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An intuitive 3D map of the Galactic warp’s precession traced by classical Cepheids


The Milky Way’s neutral hydrogen (H i) disk is warped and flared1,2. However, a dearth of accurate H i-based distances has thus far prevented the development of an accurate Galactic Disk model. Moreover, the extent to which our Galaxy’s stellar and gas disk morphologies are mutually consistent is also unclear. Classical Cepheids, primary distance indicators with distance accuracies of 3–5% (ref. 3), offer a unique opportunity to develop an intuitive and accurate three-dimensional picture. Here, we establish a robust Galactic Disk model based on 1,339 classical Cepheids. We provide strong evidence that the warp’s line of nodes is not oriented in the Galactic Centre–Sun direction. Instead, it subtends a mean angle of 17.5° ± 1° (formal) ± 3° (systematic) and exhibits a leading spiral pattern. Our Galaxy thus follows Briggs’ rule for spiral galaxies4, which suggests that the origin of the warp is associated with torques forced by the massive inner disk5. The stellar disk traced by Cepheids follows the gas disk in terms of their amplitudes; the stellar disk extends to at least 20 kpc (refs. 6,7). This morphology provides a crucial, updated map for studies of the kinematics and archaeology of the Galactic Disk.

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Fig. 1: Three-dimensional map of the Milky Way’s disk traced by Cepheids.
Fig. 2: Maximum z heights of the warps.
Fig. 3: The Milky Way’s LON.
Fig. 4: Representation of the Milky Way’s flare as traced by Cepheids.

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Data availability

The full data set of our Cepheid sample is available in Supplementary Data 1. In general, the data supporting the plots in this paper and other findings of this study are available from the corresponding author upon reasonable request.


  1. Levine, E. S., Blitz, L. & Heiles, C. The vertical structure of the outer Milky Way H i disk. Astrophys. J. 643, 881–896 (2006).

    Article  ADS  Google Scholar 

  2. Kalberla, P. M. W., Dedes, L., Kerp, J. & Haud, U. Dark matter in the Milky Way. II. The H i gas distribution as a tracer of the gravitational potential. Astron. Astrophys. 469, 511–527 (2007).

    Article  ADS  Google Scholar 

  3. Wang, S., Chen, X., de Grijs, R. & Deng, L. The near-infrared optimal distances method applied to Galactic classical Cepheids tightly constrains mid-infrared period–luminosity relations. Astrophys. J. 852, 78 (2018).

    Article  ADS  Google Scholar 

  4. Briggs, F. H. Rules of behavior for Galactic warps. Astrophys. J. 352, 15–29 (1990).

    Article  ADS  Google Scholar 

  5. Shen, J. & Sellwood, J. A. Galactic warps induced by cosmic infall. Mon. Not. R. Astron. Soc. 370, 2–14 (2006).

    Article  ADS  Google Scholar 

  6. Liu, C., Xu, Y., Wang, H. & Wan, J. Rediscovering the Galactic outer disk with LAMOST data. Proc. Int. Astron. Union Vol. 13 (eds Chiappini, C., Minchev, I., Starkenberg, E. & Valentini, M.) 109–115 (International Astronomical Union, 2018).

  7. Wang, H., Liu, C., Xu, Y., Wan, J. & Deng, L. Mapping the Milky Way with LAMOST—III. Complicated spatial structure in the outer disc. Mon. Not. R. Astron. Soc. 478, 3367–3379 (2018).

    Article  ADS  Google Scholar 

  8. Chen, X., Wang, S., Deng, L., de Grijs, R. & Ming, Y. Wide-field Infrared Survey Explorer (WISE) catalog of periodic variable stars. Astrophys. J. Suppl. Ser. 273, 28 (2018).

    Article  ADS  Google Scholar 

  9. Chen, X., Wang, S., Deng, L. & de Grijs, R. An extremely low mid-infrared extinction law toward the Galactic Center and 4% distance precision to 55 classical Cepheids. Astrophys. J. 859, 137 (2018).

    Article  ADS  Google Scholar 

  10. Gaia Collaboration. Gaia Data Release 2. Summary of the contents and survey properties. Astron. Astrophys. 616, A1 (2018).

  11. Haario, H., Laine, M., Mira, A. & Saksman, E. DRAM: efficient adaptive MCMC. Stat. Comput. 16, 339–354 (2006).

    Article  MathSciNet  Google Scholar 

  12. Abedi, H. et al. Characterizing the Galactic warp with Gaia—I. The tilted ring model with a twist. Mon. Not. R. Astron. Soc. 442, 3627–3642 (2014).

    Article  ADS  Google Scholar 

  13. Drimmel, R. & Spergel, D. N. Three-dimensional structure of the Milky Way Disk: the distribution of stars and dust beyond 0.35 R 0. Astrophys. J. 556, 181–202 (2018).

