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Thursday 3 August 2017

This Isn't The Law You're Looking For

I have a mental guideline for judging both the accuracy of press releases and scientific claims alike :
The value of a press release and the probability that the reported discovery is correct is anti-correlated with the grandiosity of the claims.
If a press release makes astonishing claims, then the chances are that it's a mistranslation from the original research article. Sadly, scientists tend to be such poor communicators that it's hard to judge if that was the case or not from the press release alone - you have to go back to the source. But the validity of the claim itself doesn't need this, whether it's in the press release or the original paper. You don't need to go back to the source to work out if, "SCIENTISTS SAY BABIES ARE SOLE CAUSE OF HEROIN ADDICTION" is bunk, and you don't need that much prior knowledge to know that, "Our research decisively rules out the existence of gravity" is also bunk.

So when scientists claim in both press releases and the original paper a discovery that's "tantamount to a new natural law", it's pretty hard to take them seriously. Claiming the discovery of a new natural law is pretty close to top of the Tree of Grandiosity. Claiming that you yourself have discovered this law, without there being any previous discussion about it (let alone a consensus) is in the uppermost branches, almost tantamount (see how insignificant that word becomes ?) to declaring, "I AM THE NEXT EINSTEIN ! COWER, BRIEF MORTALS ! LOOK UPON MY WORKS, YE MIGHTY, AND DESPAIR !".

What's this all about then ? Enter the plucky challenger, the Mass Discrepancy Acceleration Relation. Or not, because if you're looking for a concise explanation of what it's all about then you've come to the wrong place. You big silly.

MDAR : The Prelude

Galaxies, we think, are dominated by their dark matter in terms of mass. This still-mysterious and hidden component generally makes up around 90% of the mass of a galaxy, often a good deal more. Since it's gravity (i.e. mass) which dominates how things orbit within a galaxy, the dark matter should dominate internal motions. There shouldn't be much, or any, correlation between the density of normal matter and its orbital speed.

Of course gravity isn't the sole force at work. Stellar winds and supernovae also play their role, sometimes very dramatically. Occasionally we see how huge collective winds from young star clusters (which, like all young offender institutions, contain the most violent and literally explosive youngsters) drive enormous outflows of material deep into extragalactic space. Galaxies are so cool that even their vomit is beautiful.

The galaxy M82 as seen with Hubble. The two red plumes are hot, ionised hydrogen. It's thought that there's an intense starburst region near its centre, where young stars produce enormous winds and explosions that drives material outwards. 
Such winds are often produced near the centres of galaxies, where the star formation can be particularly vigorous. But there are other ways to produce a so-called "Active Galactic Nucleus". Indeed these days the term AGN is almost synonymous with another spectacular phenomenon : a supermassive black hole.

Hercules A, which features huge jets (see in radio emission in red) thought to be powered by matter orbiting around a black hole.
But such features are by far the exception rather than the rule. Many galaxies have star formation, of course, but at nice sedate levels. It also tends to occur somewhat randomly, so it's rare to see it driving large-scale outflows. The exact details of how and where stars form are complicated, to say the least.

So in normal galaxies it's the dark matter which should dominate. And it does, in that the rotation speed seems to require this enormous amount of extra material to prevent galaxies from flying apart. Yet when we look at the rotation speed in more detail, we see something more complicated. We don't usually see nice smooth curves describing how the rotation varies throughout the galaxy - we see little wiggles.
Rotation speed against distance from the centre for a bunch of galaxies, from this paper. The dots are the measurements, the solid lines are model fits. The wiggles are small, and the measurement errors of comparable size (the authors note that the true uncertainty may be about twice as large as these "formal errors", which in my experience is a good rule of thumb).
The size of the wiggles appears to be correlated with the mass of gas and stars, as though the stars and gas were influencing the dark matter. Which they shouldn't be able to do, since there's so much more dark matter than normal matter. It's not quite like throwing the proverbial peanut at the proverbial rhinoceros - a bag of sugar would be a better analogy.

