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.
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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.
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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.
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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.
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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.
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Supplementary Figs. 1–10.
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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
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DOI: https://doi.org/10.1038/s41550-024-02309-5