    Article  ADS  Google Scholar 

  14. López-Corredoira, M., Cabrera-Lavers, A., Garzón, F. & Hammersley, P. L. Old stellar Galactic Disc in near-plane regions according to 2MASS: scales, cut-off, flare and warp. Astron. Astrophys. 394, 883–899 (2002).

    Article  ADS  Google Scholar 

  15. Yusifov, I. Pulsars and the warp of the Galaxy. In The Magnetized Interstellar Medium: Proc. Conference held in Antalya, Turkey (eds Uyaniker, B., Reich, W. & Wielebinski, R.) 165–169 (Copernicus GmbH, 2004).

  16. Skrutskie, M. F. et al. The Two Micron All Sky Survey (2MASS). Astron. J. 131, 1163–1183 (2006).

    Article  ADS  Google Scholar 

  17. Amores, E. B., Robin, A. C. & Reylé, C. Evolution over time of the Milky Way’s disc shape. Astron. Astrophys. 602, A67 (2017).

    Article  ADS  Google Scholar 

  18. Poggio, E. et al. The Galactic warp revealed by Gaia DR2 kinematics. Mon. Not. R. Astron. Soc. 481, L21–L25 (2018).

    Article  ADS  Google Scholar 

  19. Burton, W. B. in Galactic and Extragalactic Radio Astronomy 2nd edn (eds Verschuur, G. & Kellermann, K.) 295–358 (Springer-Verlag, Berlin and New York, 1988).

  20. Momany, Y. et al. Outer structure of the Galactic warp and flare: explaining the Canis Major over-density. Astron. Astrophys. 451, 515–538 (2006).

    Article  ADS  Google Scholar 

  21. Bland-Hawthorn, J. & Gerhard, O. The Galaxy in context: structural, kinematic, and integrated properties. Annu. Rev. Astron. Astrophys. 54, 529–596 (2016).

    Article  ADS  Google Scholar 

  22. de Grijs, R. & Bono, G. Clustering of local group distances: publication bias or correlated measurements? IV. The Galactic Center. Astrophys. J. Suppl. Ser. 227, 5 (2016).

    Article  ADS  Google Scholar 

  23. Freedman, D. & Diaconis, P. On the histogram as a density estimator: L2 theory. Probab. Theory Relat. Fields 57, 453–476 (1981).

    MATH  Google Scholar 

  24. Reid, M. J. et al. Trigonometric parallaxes of high mass star forming regions: the structure and kinematics of the Milky Way. Astrophys. J. 783, 130 (2014).

    Article  ADS  Google Scholar 

  25. Schonrich, R., Binney, J. & Dehnen, W. Local kinematics and the local standard of rest. Mon. Not. R. Astron. Soc. 403, 1829–1833 (2010).

    Article  ADS  Google Scholar 

  26. Antoja, T. et al. A dynamically young and perturbed Milky Way disk. Nature 561, 360–362 (2018).

    Article  ADS  Google Scholar 

  27. Freeman, K. C. On the disks of spiral and S0 galaxies. Astrophys. J. 160, 811–830 (1970).

    Article  ADS  Google Scholar 

  28. Feast, M. W., Menzies, J. W., Matsunaga, N. & Whitelock, P. A. Cepheid variables in the flared outer disk of our Galaxy. Nature 509, 342–344 (2014).

    Article  ADS  Google Scholar 

  29. Berdnikov, L. N. VizieR Online Data Catalog: Photoelectric Observations of Cepheids in UBV(RI)c II/285 (2008).

  30. Soszyński, I. et al. The OGLE collection of variable stars. Classical Cepheids in the Magellanic system. Acta Astron. 65, 297–312 (2015).

    ADS  Google Scholar 

  31. Fernie, J. D., Evans, N. R., Beattie, B. & Seager, S. A database of Galactic classical Cepheids. Inform. Bull. Variable Stars 4148, 1 (1995).

    ADS  Google Scholar 

  32. Pojmanski, G., Pilecki, B. & Szczygiel, D. The All Sky Automated Survey. Catalog of variable stars. V. Declinations 0°–+28° of the Northern Hemisphere. Acta Astron. 55, 275–301 (2005).

    ADS  Google Scholar 

  33. Samus, N. N., Kazarovets, E. V., Durlevich, O. V., KireevaN. N.. & Pastukhova, E. N. General catalogue of variable stars: version GCVS 5.1. Astron. Rep. 61, 80–88 (2017).

    Article  ADS  Google Scholar 

  34. Jayasinghe, T. et al. The ASAS-SN catalogue of variable stars. I. The Serendipitous Survey. Mon. Not. R. Astron. Soc. 477, 3145–3163 (2018).

    Article  ADS  Google Scholar 

  35. Heinze, A. N. et al. A first catalog of variable stars measured by the Asteroid Terrestrial-impact Last Alert System (ATLAS). Astron. J. 156, 241 (2018).