It probably wouldn't be a good idea, but it's safe to say that the 1 kg bag of sugar wouldn't be able to move two tonnes of rhino except by annoying it.
How strange is this ? It's hard to say. It's one of those problems that occasionally flares up from time to time but few people regard as extremely serious - I show an example in point two here. The wiggles are intriguing, but they're not that large. And the authors of the above study note that there may be selection effects at work that mean the correlation isn't real.

But it's still intriguing. There's another, much stronger apparent relation between normal matter and galaxy dynamics (i.e. the dark matter) : the Tully-Fisher relation. This isn't subject to all the small-scale measurement errors or problems of star formation or other processes that might affect internal motions in very localised regions, because it's a relationship between the maximum rotation speed of a galaxy and its total mass.

Just as in the pages of any celebrity gossip magazine, so relationships in astronomy are equally complicated. OMG, is that line width just a proxy for rotation ? I don't think the resolved observations are going to be happy when they find out about that ! And have you seen the stellar mass getting off with the neutral hydrogen ? Things are getting steamy gassy !

What I mean is, originally the relation was found by comparing the rotation speed with the brightness of a bunch of galaxies :
From the discovery paper. It looks more complicated than it is. It's just plotting brightness (on the vertical axis) against rotation speed (on the horizontal axis).
As usual, some words of caution are needed. This quantity "LOG ΔV" means how fast the galaxy appears to be rotating, but direct rotation measurements are hard. That requires painstaking observations of the galaxy's speed at each point within the galaxy. It's much easier to observe the whole galaxy at once, which gives you a "line width". This is equivalent to the maximum difference in speed along the line of sight.

Say the galaxy is rotating at 200 km/s. One half will be coming towards you at 200 km/s and the other away from you at 200 km/s, and your measured "line width" will be 400 km/s. The correction is a bit more complicated than just halving the line width, because the galaxy might not be directly face-on. But this correction is relatively easy. Also, at high widths you can be pretty confident you really are measuring rotation, because unless you've got one of those cases of particularly windy galaxies there's not really much else that could create such a high line width besides rotation.

Things get trickier when you start going to lower line widths. There, rotation might not be nearly so dominant, so your assumption that you're measuring rotation is much more questionable.

Using line width rather than true rotation is done for convenience. Similar, brightness was used because that's what's actually measured rather than stellar mass. Converting brightness into the more physical parameter of stellar mass is possible, but needs some assumptions about how many massive stars there are, how many faint ones, their colours, etc. You can do it, but you need more than just one observation for this - you need to use lots of different wavelengths to properly measure the different stellar populations.

Once you make these corrections, however, something remarkable happens. There seems to be a very tight correlation indeed between the total mass of stars and gas and the rotation speed. And most interestingly of all, galaxies which don't fit the normal brightness-rotation relation do fit the mass-rotation relation !

Left : using the stellar mass (effectively, brightness). Lots of galaxies (highlighted in green) don't fit this otherwise nice relation. Right : using the total mass, combining the mass of stars and gas - now those errant galaxies have been brought back into the fold.
This "baryonic Tully-Fisher relation" (baryonic just being a fancy word for "normal matter" suggests that there really is something funky going on here. No need to worry about the problems of little wiggles - the total mass of normal matter seems to correlate very well indeed with the overall rotation. And it's the total mass that's key - stellar mass by itself doesn't work.

 Later studies found that the scatter in the relation can be reduced quite a bit with more accurate corrections - there might not be any intrinsic scatter at all ! You'd think there'd be some variation, but apparently not.

Let me emphasise this. It turns out this galaxies like this...

... sit on exactly the same relation as galaxies like this :

About a factor of 10 difference in rotation speed, 50 in size and 10,000 in stellar mass... yet they still lie on the same relation. What's particularly weird is that it's quite easy to show that the Tully-Fisher relation should have scatter, but it doesn't. The only way to make this work if there's strange "conspiracy" between the normal matter and the dark matter, which doesn't really make physical sense. What's going on ?

