Over a Triton Station there was an exchange of comments that made a good point about a distinction between MOND and dark matter particle theories that is worthy of being elevated to a post here (reformatted and with emphasis added, italic text within brackets is mine).
In a nutshell, MOND won't give you predictions about inferred dark matter equivalents when a system is out of equilibrium but it will tell you if a system is out of equilibrium and thus MOND can't be applied straightforwardly to it. For the most part, this conclusion should generalized to any modified gravity theory that would give rise to what are usually understood as dark matter phenomena.
QUESTION: David Schroeder April 14, 2020 at 8:19 am
As a fan of MOND I was a bit shocked to read the latest Starts With A Bang article by Ethan Siegel about the dwarf galaxy Segue 1, which reputedly has a visible mass of only 175 suns, but needs a whopping 600,000 solar masses of Dark Matter to explain internal motions. Might it be possible that external field effects are distorting the motions of this galaxy”s stars to mimic a much greater mass than is actually there?
ANSWER:tritonstation April 14, 2020 at 9:46 am
This has been known for over a decade, so kinda puzzled why it is “news” now.
In order to estimate the dark matter mass, one assumes that a system is in dynamical equilibrium. That’s usually a good assumption. Here, it is a terrible assumption.
Segue 1, and very nearly all of the so-called ultrafaint dwarfs, are deep in the potential of the Milky Way where they are subject to strong tidal forces. This violates the assumption of equilibrium, in any theory. There is an eternal energy source: the stars are not just responding to their own gravitational field (and that of ‘their own’ dark matter). Thus it is likely that the motions of the stars have been stirred up by the external field so that the dynamical mass is overstated.
In the dark matter galaxy formation picture, one expects small galaxies like this to be accreted by larger galaxies like the Milky Way. In that process, they are tidally stripped. First the outer parts of their dark matter halo, then down to the stars, then ultimately they’re shredded completely. There’s no good way to tell how far along this process Segue 1 is, but it and the other ulrtafaints dwarfs are the poster children for hierarchical accretion.
In MOND, I had initially thought this was a huge problem (see https://arxiv.org/abs/1003.3448). The external field effect, by itself, does not explain this observation. Long story short, it turns out that tidal effects are even stronger in MOND, and the assumption of dynamical equilibrium certainly does not hold. So – same problem.
There is one difference: in MOND, there is a quantitative criterion for when an object is not in equilibrium (see https://arxiv.org/abs/astro-ph/0005194). All of the ultrafaints, including Segue 1, fail to meet this criterion [ed. i.e. they are out of equilibrium according to the quantitative test]. There is no chance that the measured velocity dispersion reflects the equilibrium value of an isolated system. Indeed, one can see the onset of this effect in the data (see Figs 6 and 7 of arxiv:1003.3448). From that perspective, this is another successful prediction of MOND: it not only predicts correctly the velocity of stars in equilibrium systems, it also tells you when it can’t.
There is no equivalent criterion in dark matter. If things don’t work out, we infer that the system is out of equilibrium. The difference is that MOND tells you when this must be invoked. All the famous cases (e.g., And XIX, Crater 2, and a half dozen others whose names I don’t recall offhand) that are now considered to be out of equilibrium in dark matter were predicted in advance by MOND.
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