  36. Clementini, G. et al. Gaia Data Release 2: Specific characterisation and validation of all-sky Cepheids and RR Lyrae stars. Astron. Astrophys. (in the press).

  37. Churchwell, E. et al. The Spitzer/GLIMPSE surveys: a new view of the Milky Way. Publ. Astron. Soc. Pac. 121, 213–230 (2009).

    Article  ADS  Google Scholar 

  38. Wright, E. L. et al. The Wide-field Infrared Survey Explorer (WISE): mission description and initial on-orbit performance. Astron. J. 140, 1868–1881 (2010).

    Article  ADS  Google Scholar 

  39. Chen, X., de Grijs, R. & Deng, L. New open cluster Cepheids in the VVV survey tightly constrain near-infrared period–luminosity relations. Mon. Not. R. Astron. Soc. 464, 1119–1126 (2017).

    Article  ADS  Google Scholar 

  40. Matsunaga, N. et al. Three classical Cepheid variable stars in the nuclear bulge of the Milky Way. Nature 477, 188–190 (2011).

    Article  ADS  Google Scholar 

  41. Dékány, I. et al. The VVV survey reveals classical Cepheids tracing a young and thin stellar disk across the Galaxy's bulge. Astrophys. J. 812, L29 (2015).

    Article  ADS  Google Scholar 

  42. Inno, L. et al. New NIR light-curve templates for classical Cepheids. Astron. Astrophys. 576, 30 (2015).

    Article  Google Scholar 

  43. Freedman, W. L. et al. Carnegie Hubble Program: a mid-infrared calibration of the Hubble constant. Astrophys. J. 758, 24 (2012).

    Article  ADS  Google Scholar 

  44. Matsunaga, N. et al. Impact of distance determinations on Galactic structure. I. Young and intermediate-age tracers. Space Sci. Rev. 214, 74 (2018).

    Article  ADS  Google Scholar 

  45. Zasowski, G. et al. Lifting the dusty veil with near- and mid-infrared photometry. II. A large-scale study of the Galactic infrared extinction law. Astrophys. J. 707, 510–523 (2009).

    Article  ADS  Google Scholar 

  46. Xue, M. et al. A precise determination of the mid-infrared interstellar extinction law based on the APOGEE spectroscopic survey. Astrophys. J. Suppl. Ser. 224, 23 (2016).

    Article  ADS  Google Scholar 

  47. Indebetouw, R. et al. The wavelength dependence of interstellar extinction from 1.25 to 8.0 μm using GLIMPSE data. Astrophys. J. 619, 931–938 (2005).

    Article  ADS  Google Scholar 

  48. Cardelli, J. A., Clayton, G. C. & Mathis, J. S. The relationship between infrared, optical, and ultraviolet extinction. Astrophys. J. 345, 245–256 (1989).

    Article  ADS  Google Scholar 

  49. Riess, A. et al. Milky Way Cepheid standards for measuring cosmic distances and application to Gaia DR2: implications for the Hubble constant. Astrophys. J. 861, 126 (2018).

    Article  ADS  Google Scholar 

  50. Wouterloot, J. G. A., Brand, J., Burton, W. B. & Kwee, K. K. IRAS sources beyond the solar circle. II Distribution in the Galactic warp. Astron. Astrophys. 230, 21–36 (1990).

    ADS  Google Scholar 

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We are grateful for research support from the National Key Basic Research Program of China 2014CB845700. This work is also supported by the National Natural Science Foundation of China through grants U1631102, 11373010 and 11633005, the Initiative Postdocs Support Program (No. BX201600002), the China Postdoctoral Science Foundation (grant 2017M610998) and the National Key Research and Development Program of China (grant 2017YFA0402702).

Author information

Authors and Affiliations



X.C. contributed to the project planning, data preparation and analysis, modelling, simulations and writing of the final paper. S.W. contributed to the data analysis and writing of the paper. L.D. contributed to project planning and research support. R.d.G. engaged in detailed scientific discussions and contributed to writing of the paper and final editing. C.L. contributed to the exploration of the warp’s precession. H.T. contributed to implementation of the techniques used for the modelling and simulations. All authors reviewed and commented on the manuscript.

Corresponding authors

Correspondence to Xiaodian Chen, Shu Wang or Licai Deng.

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The authors declare no competing interests.

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Supplementary information

Supplementary Information

Supplementary Tables 1–2; Supplementary Video 1 caption; Supplementary Data 1 caption; Supplementary Figs. 1–5.

Supplementary Video 1

3D animation of Fig. 1a.

Supplementary Data 1

Cepheid catalogue used in the research.

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Chen, X., Wang, S., Deng, L. et al. An intuitive 3D map of the Galactic warp’s precession traced by classical Cepheids. Nat Astron 3, 320–325 (2019).

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