Behold, The Mass Discrepancy Acceleration Relation !

We've so far seen different variations of the same problem : the normal matter seems connected to the dark matter in a weird and unexpected way. We've also seen how the way we examine the problem changes how we think about it. The observational parameters that we have may be convenient, but they aren't the most basic physical properties which are at work here.

The MDAR is an attempt to reduce things down from the measurements we get directly from telescopes to the actual underlying physics : acceleration. Knowing the size, rotation and mass at any point in a galaxy, it's possible to work out how fast it's accelerating, i.e. the force it's experiencing.

"But wait !", I hear you cry. "Surely there's a problem with this ? After all, the mass in a galaxy is rotating in an unexpected way, that's how we know there's dark matter there."
"Indeed," I respond, "but what we can do is compare the expected acceleration (based only on the mass of the normal matter) with the actual acceleration based on its measured speed."
"Gosh !" you reply, "that's jolly clever."

Yes it is. The MDAR cuts through the problems of interpreting the observational parameters by bringing it back down to the physics - and it doesn't need many complicated assumptions to work these out either. The result, as shown in that famous "new law of nature" paper by Stacy McGaugh et al., is very impressive indeed.
On the horizontal axis, the expected acceleration due to the mass of the normal matter ("bar" = baryons = normal matter), On the vertical axis, the actual acceleration from the speed measurements ("obs" = observed). There isn't a nice straight slope : the important thing is that there's a trend at all. Knowing the mass of normal matter, you can predict its true acceleration.
That's just about one of the clearest results ever. At least, there's hardly any scatter and everything follows a nice trend, over a factor of about a thousand in acceleration (if not more).

Let me further emphasise how odd this is. It's a bit like being told a few basic bits of information about a horse - how large it is, how many legs it has, typical horsey sort of things - and then being able to work out exactly how fast it's going... even though no-one told you that the horse is on the back of a truck. It's weird.

To be more accurate, what the MDAR says is that once you know the theoretical acceleration of some matter, based only on the mass of that matter and its distribution, you can accurately predict its true acceleration. The problem is that no-one told you that there's also so much dark matter present that it should be dominating the acceleration, not the matter you can see. So again, it's weird.

But we like weird. Weird is cool.

Still, what does it actually mean ? In fairness, apart from the extremely silly comment about a "new law of nature", I have no complaints about the rest of the paper. I can even understand why one would be tempted to make such a comment as this (later on they call it, "a sort of Kepler's law for rotating galaxies"), but you shouldn't actually do it. The discoverers may of course hold any private opinion of "their" (see later) discovery's importance that they wish, but it's the scientific community that should be the public judge of it - not the original authors. Inevitably, however honourable their intentions, it comes across as arrogance and hubris.

Still, the authors note three possible interpretations of this result :

1) It's just the way galaxies form. That is, it can be explained using entirely conventional physics and standard models of galaxy formation. The authors aren't happy about this because of related, long-standing problems with those models.
2) It indicates that there's something we don't understand about the dark matter. Maybe it really is influenced by or somehow relates to the normal matter in a way other than purely through gravity as in the standard model. That's possible, but it would make the already complex models even more complex.
3) It undermines the dark matter paradigm. A perfectly legitimate interpretation since it seems to suggest a direct connection between the normal matter and the rotation speed, in seemingly direct contrast to the predictions of dark matter. Alternative theories of gravity like MOND might provide the answer. MOND did actually predict this relation decades ago, much to the irritation of dark matter supporters. It even makes intuitive sense in a MOND perspective, since in that scenario there isn't any dark matter - only normal matter causes acceleration.

All of these are valid possibilities. Taking this result in isolation and at face value, the second two are the most natural. But the dark matter paradigm is a formidable edifice indeed, and it's a foolish astronomer who would rush to declare it dead because of any one issue.

