Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

The stellar orbit distribution in present-day galaxies inferred from the CALIFA survey


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.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Our orbit-based modelling illustrated for galaxy NGC 0001.
Fig. 2: The orbit-circularity λ z distribution for each of 300 CALIFA galaxies.
Fig. 3: The distribution of orbital components as function of galaxy mass.
Fig. 4: The relation between intrinsic orbital angular momentum and its two proxies, a galaxy’s ordered-to-random motion and geometric flattening.

Similar content being viewed by others


  1. Mo, H., van den Bosch, F. C. & White, S. Galaxy Formation and Evolution (Cambridge Univ. Press, Cambridge, 2010).

    Book  Google Scholar 

  2. White, S. D. M. & Rees, M. J. Core condensation in heavy halos—a two-stage theory for galaxy formation and clustering. Mon. Not. R. Astron. Soc. 183, 341–358 (1978).

    Article  ADS  Google Scholar 

  3. Lagos, C. d. P. et al. Quantifying the impact of mergers on the angular momentum of simulated galaxies. Preprint available at (2017).

  4. Röttgers, B., Naab, T. & Oser, L. Stellar orbits in cosmological galaxy simulations: the connection to formation history and line-of-sight kinematics. Mon. Not. R. Astron. Soc. 445, 1065–1083 (2014).

    Article  ADS  Google Scholar 

  5. Bird, J. C. et al. Inside out and upside down: tracing the assembly of a simulated disk galaxy using mono-age stellar populations. Astrophys. J. 773, 43 (2013).

    Article  ADS  Google Scholar 

  6. Sánchez, S. F. et al. CALIFA, the calar alto legacy integral field area survey. I. Survey presentation. Astron. Astrophys. 538, A8 (2012).

    Article  Google Scholar 

  7. Aihara, H. et al. The eighth data release of the sloan digital sky survey: first data from SDSS-III. Astrophys. J. Suppl. Ser. 193, 29 (2011).

    Article  ADS  Google Scholar 

  8. Walcher, C. J. et al. CALIFA: a diameter-selected sample for an integral field spectroscopy galaxy survey. Astron. Astrophys. 569, A1 (2014).

    Article  Google Scholar 

  9. Schwarzschild, M. Self-consistent models for galactic halos. Astrophys. J. 409, 563–577 (1993).

    Article  ADS  Google Scholar 

  10. Binney, J. Rotation and anisotropy of galaxies revisited. Mon. Not. R. Astron. Soc. 363, 937–942 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  11. Cappellari, M. et al. The SAURON project—X. The orbital anisotropy of elliptical and lenticular galaxies: revisiting the (V/σ, ε) diagram with integral-field stellar kinematics. Mon. Not. R. Astron. Soc. 379, 418–444 (2007).

    Article  ADS  Google Scholar 

  12. Emsellem, E. et al. The ATLAS3D project—III. A census of the stellar angular momentum within the effective radius of early-type galaxies: unveiling the distribution of fast and slow rotators. Mon. Not. R. Astron. Soc. 414, 888–912 (2011).

    Article  ADS  Google Scholar 

  13. Brough, S. et al. The SAMI Galaxy Survey: mass as the driver of the kinematic morphology–density relation in clusters. (2017).

  14. Obreja, A. et al. NIHAO VI. The hidden discs of simulated galaxies. Mon. Not. R. Astron. Soc. 459, 467–486 (2016).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  16. Weinzirl, T., Jogee, S., Khochfar, S., Burkert, A. & Kormendy, J. Bulge n and B/T in high-mass galaxies: constraints on the origin of bulges in hierarchical models. Astrophys. J. 696, 411–447 (2009).

    Article  ADS  Google Scholar 

  17. Comerón, S. et al. Breaks in thin and thick disks of edge-on galaxies imaged in the Spitzer Survey of Stellar Structure in Galaxies (S4G). Astrophys. J. 759, 98 (2012).

    Article  ADS  Google Scholar 

  18. Lagos, C.d. P. et al. Angular momentum evolution of galaxies in EAGLE. Mon. Not. R. Astron. Soc. 464, 3850–3870 (2017).

    Article  ADS  Google Scholar 

  19. Stinson, G. S. et al. Making galaxies in a cosmological context: the need for early stellar feedback. Mon. Not. R. Astron. Soc. 428, 129–140 (2013).

    Article  ADS  Google Scholar 

  20. Vogelsberger, M. et al. Introducing the illustris project: simulating the coevolution of dark and visible matter in the Universe. Mon. Not. R. Astron. Soc. 444, 1518–1547 (2014).

    Article  ADS  Google Scholar 

  21. Schaye, J. et al. The EAGLE project: simulating the evolution and assembly of galaxies and their environments. Mon. Not. R. Astron. Soc. 446, 521–554 (2015).

