The RAR is the relation between the acceleration due to baryons and the acceleration due to dark matter. This has been measured in galaxies and it's found that there's a very tight relation between the two. This is surprising, since the mass of dark matter is heavily dominant over the baryons - you might expect that there should be a lot more scatter. But then people realised that this happened in their simulations anyway, pretty much exactly in agreement with observation.
What seems to be going on is that there's a characteristic regime in which galaxies form. You don't get galaxies above or below certain mass thresholds, thus avoiding extremely high and low accelerations, and the density profiles of dark matter halos tends to be similar. So as you move radially outwards in any galaxy, the acceleration experienced changes in the same characteristic way. Furthermore, although the baryons don't interact with dark matter except through gravity, that interaction can be strong enough to cause selection effects as to where stars form. The RAR, then, is just the result of several quite subtle but powerful and entirely expected selection effects.
The RAR was initially very interesting to modified gravity supporters, who'd predicted it ahead of time. At best, it now looks as though there's no way to distinguish between the predictions of standard dark matter theories and those of modified gravity - both give identical results. But what if we looked at totally different systems ?
This paper extends the results to galaxy clusters. If RAR is the result of modified gravity theories that predict a characteristic acceleration, the same sort of relation ought to be visible in any system, on any scale, bound by gravity. Hence the effort here to test it in galaxy clusters.
The procedure needs some adaptations. In individual galaxies, you can measure how fast the gas and stars are actually moving and directly measure their densities. So you can calculate their acceleration due to their observed baryonic mass and compare this with their actual acceleration (knowing their velocity, distance from the centre of the galaxy, and assuming stable circular orbits), which is dominated by the dark matter.
In clusters things aren't so elegant. Galaxy orbits can be trick to compute, and it's not safe to assume they're moving in neat circles. Instead, the authors use measurements of the hot intracluster gas. Unlike galaxies, the gas motion is heavily influenced by its own thermal pressure keeping it from collapsing into a dense lump in the centre, so its actual acceleration is not dominated by the dark matter. It seems the authors are able to account for this and estimate the acceleration due to dark matter without the pressure from the baryons, as well as the acceleration from the baryonic mass alone. So this should be a fair comparison with the galaxy-based RAR, which is based on only gravitational effects.
They find that the cluster-based RAR is strongly deviant from the galaxy-based relation. It seems that it does not behave in a universal, acceleration-dependent way : there is no evidence for a universal acceleration scale. Which is very odd if this is due to gravity, as MOND predicts.
Case closed for alternative theories of gravity ? They say their result does impact certain theories, but not necessarily MOND itself. Here it gets highly confused. I applaud the authors sterling efforts to remain impartial, but I think they may be going too far, exploring too many ifs and buts in too short a space, sacrificing clarity for brevity. For instance they say the calculated characteristic acceleration is almost ten times larger than the expected standard MOND value, but then immediately say that this is also somehow consistent with MOND. In support of this they cite two enormously long papers, and I'm just not interested enough to read either of them. They mention all sorts of possible modifications to MOND, like relativistic versions or even including some dark matter, which just makes the whole message hard to discern. Does the damn thing work or not ?
I know MOND behaves in a radically different way to Newtonian gravity, but I'm having an increasingly hard time buying it as a sensible theory. Gravity that works differently on different scales and still requires dark matter ? Were the issue just about galaxy rotation curves, there would be no philosophical advantage to either MOND or dark matter. But the more complex things get, the more contrived the alterations to MOND seem to become. MOND feels ever more like a bizarre and unnecessary solution, offering not a single advantage over dark matter - it now seems so complex that it's little better than magic. I'd rather postulate an unknown type of matter than accept a theory that breaks basic physics like this. I could be wrong, of course, but basic intuition is hard to surrender.
EDIT : Barely days later, here's another paper trying much the same thing. It's somewhat easier to follow in its conclusions but more difficult for its method. They use lensing for the total mass and the hot gas for the baryons, but I cannot see anywhere where they describe how they calculate the accelerations. They seem to find a broadly similar RAR as the first paper and conclude that there is no universal RAR. Their acceleration constant is much closer to the ordinary MOND value - the slope of their RAR is similar to previous calculations but the intercept is different. They say their results are consistent with CDM, but they completely avoid any discussion on MOND (probably wisely).
The radial acceleration relation in galaxy clusters
Recently, the discovery of the radial acceleration relation (RAR) in galaxies has been regarded as an indirect support of alternative theories of gravity such as Modified Newtonian Dynamics (MOND) and modified gravity. This relation indicates a tight correlation between dynamical mass and baryonic mass in galaxies with different sizes and morphology.
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