Not such a mysterious mystery ?

Actually Stacy McGaugh likes dressing as a monster and scaring off his competitors...
What quickly followed in the wake of McGaugh's publication was a series of papers showing that actually the first possibility - that the standard models could explain everything - worked just fine, thankyouverymuch, we don't believe in MOND in this neighbourhood, we're Baptists....

Not quite. Of course, I'm not suggesting that either dark matter or MOND are any kind of a cult or religion or even ideology, as regular readers will well attest to. But there was certainly more than usual element of humanity creeping in to the normally stoic research papers and analyses. Perhaps it was due to the fact that this was coming from McGaugh, a highly respected researcher who normally manages to straddle the dark matter and MOND camps without winding anyone up the wrong way, using this frankly ridiculous phrase.

The first criticism came not from angry dark matter "believers", as you might suspect, but from a much more unexpected source : Milgrom, the creator of the MOND theory !

If McGaugh used a single poor phrase, Milgrom took it to a whole new level. For example, "It is anything but a newly discovered relation"; " These results, indeed, constitute a triumph for MOND"; "McGaugh et al. have chosen to obfuscate the MOND roots of their analysis"; "No other possible origin for such a function is known"; "There is no other paradigm, certainly not the dark matter paradigm, that dictates this form."; "McGaugh et al. seem to try to justify their suppressing the role of MOND"; "the data itself is not even theirs". It was essentially the arXiv equivalent of an angry blog post. Worse was to follow, but we'll get to that.

He's already got one ! It's very nice !

Let's try to divorce the angry ranting from Milgrom's claims themselves. First the claim that it's not a new discovery, for which Milgrom cites no less than eight papers. Indeed, we've already seen how the rotation curve wiggles and Tully-Fisher relation can be seen as one way to describe this relation. I couldn't access one of the papers, but the others don't plot this precise relation though they do describe something similar... except for one. This paper by Wu & Kroupa from 2015 plots exactly the same relation as in the McGaugh paper. Look, here it is :

Is it fair to claim that this result was well-known though ? Hard to say. Certainly the other forms of this MDAR are well-known, and McGaugh describes them himself in the introduction. But this particular form ? I don't think so. The Wu paper has been cited 20 times (a very good rate - better than any of mine ! - but not astonishing) and McGaugh (until this year) was never on any paper that cited it. Wu notes that a similar study had been done in 2006, but that references a conference proceedings. People often deliberately avoid these as they're seldom up to the same standards of rigour as normal papers, so although it should be cited it's understandable that it was not.

The Wu paper is 17 pages long and quite technical (and doesn't call this relation a new fundamental law of nature !), so you'll have to forgive me for not reading it thoroughly*. As far as I can tell, it only cites that conference proceedings in support of this previous formulation of the MDAR. But it also notes that the standard "mass discrepancy relation" is basically the same thing. That relation definitely is well known, but this particular form of it ? Probably not. Milgrom is correct that McGaugh should have been more explicit about describing the MDAR as a well-known problem, but it seems forgivable that he might not have known that this plot had already been produced. I've met Stacy McGaugh a few times and Pavel Kroupa many, many times, and while I'm not privy to their private communications, I can't say I've ever noticed Pavel being upset that Stacy didn't cite him.

* For all other papers I read them in their entirety, quite carefully, before referencing them. That's why these posts are infrequent.

Been there, done that

What of Milgrom's claim that McGaugh "suppress" the role of MOND in their analysis ? No, sorry - this one is silly. McGaugh says it directly in the paper : "Indeed, our results were anticipated over three decades ago by MOND. Whether this is a situation in which it would be necessary to invent MOND if it did not already exist is worthy of contemplation."

That seems like plenty of endorsement and acknowledgement to me. And since it's a letter, space is at a premium so brevity is crucial. It's folly to ask for anything more in the space available.

