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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.

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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


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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.

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    Supplementary Figures 1–7, Supplementary Tables 1–3

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