Galaxies have some pretty odd dynamical relations, two of which I find particularly interesting. One is the oddly simple Tully Fisher relation. The TFR is the tight relation between rotation speed and baryonic (normal matter like gas and stars) mass content. That's not a problem in itself - things which spin faster are more massive, big whoop. What's odd is that theoretical predictions show it should have a lot more scatter than it does. The second weird relation is that there's a neat correlation between the "wiggles" in a rotation curve and the baryonic density, which is unexpected because the mass - and therefore rotation speed - should be dominated by dark matter, not the baryons.
Why is this interesting ? Well, the neat relations between baryons and their own dynamics suggest a direct connection between the two, and that (arguably !) doesn't fit well with the idea of dark matter at all.
To test this idea of a direct mass-velocity link, it'd be nice to have something more fundamental than either the TFR or wiggly rotation curves. Both are similar in that they're relations between mass and speed, just on different scales, but both are also subject to a host of implicit assumptions that have nothing much to do with gravity or dynamics. That's where the radial acceleration relation is supposed to come charging to the rescue.
It turns out that there's a neat relation between the observed acceleration and the expected acceleration due to visible baryonic matter. This relationship isn't linear, but it does appear to be pretty tight. It's been said quite often that this is the fundamental relation from which the TFR and wiggly curves can ultimately be derived.
This latest paper looks at the wiggly aspect. In short, it says, "actually no, this isn't what's making things all wiggly"*. And that could well be a problem for anyone trying to rid the universe of dark matter... but it also has problems for everyone else too. Everyone's a loser !
* Sadly not in these exact words.
The paper starts with the best introduction on the problem I've ever seen. According to the standard dark matter paradigm, galaxies of similar rotation speed should have rotation curves of very similar shapes. But as they show, they don't. Some galaxies do get it about right, but others, despite having the same outer rotation speed, can have curves which rise too quickly or too slowly, but in either case are well outside the standard model's predictions.
What could be going on here ? They note four possible explanations. (1) Since there's never very much dark matter in the innermost regions of galaxies, all the baryonic material slooshing about could be disrupting the dark matter there by dragging it around gravitationally, thus mucking up the rotation curves. (2) Or, more radically, dark matter could be self-interacting and so change its own distribution. (3) On the other hand it could be something as mundane as observational errors in extracting the true rotation velocity. (4) Finally, it could indeed be there's a more direct relationship between baryons and dynamics, as RAR enthusiasts generally seem to prefer because that would be extremely cool.
They investigate all these possibilities by using a whole suite of the latest all-singing, all-dancing, super high resolution simulations. And not just one specific model either, but four of the darn things (they also comment quite a lot on real observations, which is nice).
INTERMISSION
... but first, a word on terminology, because it's truly barbaric. As in the literal, original meaning of the word : "bar bar" nosies that don't make any sense. Galaxies which have slowly rising rotation curves are called "cored", because it looks like their inner dark matter has a fixed density within some "core" region. Those with curves matching theoretical expectations are deemed to be "cuspy" because the density continues to rise right down to the very centre (blowed if I know when "cusp" became a synonym of "spike"). And those which rotate too quickly in the centre don't have a special term at all, presumably due to racism or something.
Let's sort this mess out before we go any further. Sod convention, it's confusing because it's stupid. I shall use the following :
- Galaxies with inner curves that rise too slowly, and therefore seem to lack dark matter in their centres, are to be known as "lazy buggers".
- Galaxies with inner curves that match theoretical predictions I shall call "boring bastards".
- Galaxies with inner curves that rise too quickly, so having more inner mass than expected, are to be known as "greedy bitches" (I ran out of profanities beginning with b, although at the time of writing Wikipedia assures me that "Brexiteer" is also vulgar slang).
Got that ? Good.
WE NOW RETURN TO OUR FEATURE PRESENTATION
1. It's due to the baryons doing funky things in the centre of galaxies
This doesn't work well at all. As they say, only (real, observed) galaxies with low overall baryon densities show slowly-rising rotation curves, but not all low density galaxies show this : some are perfectly normal, others rise too fast. Those with the slowest rises - the laziest buggers - imply they have the least inner dark matter, meaning they need the strongest movement of baryons (through supernovae and suchlike) to disturb it. That in turns means they should have the lowest overall baryonic density... but they don't. So baryonic density alone can't be the direct cause of these relations.
While we're at it, this also means that it the oddities can't simply be due to the sheer mass of baryons either - except for the greedy bitches. These, they say, are relatively easy to explain as being galaxies which have more inner baryons than normal, rather than there being anything weird about the dark matter (presumably they have the same central spike as the boring bastards, but with extra baryons thrown in as well). It's the lazy buggers which are the real problem.
