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.

Absence of a fundamental acceleration scale in galaxies

Matters Arising to this article was published on 27 January 2020


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.

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

Access options

Rent or buy this article

Prices vary by article type



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

Fig. 1: Posterior probability distributions of a0 for the galaxies of the SPARC database.
Fig. 2: Comparison of the RAR with the standard and simple interpolating functions.


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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. Li, P., Lelli, F., McGaugh, S. & Schormbert, J. Fitting the radial acceleration relation to individual SPARC galaxies. Preprint at (2018).

  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

Authors and Affiliations



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.

Corresponding authors

Correspondence to Davi C. Rodrigues or Valerio Marra.

Ethics declarations

Competing interests

The authors declare no competing interests.

Supplementary information

Supplementary Information

Supplementary Figures 1–7, Supplementary Tables 1–3

Supplementary Data 1

Supplementary Data 2

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rodrigues, D.C., Marra, V., del Popolo, A. et al. Absence of a fundamental acceleration scale in galaxies. Nat Astron 2, 668–672 (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