Galaxy formation entails the hierarchical assembly of mass, along with the condensation of baryons and the ensuing, self-regulating star formation1,2. The stars form a collisionless system whose orbit distribution retains dynamical memory that can constrain a galaxy’s formation history3. The orbits dominated by ordered rotation, with near-maximum circularity λ z  ≈ 1, are called kinematically cold, and the orbits dominated by random motion, with low circularity λ z  ≈ 0, are kinematically hot. The fraction of stars on ‘cold’ orbits, compared with the fraction on ‘hot’ orbits, speaks directly to the quiescence or violence of the galaxies’ formation histories4,5. Here we present such orbit distributions, derived from stellar kinematic maps through orbit-based modelling for a well-defined, large sample of 300 nearby galaxies. The sample, drawn from the CALIFA survey6, includes the main morphological galaxy types and spans a total stellar mass range from 108.7 to 1011.9 solar masses. Our analysis derives the orbit-circularity distribution as a function of galaxy mass and its volume-averaged total distribution. We find that across most of the considered mass range and across morphological types, there are more stars on ‘warm’ orbits defined as 0.25 ≤ λ z  ≤ 0.8 than on either ‘cold’ or ‘hot’ orbits. This orbit-based ‘Hubble diagram’ provides a benchmark for galaxy formation simulations in a cosmological context.

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This study uses the data provided by the Calar Alto Legacy Integral Field Area (CALIFA) survey (http://califa.caha.es) based on observations collected at the Centro Astronómico Hispano Alemán at Calar Alto, operated jointly by the Max-Planck Institut für Astronomie and the Instituto de Astrofísica de Andalucía. We thank A. van der Wel, K. Jahnke, V. Debattista and M. Fouesneau for discussions. G.v.d.V. and J.F.-B. acknowledge support from the DAGAL network from the People Programme (Marie Curie Actions) of the European Unions Seventh Framework Programme FP7/2007–2013 under REA grant agreement number PITN-GA-2011-289313. G.v.d.V. also acknowledges support from the Sonderforschungsbereich SFB 881 “The Milky Way System” (subprojects A7 and A8) funded by the German Research Foundation, and funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 724857 (Consolidator grant ‘ArcheoDyn’). This work was supported by the National Science Foundation of China (grant no. 11333003, 11390372 to SM). A.O. has been funded by the Deutsche Forschungsgemeinschaft (German Research Foundation) – MO 2979/1–1. J.F.-B. acknowledges support from grant AYA2016-77237-C3-1-P from the Spanish Ministry of Economy and Competitiveness. R.J.J.G. acknowledges support by the DFG Research Centre SFB-881 ‘The Milky Way System’ through project A1.

Author information


  1. Max Planck Institute for Astronomy, Heidelberg, Germany

    • Ling Zhu
    • , Glenn van de Ven
    • , Remco van den Bosch
    • , Hans-Walter Rix
    •  & Marie Martig
  2. European Southern Observatory, Munich, Germany

    • Glenn van de Ven
    •  & Mariya Lyubenova
  3. Kapteyn Astronomical Institute, University of Groningen, Groningen, The Netherlands

    • Mariya Lyubenova
  4. Instituto de Astrofísica de Canarias (IAC), La Laguna, Tenerife, Spain

    • Jesús Falcón-Barroso
  5. Universidad de La Laguna, Dpto. Astrofísica, La Laguna, Tenerife, Spain

    • Jesús Falcón-Barroso
  6. Astrophysics Research Institute, Liverpool John Moores University, Liverpool, UK

    • Marie Martig
  7. Physics Department and Tsinghua Centre for Astrophysics, Tsinghua University, Beijing, China

    • Shude Mao
  8. National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China

    • Shude Mao
    •  & Yunpeng Jin
  9. Jodrell Bank Centre for Astrophysics, The University of Manchester, Manchester, UK

    • Shude Mao
  10. Heidelberg Institute for Theoretical Studies, Heidelberg, Germany

    • Dandan Xu
    •  & Robert J. J. Grand
  11. Universitäts-Sternwarte, Ludwig-Maximilians-Universität München, Munich, Germany

    • Aura Obreja
  12. New York University Abu Dhabi, Abu Dhabi, United Arab Emirates

    • Aura Obreja
    • , Aaron A. Dutton
    •  & Andrea V. Macciò
  13. Zentrum für Astronomie der Universität Heidelberg, Astronomisches Recheninstitut, Heidelberg, Germany

    • Robert J. J. Grand
  14. Instituto de Investigación Multidisciplinar en Ciencia y Tecnología, Universidad de La Serena, La Serena, Chile

    • Facundo A. Gómez
  15. Departamento de Física y Astronomía, Universidad de La Serena, La Serena, Chile

    • Facundo A. Gómez
  16. Leibniz-Institut für Astrophysik Potsdam (AIP), Potsdam, Germany

    • Jakob C. Walcher
  17. Instituto de Astrofísica de Andalucía (CSIC), Granada, Spain

    • Rubén García-Benito
  18. Osservatorio Astrofisico di Arcetri Largo Enrico Fermi 5, Florence, Italy

    • Stefano Zibetti
  19. Instituto de Astronomía, Universidad Nacional Autonóma de México, Mexico D.F., Mexico

    • Sebastian F. Sánchez


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Text, figures and interpretation are by L.Z., G.v.d.V., H.-W.R., M.M. and S.M. Modelling is by L.Z., R.v.d.B. and G.v.d.V. Observational data are from J.F.B., M.L., G.v.d.V., J.C.W., R.G.B., S.Z. and S.F.S. Methodology is by L.Z., D.X., Y.J., A.O., R.J.J.G., A.V.M., A.A.D. and F.A.G.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Ling Zhu.

Supplementary information

  1. Supplementary Information

    Supplementary Tables 1–3, Supplementary Figures 1–4