Abstract
The shape of the dark matter (DM) halo is key to understanding the hierarchical formation of the Galaxy. Despite extensive efforts in recent decades, however, its shape remains a matter of debate, with suggestions ranging from strongly oblate to prolate. Here, we present a new constraint on its present shape by directly measuring the evolution of the Galactic disk warp with time, as traced by accurate distance estimates and precise age determinations for about 2,600 classical Cepheids. We show that the Galactic warp is mildly precessing in a retrograde direction at a rate of ω = −2.1 ± 0.5 (statistical) ± 0.6 (systematic) km s−1 kpc−1 for the outer disk over the Galactocentric radius [7.5, 25] kpc, decreasing with radius. This constrains the shape of the DM halo to be slightly oblate with a flattening (minor axis to major axis ratio) in the range 0.84 ≤ qΦ ≤ 0.96. Given the young nature of the disk warp traced by Cepheids (less than 200 Myr), our approach directly measures the shape of the present-day DM halo. This measurement, combined with other measurements from older tracers, could provide vital constraints on the evolution of the DM halo and the assembly history of the Galaxy.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 digital issues and online access to articles
$119.00 per year
only $9.92 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
Data availability
The Cepheids data used in this paper are publicly available from the Gaia Archive: https://archives.esac.esa.int/gaia. The other data supporting the plots in this paper and other findings of this study are available from the corresponding authors upon reasonable request.
Code availability
We use standard data analysis tools in the Python environments, including methods in Astropy, NumPy, Matplotlib, SciPy and emcee. All these packages are publicly available through the Python Package Index (https://pypi.org). Specifically, the fit analysis in this study was performed using the Python package scipy.curve_fit and emcee.
References
Kerr, F. J. A Magellanic effect on the Galaxy. Astron. J. 62, 93 (1957).
Burke, B. F. Systematic distortion of the outer regions of the Galaxy. Astron. J. 62, 90 (1957).
Sancisi, R. Warped H i disks in galaxies. Astron. Astrophys. 53, 159–161 (1976).
López-Corredoira, M. et al. Old stellar Galactic disc in near-plane regions according to 2MASS: scales, cut-off, flare and warp. Astron. Astrophys. 394, 883–899 (2002).
Chen, X. et al. An intuitive 3D map of the Galactic warp’s precession traced by classical Cepheids. Nat. Astron. 3, 320–325 (2019).
Skowron, D. M. et al. A three-dimensional map of the Milky Way using classical Cepheid variable stars. Science 365, 478–482 (2019).
Binney, J. Warps. Annu. Rev. Astron. Astrophys. 30, 51–74 (1992).
Shen, J. & Sellwood, J. A. Galactic warps induced by cosmic infall. Mon. Not. R. Astron. Soc. 370, 2–14 (2006).
Jiang, I.-G. & Binney, J. WARPS and cosmic infall. Mon. Not. R. Astron. Soc. 303, L7–L10 (1999).
Jeon, M., Kim, S. S. & Ann, H. B. Galactic warps in triaxial halos. Astrophys. J. 696, 1899–1917 (2009).
Sparke, L. S. & Casertano, S. A model for persistent galactic warps. Mon. Not. R. Astron. Soc. 234, 873–898 (1988).
Dubinski, J. & Chakrabarty, D. Warps and bars from the external tidal torques of tumbling dark halos. Astrophys. J. 703, 2068–2081 (2009).
Weinberg, M. D. & Blitz, L. A Magellanic origin for the warp of the Galaxy. Astrophys. J. Lett. 641, L33–L36 (2006).
Battaner, E., Florido, E. & Sanchez-Saavedra, M. L. Intergalactic magnetic field and galactic warps. Astron. Astrophys. 236, 1–8 (1990).
Poggio, E. et al. Evidence of a dynamically evolving Galactic warp. Nat. Astron. 4, 590–596 (2020).
Cheng, X. et al. Exploring the Galactic warp through asymmetries in the kinematics of the Galactic disk. Astrophys. J. 905, 49–63 (2020).
Chrobáková, Ž. & López-Corredoira, M. A case against a significant detection of precession in the Galactic warp. Astrophys. J. 912, 130–138 (2021).
Dehnen, W., Semczuk, M. & Schönrich, R. A twisted and precessing Cepheid warp in the outer Milky Way disc. Mon. Not. R. Astron. Soc. 523, 1556–1564 (2023).
Gaia Collaboration. Gaia Data Release 3. Summary of the content and survey properties. Astron. Astrophys. 674, A1–A22 (2022).
Ripepi, V. et al. Gaia Data Release 3. Specific processing and validation of all sky RR Lyrae and Cepheid stars: the Cepheid sample. Astron. Astrophys. 674, A17–A51 (2022).
Hao, C. J. et al. Open clusters housing classical Cepheids in Gaia DR3. Astron. Astrophys. 668, A13–A25 (2022).
