Rotation curves of galaxies seem to require more mass than observed - the conventional solution is the introduction of Dark Matter.

Reading some articles on this topic (in particular a recent philosophical investigation of cosmology) showed a remarkable relation between the apparent missing mass of galaxies and the acceleration at that position of the galaxy (Fig 2 in the article):

enter image description here The x-axis is the acceleration, and the y-axis stands for the apparent mass-discrepancy. The data-points stem from many different galaxies and positions within those galaxies As it is known, the further out [=smaller acceleration] one looks, the larger the apparent requirement for dark matter.

Discovery of this particular plot go back to a paper in 1990 by Sanders. Unfortunatly I was not able to find any theoretical explanation from the standard-model of cosmology ΛCDM. Why would dark matter behave exactly like that - as far as I understand, predictable from visibile matter?

Concretely, my two questions:

  1. How can this phenomenon be described with ΛCDM?
  2. Is it related to a recent article on rotational velocities in PRL, which finds also very simple empirical laws on galaxy rotations without the need of dark matter?

2 Answers 2


The mass-discrepancy-acceleration relation is one of the many ways people have been observing that there is an acceleration scale in the rotation curves of galaxies. To see this more clearly, you can realise that the velocity and acceleration are related as $V^2/r = a$, so that $V^2/V_{N}^2 = a/a_N$, where $a$ is the effective radial acceleration. Your plot is then talking about the relation between the observed and expected radial acceleration. This is also the subject of the paper of McGaugh, Lelli, and Schombert from (2016) which you link, so I will treat both these results as the same issue.

One of the historically earliest observations of these kind of relations would be the baryonic Tully-Fisher relation discovered in 1977. What one essentially sees in the rotation curves is that for gravitational acceleration well above a certain $g_0 \approx 10^{-10} m s^{-2}$, the rotation curves agree with the one computed from Newtonian gravity and the presence of matter, and for accelerations where Newtonian theory would predict acceleration well below $g_0$, there is a discrepancy.

This lead M. Milgrom to publish a paper in 1983 proposing a possible modification of Newtonian gravity which implements this acceleration scale in a framework called MOND. By fitting this one parameter $g_0$, MOND is then able to reproduce any of the mass-discrepancy-acceleration or Tully-Fisher relations almost perfectly. The paper of McGaugh, Lelli, and Schombert from (2016) does a fit closely analogous to what Milgrom did, just on new data.

In the framework of $\Lambda$CDM, one can explain this tight acceleration relation across galaxies as emergent from a combination of non-linear and dissipative effects. Specifically, Keller & Wadsley (2017) included dissipative collapse of baryons in their cosmological simulation and obtained exactly the relations you link to. I would not say that this issue is entirely settled, and surely more work has to be invested to fully understand this universal acceleration scale in cosmology.

  • $\begingroup$ @NiceDean Well, MOND is exactly taking the acceleration scale identifiable in the Mass-Dicrepancy-Acceleration relation and implementing it in some kind of theory. Additionally the PRL paper you link essentially uses a MOND prescription of this sort. I thought that this was obvious, but perhaps I should clarify this. $\endgroup$
    – Void
    Dec 10, 2017 at 19:10
  • $\begingroup$ @NiceDean I see, you can then understand the comments on MOND as redundant, the paper of Keller & Wadsley I link and shortly comment on still provides an answer to your question. $\endgroup$
    – Void
    Dec 10, 2017 at 19:51

Void's answer is perfectly good, but I'll add a couple of thoughts anyway, specifically addressing your "concrete questions".

Regarding how this phenomenon can be reconciled with ΛCDM, to put it very simply the proposed picture is that galaxies do not form randomly in their dark matter halos: there are strong correlations between the size, (stellar/gas) mass and halo mass. The origin of these correlations is not especially straightforward - galaxy formation is a complicated physics problem - but one of the empirical results is the existence of such correlations. It happens that these correlations give rise to the mass discrepancy-acceleration relation (MDAR). Galaxies could in principle exist that do not lie on the relation, but it seems that the laws of nature do not cause these to form. These sorts of arguments have been discussed recently in e.g. Di Cintio & Lelli (2016), Keller & Wadsley (2017), Ludlow et al. (2017), Navarro et al. (2017). (For transparency's sake, I am an author on the last two.)

As to whether the MDAR is related to the relation discussed in the McGaugh, Lelli & Schombert (2016) PRL paper you linked, yes, very much so: what they term the radial acceleration relation (RAR) is really just the MDAR parametrized slightly differently. Indeed, the latter 3 papers I linked above were published as more or less direct responses to the PRL article, and F. Lelli is a common author on the remaining one.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.