matter density, baryonic mass distribution, APOGEE, Gaia, WISE, 2MASS
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