A mysterious mystery gets less mysterious

Which brings us to the third, most important claim by Milgrom : that there's no way the dark matter model can account for this result. The first challenge to this came out within weeks of the McGaugh paper. Keller & Wadsley used standard dark matter simulations but with better physics for the normal matter, and they were able to reproduce the MDAR strikingly well.

McGaugh's observational result is on the left, Keller & Wadsely's simulation on the right.
What was the secret to this astonishing success ? Unfortunately, they're not very clear on that one. They state only that it's due to, "simple dissipational collapse of gas", which means that the gas can cool and lose energy, but that's not a tremendously detailed explanation.

More convincingly, they show that this relation would look very different in the early Universe, when star formation was higher and those huge windy outflows were much stronger. In their simulations, this relation evolves over time, starting out quite different (because of the strong stellar winds) but then evolving naturally into the relationship we see today (as the winds die down). So I'm sold on their simulations reproducing the results, but I don't think they give any sort of reason why this relationship exists. Ho hum.

Milgrom flew into an outright rage at this point. The reason appears to be that the original title of the paper contained the phrase, "La Fin Du MOND ?". In fact the paper barely even mentioned MOND at all - it was much more focused on showing that the standard model could produce this MDAR.

But Milgrom's wrath was terrible; his retribution swift. He said that authors "smugly suggested" that the end of MOND was nigh (they didn't, they just asked a question); that they only "claim" to have simulations which show the presented results (this is - ouch - tantamount to calling them liars); that the reasons for the agreement were "trivial" (they weren't and aren't); that they had too few galaxies in their sample and no dwarf galaxies (this was true in the first draft but corrected in later versions); that they made "unwarranted extrapolations, they seem to imply that CDM [the standard model] is consistent with all the observed galaxy properties predicted by MOND" (absolute nonsense, they did nothing of the sort); and made some odd comments about the choice of which parts of the galaxies to sample (which the authors describe well and they seem fine to me). He even made a bizarre comment about the simulations trying to make guesses as to "unknowable events and processes" - which is frankly laughable. All simulations do that; if we knew everything that was happening, we wouldn't need simulations !

Milgrom's only objection of any real substance, so far as I can tell, was that half of the galaxies used in the simulations did not have realistic rotation curves. Yet the other half did. To my mind, they showed convincingly that this result dropped out naturally from their simulations, with absolutely no attempt to force things to work.

At this point one has to wonder, "Milgrom, what are you on about man ? Did Keller deliberately run over your dog ? Did Wadsley break your house and burn your legs down ? 'La Fin Du MOND' might be a bit snarky - condescending even - but come on, it's not that snarky."

Anyway another paper came out a bit later, from another team using a completely different set of simulations, measured in a different way... and what did they find ? Guess what. Pretty much exactly the same as Keller & Wadsley !
Well well well, doesn't this look eerily familiar.
Unfortunately this paper, lead author Aaron Ludlow, didn't really offer much more in the way of what causes this relation either. But they offered some hints. They say that it doesn't really matter what "scaling relations" the galaxies in their simulations obey - that is, how much normal matter they contain at different total masses - they all obey a relationship like the one seen in the graphs. Maybe not the same one though. They're not quite as clear as I would like on this point, but they seem to say that if the galaxies in the simulations obey the scaling relations that normal galaxies do, then they reproduce the observed MDAR. There's nothing profound about it; it just happens naturally.

EDIT : Some considerable time later, another paper came out which does a much better job of explaining why this happens. You can read my detailed summary and find the original paper here. In brief, there are a few things at work. Detectable galaxies can't form in the largest or smallest halos (they either don't accumulate enough gas, or so much gas causes runaway star formation and stops any more gas from getting in), limiting the acceleration baryonic matter ever experiences. And the acceleration withing each galaxy varies in a characteristic way depending on the distribution of dark matter, which in turn controls the distribution of mass. There are some important subtleties explained in the link, but if you want my opinion (and I guess you do because you're still reading) this is a convincing explanation.

Which doesn't mean that it disproves MOND or proves the standard model : it's not even that useful. In fact, as a way to test between them, it appears to be utterly useless. Even without fully understanding its cause.

The next response was published early this year.... unfortunately. Well, unfortunate in the sense that all the players involved decided to put their papers on the pre-print hosting service arXiv before they were accepted for publication. This is an unfortunately common practise, occasionally justified (if you've made a fun discovery and you want to stake your claim to it, or if you need help from the community and don't have many of your own personal contacts) but not usually. The result was that each of the papers went through several iterations all responding, very confusingly, to different iterations of the other papers, which all took different amounts of time to get through the review process. It's all a bit of a mess, really.

Not quite this messy, though.
On this paper the lead author was a certain Federico Lelli, with McGaugh taking a back seat. It has the catchy title, "One Law To Rule Them All", which is at least a little bit humorous, but then they go on to again say that it's tantamount to a natural law. You bunch of bloody muppets. Don't get get how damaging this stupid rhetoric is for science communication ?

Anyway, the "original" McGaugh paper was just a letter, which are short reports on particularly exciting things. The Lelli paper is the more detailed follow-up (and this time it does cite the earlier discoveries of this relation). Much more detailed. Despite this single daft bit of drama, I'm forced to admit that it's a first-rate paper. It's clear, detailed, well-explained and readable. All the figures that you might want are there. Many different interpretations and parameterisations have been explored.

By far the most interesting result was this plot :

It's the same MDAR we've seen umpteen times already, but now with the addition of dwarf spheroidal galaxies. These are galaxies which are dwarfs... and spheroidal. Photogenically they're deafeningly dull.

But they are nevertheless extremely interesting and confusing little buggers. As we saw last time, sometimes the faintest galaxies are interesting precisely because they're so bloody faint. Which in this case is because they're a good test for very low accelerations. Did McGaugh cheat by not including them in the original paper ? No, not at all. The problem is that they're so faint you can only estimate accelerations at the outermost edge. Essentially, the provide only a single data point each, whereas for all the other galaxies it was possible to estimate accelerations in many different places. And one of the really neat things about the MDAR is that it really seems that it's acceleration that matters. The overall properties of each individual galaxy don't seem to be important at all - if the predicted acceleration is the same in two galaxies, then the actual acceleration is the same, no matter the total mass or size of the galaxies.

Except for these pesky dwarf spheroidals, it seems. Since they're so faint, they're hard to measure, so their data isn't as reliable. But when the selection is limited to the sample where Lelli et al. believe the data is of the highest quality, it still seems that they deviate from the relation and have more scatter (right hand panel, above).

If we're feeling very stupid indeed, we might take this relation at face value. We'd conclude, "HAH ! You SUCK McGaugh ! There's no law there at all ! How can acceleration behave differently in different galaxies ? That's feckin' stupid. Jeez, I don't know why I wasted my time on this."

And that definitely would be a very stupid thing to do. Even in the high quality sample, the observational errors are still large. So we just don't know if there's a stronger intrinsic scatter there or not, as yet. But is there a systematic offset, a flattening of the relation at low accelerations that would mean we wouldn't have to change the laws in different galaxies ? Possibly. Lelli & Co. think so, noting that the they can't fit the same equation for the dwarf spheroidals as for the rest. They're also very cautious about the nature of these objects, and it's possible that because they're so faint they might actually be more disturbed than we think they are, in which case we wouldn't expect them to obey a nice relation.

That's one possibility, but it's not the only one. Lelli et al. note that it could be explained in the standard models if there's some sort of threshold for how much dark matter you need to form stars (which is not crazy - dark matter clouds which are too low mass might never accumulate enough gas to form any stars at all). Certainly if this deviation (especially the scatter) is true then it does make it much less likely that this points towards any new physics - it looks much more like the galaxy assembly process might somehow be to blame.

On the other hand, it could point out unexpected physics of the dark matter or even gravity itself. If you change the form of the MDAR just slightly, Lelli says you can get the dwarf spheroidals to agree with the normal galaxies pretty darn well :

What they do in the above plot is very clever. They now combine the expected acceleration due to the normal matter with the expected acceleration due to the host galaxy, for satellite galaxies. For some reason that seems to work. It doesn't get rid of the high scatter, but it does put everything on the same overall relation. That does rather suggest that the original form of the MDAR isn't such a fundamental law after all - it seems that something more funky's going on. The physical motivation of combining these two quantities is, in my view, highly questionable, but we'll get back to that shortly.

The other option suggested of the dwarves not really being stable - well, they're famous for going "swimming with little hairy women", so that's not such a surprise - has recently been examined in another paper by Fattahi et al. (still under review !) :
Observations on the left, simulations on the right. The satellite galaxies in their simulations are being tidally disrupted and deviate from the MDAR, whereas isolated galaxies aren't and don't.
It's fairly okay, I guess, but it's not a fantastic agreement. They show that these gravitational encounters can cause more scatter, but they don't reproduce the size of the scatter very well. Also, Fattahi seem to be unaware that Lelli already plotted this strong scatter, saying that it, "seriously calls into question the idea that MDAR might encode a `natural law'". I agree, it does call it into question, but they don't cite the Lelli paper, which is very strange. On the other hand, one of the few possibilities the Lelli paper doesn't discuss is that these galaxies might indicate that it's not really a law at all. And if you compare the simulations with only the high quality dwarf spheroidal data (scroll up a few figures), you'll see the agreement is very much better.


So what's going on ? Does this discovery have any hope of being a new natural law, or is it just wild-eyed crazy hype ? Does it provide evidence that our theory of gravity is wrong or not ?

Currently I'd have to say "no". It appears to be useless : it's been reproduced directly in two independent sets of standard model simulations, and occurs without tweaking them to make it work. It's true MOND predicted it well ahead of time*, but dark matter - thus far - appears to be doing an equally capable job of reproducing it. So there's no clear reason to prefer one to the other.

* However, as far as I can tell none of these current papers actually show the specific MOND prediction, nor do they explain whether MOND predicts the flattening seen at the low acceleration end with the dwarf spheroidals.

Lelli raise some objections to the dark matter simulations. Unfortunately, because everyone did this silly thing of posting every version of their paper online before it was accepted, Lelli's objections (like Milgrom's) are no longer accurate. For instance he says that Keller & Wadsley only use giant galaxies; in fact they now use a range of galaxies with the largest being more than 100 times as massive as the smallest. Most of Lelli's objections to Ludlow's work seem to be more nit-picking than anything else - the size of the scatter isn't quite right, the measurement techniques weren't quite right. This doesn't seem critical to Ludlow's conclusion : that some version of the MDAR arises naturally in standard simulations, though the precise relation does depend on the galaxy parameters.

You might think that the galaxy mass range objection also isn't critical. After all, if you go to large enough distances from giant galaxies then you experience very low accelerations, so you don't need to simulate a dwarf galaxy to fill in the faint end of the MDAR (this was also one of Milgrom's objections). Indeed this is true, and exactly what was done in the earlier version of the Keller & Wadsley paper. And you'd surely think that if it's really due to new physics, then acceleration is acceleration wherever you are. It shouldn't matter if you're inside a giant galaxy or a mouse's fart : as long as you only calculate gravity, the results should be the same using the same laws.

This is true in the standard model. But it is not true using MOND, which predicts that the behaviour changes depending on the distribution of matter. As Lelli say, in some versions of MOND the acceleration, "could vary from galaxy to galaxy or even within the same galaxy". Although not strictly the same, that's what motivated their choice to include the acceleration from the host galaxy that brings the dwarfs back into agreement with the MDAR. So MOND's prediction of the MDAR is based on a totally, radically different approach to the standard model. That's why it's important to test if dark matter's predictions do still hold true in very low-mass galaxies. Lelli's objection is still valid in that the simulations haven't shown what should happen over the same galaxy property range as is actually observed, though it should be noted that when Kelly & Wadsley took their simulations to less massive galaxies they found exactly the same as for the giants. It feels just a little bit desperate to suggest that a problem might crop up if we just keep doing the same exploration of ever-lower masses.

Personally I don't like the MONDian approach. Classically we're used to physics being the same everywhere in all conditions : sure the final numbers depend on the precise conditions, but the underlying processes never vary. With MOND it's more like (though not quite the same as) the idea of physics changing locally to give different result : gravity works differently depending on the local conditions, albeit in a predictable, ordered way. I find this deeply unsatisfying. Sure, of course the Universe might work like that, but I'd put that one in the "last resort" options box.

Many objections MONDers have to the standard model are now beginning to feel a bit dated. Not so very long ago, dark matter simulations could only use dark matter. But for several years they've been able to employ ever more complex physics of the gas and stars. It's true we don't fully understand many of these processes, and there are many parameters we don't have independent constraints for. But that doesn't invalidate the success of the models, nor does every minor failure point to a fundamental problem. MOND still doesn't have any published simulations using the complex gas physics, and when it does it's going to have just as many difficulties as the standard model.

The Fattahi paper (not yet accepted for publication) claims to have found a "possibly insurmountable" challenge to MOND. The rotational speed of those same faint dwarves appears to be in very stark disagreement with MOND's predictions even if you account for the MONDian weirdness. It's intriguing, but MOND has survived such challenges before... somewhat. I'm not at all convinced that the MOND interpretations of some phenomena are nearly as sensible as devotees seem to think they are.

Whenever I do these posts about whether dark matter is really real, I like to stop and see if anything I've read has caused me to re-evaluate my position. The approach I like to try and numerically quantify which I prefer the most, because that forces room for doubt. Last time I ended up increasing my bias towards dark matter from 75:25 to 80:20 in favour of dark matter versus something else (I reserve about 5% for MOND, so it's really 80:15:5).

This time, nothing has changed. All that analysis has been essentially for nothing, because neither side has any advantage over the other.

Is there at least any scope for future developments ? Well I'd like to see a MOND group actually show their predicted MDAR instead of just claiming that they've got one. Or a dark matter group do simulations of those very faint dwarf galaxies. But these are at the "it might be nice" level. What I suspect will happen is that we'll see a few more papers on this over the next year before everyone becomes horribly disillusioned, gives up and goes home.


  1. > Well I'd like to see a MOND group actually show their predicted MDAR instead of just claiming that they've got one.

    Way to go showing you didn't bother to read the actual MOND literature. The prediction can be found in Bekenstein & Milgrom 1984 equation 1b. See sections 1 and 2 for the derivation of said equation. Close to a0 where the prediction switches from Milgromian to Newtonian, this depends on the choice of interpolation function. There are several known as the "simple", "standard", "exponential", "Bekenstein" and "Hees" interpolating functions. The RAR is the usual MOND law with an exponential interpolation. These functions all produce the same results for accelerations more than a0 away from a0 and are nearly identical at a0 (they vary the sharpness of the transition). For that see section 6.2 of the main MOND review by Famaey en McGaugh (2012).

    These two papers are the absolute minimum knowledge concerning MOND. If you haven't read those two you just haven't read up on MOND.

    1. Thanks for the reference ! The problem is I'm an observer, not a theoretician. So I was looking for a figure, not an equation, and I couldn't find one. I didn't DOUBT that they had the calculation, I just wanted to SEE it for myself (if the text came across differently then that's my fault).

      But no, I am not a MOND expert. This doesn't mean I can't judge if two things agree with each other or not.


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