De Somma, G. et al. Period–age–metallicity and period–age–colour–metallicity relations for classical Cepheids: an application to the Gaia EDR3 sample. Mon. Not. R. Astron. Soc. 508, 1473–1488 (2021).
Zhou, X. & Chen, X. Galactic open cluster Cepheids – a census based on Gaia EDR3. Mon. Not. R. Astron. Soc. 504, 4768–4787 (2021).
Poggio, E. et al. The kinematic signature of the Galactic warp in Gaia DR1. I. The Hipparcos subsample. Astron. Astrophys. 601, A115–A128 (2017).
Burton, W. B. in Galactic and Extragalactic Radio Astronomy (eds Verschuur, G. L. & Kellermann, K. I.) 295–358 (Springer, 1988).
Li, X.-Y. et al. Mapping the Galactic disk with the LAMOST and Gaia red clump sample. IV. The kinematic signature of the Galactic warp. Astrophys. J. 901, 56–61 (2020).
Han, J. J., Conroy, C. & Hernquist, L. A tilted dark halo origin of the Galactic disk warp and flare. Nat. Astron. 7, 1481–1485 (2023).
Sanders, J. L. & Binney, J. Stream–orbit misalignment. II. A new algorithm to constrain the Galactic potential. Mon. Not. R. Astron. Soc. 433, 1826–1836 (2013).
Bovy, J. et al. The shape of the inner Milky Way Halo from observations of the Pal 5 and GD–1 stellar streams. Astrophys. J. 833, 31–45 (2016).
Bowden, A., Belokurov, V. & Evans, N. W. Dipping our toes in the water: first models of GD-1 as a stream. Mon. Not. R. Astron. Soc. 449, 1391–1440 (2015).
Küpper, A. H. W. et al. Globular cluster streams as Galactic high-precision scales—the poster child Palomar 5. Astrophys. J. 803, 80–105 (2015).
Loebman, S. R. et al. The Milky Way tomography with Sloan Digital Sky Survey. V. Mapping the dark matter halo. Astrophys. J. 794, 151–176 (2014).
Wegg, C., Gerhard, O. & Bieth, M. The gravitational force field of the Galaxy measured from the kinematics of RR Lyrae in Gaia. Mon. Not. R. Astron. Soc. 485, 3296–3316 (2019).
Posti, L. & Helmi, A. Mass and shape of the Milky Way’s dark matter halo with globular clusters from Gaia and Hubble. Astron. Astrophys. 621, A56–A65 (2019).
Cataldi, P. et al. Redshift evolution of the dark matter haloes shapes. Mon. Not. R. Astron. Soc. 523, 1919–1932 (2023).
GRAVITY Collaboration. A geometric distance measurement to the Galactic center black hole with 0.3% uncertainty. Astron. Astrophys. 625, L10–L19 (2019).
Jurić, M. et al. The Milky Way tomography with SDSS. I. Stellar number density distribution. Astrophys. J. 673, 864–914 (2008).
Schönrich, R., Binney, J. & Dehnen, W. Local kinematics and the local standard of rest. Mon. Not. R. Astron. Soc. 403, 1829–1833 (2010).
Reid, M. J. & Brunthaler, A. The proper motion of Sagittarius A*. II. The mass of Sagittarius A*. Astrophys. J. 616, 872–884 (2004).
Clementini, G. et al. Gaia Data Release 3. Specific processing and validation of all-sky RR Lyrae and Cepheid stars: the RR Lyrae sample. Astron. Astrophys. 674, A18–A69 (2023).
Negueruela, I. et al. Berkeley 51, a young open cluster with four yellow supergiants. Mon. Not. R. Astron. Soc. 477, 2976–2990 (2018).
Feast, M. W. & Catchpole, R. M. The Cepheid period-luminosity zero-point from HIPPARCOS trigonometrical parallaxes. Mon. Not. R. Astron. Soc. 286, L1–L5 (1997).
Hayden, M. R. et al. Chemical cartography with APOGEE: large-scale mean metallicity maps of the Milky Way disk. Astron. J. 147, 116–131 (2014).
Huang, Y. et al. On the metallicity gradients of the Galactic disk as revealed by LSS-GAC red clump stars. Res. Astron. Astrophys. 15, 1240–1263 (2015).
da Silva, R. et al. Oxygen, sulfur, and iron radial abundance gradients of classical Cepheids across the Galactic thin disk. Astron. Astrophys. 678, A195–A215 (2023).
Zhou, Y. et al. The circular velocity curve of the Milky Way from 5–25 kpc using luminous red giant branch stars. Astrophys. J. 946, 73–87 (2023).
Antoja, T. et al. A dynamically young and perturbed Milky Way disk. Nature 561, 360–362 (2018).
Flynn, C. et al. On the mass-to-light ratio of the local Galactic disc and the optical luminosity of the Galaxy. Mon. Not. R. Astron. Soc. 372, 1149–1160 (2016).