    Article  ADS  Google Scholar 

  22. Wang, L. et al. NIHAO project—I. Reproducing the inefficiency of galaxy formation across cosmic time with a large sample of cosmological hydrodynamical simulations. Mon. Not. R. Astron. Soc. 454, 83–94 (2015).

    Article  ADS  Google Scholar 

  23. Hopkins, P. F. et al. Galaxies on FIRE (Feedback In RealisticEnvironments): stellar feedback explains cosmologically inefficient star formation. Mon. Not. R. Astron. Soc. 445, 581–603 (2014).

    Article  ADS  Google Scholar 

  24. Falcón-Barroso, J. et al. Stellar kinematics across the Hubble sequence in the CALIFA survey: general properties and aperture corrections. Astron. Astrophys. 597, A48 (2017).

    Article  Google Scholar 

  25. Sánchez, S. F. et al. CALIFA, the Calar Alto legacy integral field area survey. IV. Third public data release. Astron. Astrophys. 594, A36 (2016).

    Article  Google Scholar 

  26. Cappellari, M. & Copin, Y. Adaptive spatial binning of integral-field spectroscopic data using Voronoi tessellations. Mon. Not. R. Astron. Soc. 342, 345–354 (2003).

    Article  ADS  Google Scholar 

  27. Kroupa, P. On the variation of the initial mass function. Mon. Not. R. Astron. Soc. 322, 231–246 (2001).

    Article  ADS  Google Scholar 

  28. Schwarzschild, M. A numerical model for a triaxial stellar system in dynamical equilibrium. Astrophys. J. 232, 236–247 (1979).

    Article  ADS  Google Scholar 

  29. van den Bosch, R. C. E., van de Ven, G., Verolme, E. K., Cappellari, M. & de Zeeuw, P. T. Triaxial orbit based galaxy models with an application to the (apparent) decoupled core galaxy NGC 4365. Mon. Not. R. Astron. Soc. 385, 647–666 (2008).

    Article  ADS  Google Scholar 

  30. Zhu, L., van den Bosch, R. & van de Ven, G. Orbital decomposition of CALIFA spiral galaxies. Mon. Not. R. Astron. Soc. 473, 3000–3018 (2018).

    Article  ADS  Google Scholar 

  31. Cappellari, M. Efficient multi-Gaussian expansion of galaxies. Mon. Not. R. Astron. Soc. 333, 400–410 (2002).

    Article  ADS  Google Scholar 

  32. Dutton, A. A. & Macciò, A. V. Cold dark matter haloes in the Planck era: evolution of structural parameters for Einasto and NFW profiles. Mon. Not. R. Astron. Soc. 441, 3359–3374 (2014).

    Article  ADS  Google Scholar 

  33. Falcón-Barroso, J. et al. Stellar kinematics across the Hubble sequence in the CALIFA survey: General properties and aperture corrections. Astron. Astrophys. 597, A48 (2017).

    Article  Google Scholar 

  34. Shen, J. et al. Our Milky Way as a pure-disk galaxy: a challenge for galaxy formation. Astrophys. J. Lett. 720, L72–L76 (2010).

    Article  ADS  Google Scholar 

  35. Grand, R. J. J. et al. The Auriga Project: the properties and formation mechanisms of disc galaxies across cosmic time. Mon. Not. R. Astron. Soc. 467, 179–207 (2017).

    ADS  Google Scholar 

  36. Nelson, D. et al. The Illustris simulation: public data release. Astron. Comput. 13, 12–37 (2015).

    Article  ADS  Google Scholar 

  37. Stinson, G. S. et al. NIHAO III: the constant disc gas mass conspiracy. Mon. Not. R. Astron. Soc. 454, 1105–1116 (2015).

    Article  ADS  Google Scholar 

  38. Marinacci, F. et al. Properties of H i discs in the Auriga cosmological simulations. Mon. Not. R. Astron. Soc. 466, 3859–3875 (2017).

    Article  ADS  Google Scholar 

  39. Barnes, J. & Hut, P. A hierarchical O(N log N) force-calculation algorithm. Nature 324, 446–449 (1986).

    Article  ADS  Google Scholar 

Download references


This study uses the data provided by the Calar Alto Legacy Integral Field Area (CALIFA) survey ( 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

Authors and Affiliations



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.

Corresponding author

Correspondence to Ling Zhu.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Tables 1–3, Supplementary Figures 1–4

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhu, L., Ven, G., Bosch, R. et al. The stellar orbit distribution in present-day galaxies inferred from the CALIFA survey. Nat Astron 2, 233–238 (2018).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing