Letter | Published:

Absence of a fundamental acceleration scale in galaxies

Nature Astronomyvolume 2pages668672 (2018) | Download Citation


Dark matter is currently one of the main mysteries of the Universe. There is much strong indirect evidence that supports its existence, but there is yet no sign of a direct detection1,2,3. Moreover, at the scale of galaxies, there is tension between the theoretically expected dark matter distribution and its indirectly observed distribution4,5,6,7. Therefore, phenomena associated with dark matter have a chance of serving as a window towards new physics. The radial acceleration relation8,9 confirms that a non-trivial acceleration scale a0 can be found from the internal dynamics of several galaxies. The existence of such a scale is not obvious as far as the standard cosmological model is concerned10,11, and it has been interpreted as a possible sign of modified gravity12,13. Here, we consider 193 high-quality disk galaxies and, using Bayesian inference, show that the probability of existence of a fundamental acceleration is essentially 0: the null hypothesis is rejected at more than 10σ. We conclude that a0 is of emergent nature. In particular, the modified Newtonian dynamics theory14,15,16,17—a well-known alternative to dark matter based on the existence of a fundamental acceleration scale—or any other theory that behaves like it at galactic scales, is ruled out as a fundamental theory for galaxies at more than 10σ.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


  1. 1.

    Akerib, D. S. et al. Results from a search for dark matter in the complete LUX exposure. Phys. Rev. Lett. 118, 021303 (2017).

  2. 2.

    Aprile, E. et al. First dark matter search results from the XENON1T experiment. Phys. Rev. Lett. 119, 181301 (2017).

  3. 3.

    Liu, J., Chen, X. & Ji, X. Current status of direct dark matter detection experiments. Nat. Phys. 13, 212–216 (2017).

  4. 4.

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

  5. 5.

    Del Popolo, A. & Le Delliou, M. Small scale problems of the ΛCDM model: a short review. Galaxies 5, 17 (2017).

  6. 6.

    Bullock, J. S. & Boylan-Kolchin, M. Small-scale challenges to the ΛCDM paradigm. Ann. Rev. Astron. Astrophys. 55, 343–387 (2017).

  7. 7.

    Rodrigues, D. C., del Popolo, A., Marra, V. & de Oliveira, P. L. C. Evidences against cuspy dark matter halos in large galaxies. Mon. Not. R. Astron. Soc. 470, 2410–2426 (2017).

  8. 8.

    McGaugh, S., Lelli, F. & Schombert, J. Radial acceleration relation in rotationally supported galaxies. Phys. Rev. Lett. 117, 201101 (2016).

  9. 9.

    Li, P., Lelli, F., McGaugh, S. & Schormbert, J. Fitting the radial acceleration relation to individual SPARC galaxies. Preprint at https://arxiv.org/abs/1803.00022 (2018).

  10. 10.

    Ludlow, A. D. et al. Mass-discrepancy acceleration relation: a natural outcome of galaxy formation in cold dark matter halos. Phys. Rev. Lett. 118, 161103 (2017).

  11. 11.

    Navarro, J. F. et al. The origin of the mass discrepancy–acceleration relation in ΛCDM. Mon. Not. R. Astron. Soc. 471, 1841 (2017).

  12. 12.

    Lelli, F., McGaugh, S. S., Schombert, J. M. & Pawlowski, M. S. One law to rule them all: the radial acceleration relation of galaxies. Astrophys. J. 836, 152 (2017).

  13. 13.

    Smolin, L. MOND as a regime of quantum gravity. Phys. Rev. D96, 083523 (2017).

  14. 14.

    Milgrom, M. A modification of the Newtonian dynamics—implications for galaxies. Astrophys. J. 270, 371–389 (1983).

  15. 15.

    Sanders, R. H. & McGaugh, S. S. Modified Newtonian dynamics as an alternative to dark matter. Ann. Rev. Astron. Astrophys. 40, 263–317 (2002).

  16. 16.

    Famaey, B. & McGaugh, S. Modified Newtonian dynamics (MOND): observational phenomenology and relativistic extensions. Living Rev. Rel. 15, 10 (2012).

  17. 17.

    Milgrom, M. Road to MOND: a novel perspective. Phys. Rev. D92, 044014 (2015).

  18. 18.

    Famaey, B. & Binney, J. Modified Newtonian dynamics in the Milky Way. Mon. Not. R. Astron. Soc. 363, 603–608 (2005).

  19. 19.

    Gentile, G., Famaey, B. & de Blok, W. THINGS about MOND. Astron. Astrophys. 527, A76 (2011).

  20. 20.

    Hees, A., Famaey, B., Angus, G. W. & Gentile, G. Combined Solar System and rotation curve constraints on MOND. Mon. Not. R. Astron. Soc. 455, 449–461 (2016).

  21. 21.

    De Blok, W. J. G. & McGaugh, S. S. Testing modified Newtonian dynamics with low surface brightness galaxies: rotation curve FITS. Astrophys. J. 508, 132–140 (1998).

  22. 22.

    McGaugh, S. S., Schombert, J. M., Bothun, G. D. & de Blok, W. The baryonic Tully–Fisher relation. Astrophys. J. 533, L99–L102 (2000).

  23. 23.

    Dodelson, S. The real problem with MOND. Int. J. Mod. Phys. D20, 2749–2753 (2011).

  24. 24.

    Sanders, R. H. Clusters of galaxies with modified Newtonian dynamics (MOND). Mon. Not. R. Astron. Soc. 342, 901 (2003).

  25. 25.

    Angus, G. W. Are sterile neutrinos consistent with clusters, the CMB and MOND? Mon. Not. R. Astron. Soc. 394, 527 (2009).

  26. 26.

    Milgrom, M. Bimetric MOND gravity. Phys. Rev. D80, 123536 (2009).

  27. 27.

    Babichev, E., Deffayet, C. & Esposito-Farese, G. Improving relativistic MOND with Galileon k-mouflage. Phys. Rev. D84, 061502 (2011).

  28. 28.

    Verlinde, E. P. Emergent gravity and the Dark Universe. SciPost Phys. 2, 016 (2017).

  29. 29.

    Iocco, F., Pato, M. & Bertone, G. Testing modified Newtonian dynamics in the Milky Way. Phys. Rev. D92, 084046 (2015).

  30. 30.

    Randriamampandry, T. & Carignan, C. Galaxy mass models: MOND versus dark matter haloes. Mon. Not. R. Astron. Soc. 439, 2132–2145 (2014).

  31. 31.

    Lelli, F., McGaugh, S. S. & Schombert, J. M. SPARC: mass models for 175 disk galaxies with Spitzer photometry and accurate rotation curves. Astron. J. 152, 157 (2016).

  32. 32.

    Walter, F. et al. THINGS: the HI Nearby Galaxy Survey. Astron. J. 136, 2563–2647 (2008).

  33. 33.

    De Blok, W. J. G. et al. High-resolution rotation curves and galaxy mass models from THINGS. Astron. J. 136, 2648–2719 (2008).

  34. 34.

    Famaey, B., Khoury, J. & Penco, R. Emergence of the mass discrepancy–acceleration relation from dark matter–baryon interactions. J. Cosmol. Astropart. Phys. 1803, 038 (2018).

Download references


We thank S. McGaugh for clarifications regarding the SPARC sample and comments on a previous version of this paper. This work made use of SPARC (Spitzer Photometry & Accurate Rotation Curves) and of THINGS (The HI Nearby Galaxy Survey). D.C.R. and V.M. thank CNPq and FAPES for partial financial support. A.d.P. was supported by the Chinese Academy of Sciences and its President’s International Fellowship Initiative (grant number 2017 VMA0044). Z.D. thanks the Ministry of Science, Research and Technology of Iran for financial support.

Author information


  1. Center for Astrophysics and Cosmology, CCE, Federal University of Espírito Santo, Vitória, Brazil

    • Davi C. Rodrigues
    •  & Valerio Marra
  2. Department of Physics, CCE, Federal University of Espírito Santo, Vitória, Brazil

    • Davi C. Rodrigues
    •  & Valerio Marra
  3. Dipartimento di Fisica e Astronomia, Università di Catania, Catania, Italy

    • Antonino del Popolo
  4. Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, China

    • Antonino del Popolo
  5. INFN Sezione di Catania, Catania, Italy

    • Antonino del Popolo
  6. Department of Physics, Bu Ali Sina University, Hamedan, Iran

    • Zahra Davari


  1. Search for Davi C. Rodrigues in:

  2. Search for Valerio Marra in:

  3. Search for Antonino del Popolo in:

  4. Search for Zahra Davari in:


D.C.R. and A.d.P. proposed the study. D.C.R. developed the MAGMA package, performed the χ2 minimization analysis, and contributed to interpretation and design. V.M. developed the mBayes package, performed the Bayesian analysis, and contributed to interpretation and design. Z.D. carried out the THINGS sample analysis and raised issues that were essential for the beginning of this project. The first draft was written by D.C.R. and V.M., and all the authors contributed to its development.

Competing interests

The authors declare no competing interests.

Corresponding authors

Correspondence to Davi C. Rodrigues or Valerio Marra.

Supplementary information

  1. Supplementary Information

    Supplementary Figures 1–7, Supplementary Tables 1–3

  2. Supplementary Data 1

  3. Supplementary Data 2

About this article

Publication history