Bovy, J. & Rix, H.-W. A direct dynamical measurement of the Milky Way’s disk surface density profile, disk scale length, and dark matter profile at 4 kpc < R̃ < 9̃ kpc. Astrophys. J. 779, 115–144 (2013).
Bland-Hawthorn, J. & Gerhard, O. The Galaxy in context: structural, kinematic, and integrated properties. Annu. Rev. Astron. Astrophys. 54, 529–569 (2016).
Navarro, J. F., Frenk, C. S. & White, S. D. M. The structure of cold dark matter halos. Astrophys. J. 462, 563–575 (1996).
Binney, J. & Tremaine, S. Galactic Dynamics 2nd edn (Princeton Univ. Press, 2008).
Acknowledgements
Y.H. acknowledges the National Key R&D Programme of China (Grant No. 2019YFA0405503) and the National Science Foundation of China (NSFC; Grant Nos. 11903027 and 11833006). T.K. acknowledges support from the NSFC (Grant No. 12303013) and support from the China Postdoctoral Science Foundation (Grant No. 2023M732250). H.W.Z. acknowledges the National Key R&D Programme of China (Grant No. 2019YFA0405504) and the NSFC (Grant Nos. 12090040 and 12090044). J.F.L. acknowledges support from the NSFC (Grant Nos. 11988101 and 11933004) and support from the New Cornerstone Science Foundation through the New Cornerstone Investigator Programme and the XPLORER PRIZE. J.S. acknowledges support from the NSFC (Grant Nos. 12025302 and 11773052), support from the 111 Project of the Ministry of Education of China (Grant No. B20019) and support from the China Manned Space Project (Grant No. CMS-CSST-2021-B03). J.S. also acknowledges support from a Newton Advanced Fellowship awarded by the Royal Society and the Newton Fund. J.S. also acknowledges support from the Gravity Supercomputer at the Department of Astronomy, Shanghai Jiao Tong University, and the Center for High Performance Computing at Shanghai Astronomical Observatory. T.C.B. acknowledges partial support for this work from an award by the US National Science Foundation to the Physics Frontier Center/JINA Center for the Evolution of the Elements (Grant No. PHY 14-30152) and from an award by the US National Science Foundation to the International Research Network for Nuclear Astrophysics (Grant No. OISE-1927130). S.W. acknowledges support from the NSFC (Grant No. 12273057). We also express thanks for the valuable suggestions and comments from the Frontier Discussion of Top Sciences, regularly held at the National Astronomical Observatories, Chinese Academy of Sciences, where we presented the main results of this study on 28 October 2022. This work presents results from the European Space Agency’s space mission Gaia. Gaia data are processed by the Gaia Data Processing and Analysis Consortium, which is funded by national institutions, in particular the institutions participating in the Gaia MultiLateral Agreement. The Gaia mission website is https://www.cosmos.esa.int/gaia. The Gaia Archive website is https://archives.esac.esa.int/gaia.
Author information
Authors and Affiliations
Contributions
Y.H. contributed to the design of this project and writing of the final paper. Q.K.F. contributed to sample preparation, modelling and data analysis and wrote the manuscript together with Y.H. T.K. contributed to the data analysis and revisions of the text. H.W.Z. contributed to the project planning and research support. J.F.L. contributed to the design of this project and revised the text. T.C.B. contributed to the interpretation and revisions of the text. J.S. contributed to the theoretical computation of the warp-precession rate, interpretation of the result and text revision. Y.J.L. contributed to the interpretation of the result. S.W. and H.B.Y. contributed to the data analysis and revisions of the text.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature Astronomy thanks the anonymous reviewers for their contribution to the peer review of this work.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Extended data
Extended Data Fig. 1 The age distribution of our final Cepheid sample.
Their ages are derived by the PAZ relation. Most of our sample stars are younger than 200 Myr.
Extended Data Fig. 2 The spatial distribution of the final sample of 2,613 Cepheids.
(a) The X -Y projection. The black dot and red star represent the location of the Galactic centre and the Sun, respectively. (b) The Y - Z projection. The red line denotes the best-fit model with Galactic azimuth angle ϕ = ± 50∘. Note that the warp amplitude is exaggerated, as the Y - Z axes are not on the same scale.
Extended Data Fig. 3 The residual precession rates, after subtracting the disk contributions, in the three radial bins.
In the range of 2 to 4 kpc for Rd,thin, all the residual precession rates are clearly non-zero.
Supplementary information
Supplementary Information
Supplementary Figs. 1–10.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Huang, Y., Feng, Q., Khachaturyants, T. et al. A slightly oblate dark matter halo revealed by a retrograde precessing Galactic disk warp. Nat Astron (2024). https://doi.org/10.1038/s41550-024-02309-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s41550-024-02309-5