What about simulations ? None of them are able to reproduce the full range of observed properties. Some do better than others, and it does depend on the resolution and the properties of star formation and feedback that's used. But in the end, it seems that either all simulated galaxies are lazy buggers or boring bastards (and I guess greedy bitches as well) : they can't get a mix of both. Maybe there's a sweet spot if they were to fine-tune the simulations really carefully, but this wouldn't be a natural solution.
2. Dark matter is self-interacting
If dark matter could collide with itself, this would stop it from building a massive central spike. The problem is that this should lead to all galaxies becoming lazy buggers, and greedy bitches would be harder to explain : they'd have to have much stronger excesses of baryons than normal galaxies. And too many baryons means extremely high star formation activity, so the resulting supernovae and stellar winds should eventually prevent further baryonic infall. Worse, there are many greedy bitches which don't have many baryons, as well as lazy buggers which do have lots of baryons in their inner regions.
Using both analytic and numerical models, they quantify that this idea doesn't work. Oh, it can work, they say, if you very carefully choose the properties of the dark matter halos. But it's not at all likely to work given the distribution that naturally falls out of simulations. I'm not sure this is terribly convincing, given how many parameters there might be to play with for self-interacting dark matter, but never mind.
3. We're interpreting the velocities incorrectly
We infer dark matter by assuming that the measured velocities correspond to those of stable circular orbits. But maybe it's not as simple as that, since the orbits might not be neat circles - especially given the shape of the dark matter halo. That couldn't mean we've got the whole dark matter paradigm itself wrong, but it could mean we've interpreted the wiggly curves in a silly way.
They make mock observations from the simulations and this idea does seem to basically work. Individual galaxies could be completely misclassified according to the measurements, and it reproduces the scatter in the rotation curves very well. So this could indeed by a major contributing factor. What spoils this is that many lazy buggers show well-ordered velocity fields where non-circular motions don't seem very likely, and the fact that all lazy buggers are of low density - and there's no obvious reason, they say, why low density galaxies should be more prone to non-circular motions than dense ones. I'd have thought the lower density makes them more vulnerable to internal effects, but that needs a lot more examination. Anyway, this seems like the best bet so far.
4. It's an effect of the radial acceleration relation
The big one. This relation was touted as a "new law of physics", much to everyone's disgust, but it does have an appeal : it gets back to fundamental physics instead of all that wishy-washy baryonic stuff. As they say, if this is truly a law, you should be able to derive the rotation curve from baryon distribution alone.
(Of course, it isn't truly a law at all - it's a rather subtle effect of galaxy scaling relations, and is very well reproduced in perfectly normal simulations that use standard physics. But let's indulge the speculation for the sake of interest)
If that's true, then knowing the baryonic distribution for any galaxy, you should be able to predict if it has a wiggly curve of any type, from boring bastard to lazy bugger. Can you ? No, you can't. Using the RAR to predict the dynamical relations gets a much lower scatter than the observations. In particularly, baryon-rich lazy buggers should not exist according to the RAR, but they patently do.
Another issue is that RAR-enthusiasts have this tendency to plot the data with 2D histograms, so that more densely-populated regions on the expected-observed acceleration plot are more visible. This is good for discerning the possibly underlying trend, but it reduces the visible scatter. Here, they don't do this trick, and show the data as raw points. Although most galaxies do follow the trend well (rather better, I think, than the "only approximately" the authors state), it's clear the scatter is pretty large. And the outlying galaxies are, very clearly, all lazy buggers.
Couldn't we combine this with the the idea that the velocities have been misinterpreted ? In fact, we'd have to, since the RAR doesn't predict the observed deviations. But they say that if the same velocity measurements used to derive the RAR are deemed to be wrong, that would undermine the basis for the RAR in the first place - essentially, unjustly throwing away data points that don't fit the trend. At the very least, the RAR is quite definitely not enough by itself to explain things... if you're allowed to say that these galaxies have errors, you need some reason to say why these galaxies in particular and not the others.
What's both nice and frustrating about this paper is that they don't come to any firm conclusions. Practically any scenario could probably explain the trend with enough work, but none is entirely satisfactory. So something of a mystery remains, although to my mind the problem of interpreting the velocities looks by far the most promising.
As to their main point about RAR not being a law, this feels a bit like a highly ingenious way to say what we already knew : there's very high scatter at the low accelerations. Although I'm not at all convinced RAR is any kind of fundamental breakthrough, I don't think they here sufficiently explained why it couldn't be that the outliers had problems with their velocities. It's a really nice piece of work, but it left me scratching my head and going "hmmm" more than I would like.
Baryonic clues to the puzzling diversity of dwarf galaxy rotation curves
We use a compilation of disc galaxy rotation curves to assess the role of the luminous component ("baryons") in the rotation curve diversity problem. As in earlier work, we find that rotation curve shape correlates with baryonic surface density: high surface density galaxies have rapidly-rising rotation curves consistent with cuspy cold dark matter halos; slowly-rising rotation curves (characteristic of galaxies with inner mass deficits or "cores") occur only in low surface density galaxies.
