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Reply to ‘Presence of a fundamental acceleration scale in galaxies’ and ‘A common Milgromian acceleration scale in nature’

Nature Astronomy volume 2, pages 927–929 (2018)Cite this article

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Rodrigues et al. reply — The correspondences by McGaugh et al.1 and Kroupa et al.2 question our results3 (hereafter R18). In essence, they state that our results are in conflict with Li et al.4 (hereafter L18) and criticize the priors that we used in our analysis. We show that L18 has no implication for our results and that our priors are adequate for our analysis.

We were generous with the Υ* constraints: we used flat priors in a 3σ interval7 centred on the disk and bulge values that most favour the fundamental a0 interpretation5. For D we used a 20% flat prior on the SPARC reference values for all of the galaxies, without considering the merits of each type of distance estimation. The chosen tolerance is larger than the median value of the relative uncertainties (14%). Considering the comments by Kroupa et al.2, flat priors provide larger credible intervals than using the corresponding Gaussian priors. Also, if a galaxy cannot be well fitted with this constraint, it is removed from our sample due to our quality cuts3. That said, it is worthwhile to evaluate the dependence of our results on the galaxies with the largest relative uncertainties — this is shown in Fig. 2. By removing either galaxies with distance uncertainties larger than 20% or those measured from the Hubble flow, a fundamental acceleration scale is still rejected at more than 10σ (see also R18 for further details).

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Fig. 1: Analyses of the χ2ν CDF.
Fig. 2: Posterior probability distributions of a0.

References

  1. McGaugh, S. S., Li, P., Lelli, F. & Schombert, J. M. Nat. Astron. https://doi.org/10.1038/s41550-018-0615-9 (2018).

  2. Kroupa, P. et al. Nat. Astron. https://doi.org/10.1038/s41550-018-0622-x (2018).

  3. Rodrigues, D. C., Marra, V., Del Popolo, A. & Davari, Z. Nat. Astron. 2, 668–672 (2018).

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  4. Li, P., Lelli, F., McGaugh, S. & Schormbert, J. Astron. Astrophys. 615, A3 (2018).

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Acknowledgements

D.C.R. and V.M. thank CNPq and FAPES (Brazil) for partial financial support. A.D.P. was supported by the Chinese Academy of Sciences and by the President’s International Fellowship Initiative, grant number 2017 VMA0044. Z.D. thanks the Ministry of Science, Research and Technology of Iran for financial support.

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Authors and Affiliations

  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. Dipartamento di Fisica e Astronomia, Università di Catania, Catania, Italy

    Antonino Del Popolo

  4. Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, People’s Republic of 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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  1. Davi C. Rodrigues
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  2. Valerio Marra
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  4. Zahra Davari
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Correspondence to Davi C. Rodrigues or Valerio Marra.

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Rodrigues, D.C., Marra, V., Del Popolo, A. et al. Reply to ‘Presence of a fundamental acceleration scale in galaxies’ and ‘A common Milgromian acceleration scale in nature’. Nat Astron 2, 927–929 (2018). https://doi.org/10.1038/s41550-018-0614-x

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