Since the MDAR is back in the news on arXiv again, and I had a 5-hour train trip without wifi, I decided to catch up on my reading. I read this paper last year when it came out, but I never got around to annotating it or translating it into a slightly friendlier form.

For those who've forgotten all about it, there was a great furore last year because of a discovery in galaxy dynamics that didn't seem to fit the standard model. Specifically, there's a relationship between the acceleration predicted by the measured mass and distribution of stars and gas and the acceleration they're observed to be experiencing. Why is that weird and why would anyone care about some obscure piece of mathematical analysis ? Wouldn't they rather be eating cake ?

Possibly. But the MDAR[1] is quite interesting[2]. A whole slew of observations and theory have pointed to the need for dark matter to dominate galaxy rotation, typically by a factor of a few to a few tens. Ordinary (baryonic) matter is just the icing on the rich, deliciously dark cake[3]. So there ought to be a strong discrepancy between the acceleration predicted just from normal matter (without accounting for dark matter) and its observed value. Naively, we might not expect there to be much of a relationship at all, with galaxies lying all over the shop. The mass of baryonic matter shouldn't really tell us anything about the dark matter.

[1] Mass Discreprency Acceleration Relation. Or maybe it's RAR, the Radial Acceleration Relation. Different authors seem to prefer different things, so I'm going with MDAR.
[2] So interesting that people started calling it a new law of nature, which made a lot of people very upset.
[3] I'm hungry.

But that's not what was found. Although there isn't a neat 1:1 correlation, there is a very tight relation between the normal and dark matter. In effect, the mass of the normal matter allows you to predict with a fair precision the mass of dark matter. This was exactly what everyone's favourite alternative gravity theory (MOND) has long predicited.

In response to this there was a slew of papers back and forth by the various sides trying to work out if this was a really cool discovery or if it was all just a bit silly. Almost instantly, papers came out showing that the MDAR happened in standard model simulations without any tweaking whatsoever. No-one gave a clear explanation as to why it happened, much to the disgust of the MOND supporters, but happen it certainly did.

This paper attempts to provide that explanation. And it's not exactly simple, so bear with me.

In the standard model, galaxies which form in isolation can only do so in a quite narrow range of dark matter "halo" masses. Or more specifically, detectable galaxies. Too small and supernovae blast out all the gas, or hot young stars blow it out with strong winds, preventing any more star formation. Dark matter halos might well exist below this lower limit, but they can't host detectable galaxies. Going in the other direction, galaxies which become too massive have powerful feedback from active galactic nuceli (supermassive black holes with accretion discs and jets and whatnot) and the gas takes longer to cool and form stars. So galaxy growth is heavily restricted.

That means, in effect, that you can't get galaxies outside a certain, reasonably narrow acceleration window : no discs ever rotate faster than ~300 km/s, and none slower than ~30 km/s. Since their size doesn't vary all that much, neither does their acceleration.

Above a characteristic acceleration, all galaxies are dominated by their baryons - making the relationship of predicted/observed acceleration steeper the closer you get to this acceleration value. The baryon/dark matter ratio, which varies with total mass, is something that's reasonably (though not brilliantly) already predicted by the cold dark matter (CDM) model.

In addition, CDM makes a very specific prediction for how the dark matter is distributed within each halo, whereas stars, we know from observations, are distributed quite differently. All of this combines to give a very tight behaviour of the acceleration of matter within a galaxy. In the inner regions it tends to be dominated by the dense baryonic matter, whereas in the outer regions it's more about the dark matter. And you can't observe the acceleration beyond a certain radius (where acceleration is very low and dark matter dominated) because the detectable matter just doesn't extend that far - or equivalently, below a certain characteristic acceleration.

This lower acceleration is pretty close to the value where dark matter dominates. So for galaxies of very low baryonic content, at any radius they will be more strongly dominated by dark matter than baryons - and so the MDAR becomes shallower (and you only get galaxies of very low baryon content at low total masses), and galaxies tend to deviate a bit more from the standard MDAR relation. Moreover, if you consider the acceleration variation within individual (faint, low mass) galaxies , it will still be dominated by dark matter at all points, giving the same characteristic slope. Hence the MDAR is visible if consider either entire galaxies (choosing some well-defined point at which to measure their acceleration) or the acceleration at many points within each galaxy.

Another, more crude way to think about this is to imagine you're sitting at the edge of a galaxy's stellar disc, inasmuch as it ever has one. You'll be experiencing some acceleration due to the stars and some due to the dark matter. The more massive the galaxy, the more important the stars are : CDM explains pretty well why larger galaxies are better at forming stars; at any given galaxy mass, you must, therefore, be experiencing some very particular acceleration. But if you move around within any galaxy, your acceleration varies in a very similar way to changing the galaxy's mass, because the shape of the dark matter profile and stellar distribution are closely connected. It's the dark matter controlling things, not the stars : but that still means you can go the other way around and use the stars to examine the dark matter.

So there's no magic here. It's not a silly discovery, but it doesn't point to any new physics either. MOND can do it, but CDM can do it too. Lately I've been witnessing a lot of abuse of the word "consistency", which is necessary but not sufficient for evidence to favour one position over another. Taken purely by itself, if your information is consistent with theory X, that by no means automatically makes it inconsistent with theory Y - which may be radically different or even opposite to theory X ! A dead cow is consistent with alien mutilation, but it's also consistent with El Chupacabra, a werewolf, and a very hungry carnivorous ostrich named Derek.

Could the MDAR still prove interesting ? Well, if more regimes of acceleration could be probed, then possibly. There should be more deviations at the low-mass end, where dark matter dominates - and that seems in fact to be the case. Low baryonic mass galaxies in massive dark matter halos would also be interesting, but they don't seem to exist. Galaxies which are forming in the early universe might be so rich in baryons that they might probe much higher accelerations than the ones we see today, but we don't have good data for those yet. What would be especially interesting would be an isolated galaxy (galaxies which are interacting with each other can do whatever fancy shennangigans they like; all of these predictions are concerned with isolated objects) that deviates from MDAR, which CDM would find problematic. It would also be pretty awful for MOND supporters, so we'd all be up the proverbial creek together, merrily singing a jaunty tune as the canoe sinks beneath us, and nobody would get any cake at all.

Well anyway, that's my attempt to make this paper understandable without (hopefully) being woefully innacurate. For more on the MDAR and the assorted angry rants it triggered :
... which I'll update soon to account for this, now that I think I finally understand it.
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