Dark Matter: Just Fine, Thanks

Astrophysical ambulance-chasers everywhere got a bit excited this week, and why wouldn’t they? Here are some of the headlines we read:

Wow. More evidence against dark matter? I didn’t know about the original evidence.

Sadly (and I mean that — see below) there is no evidence against dark matter here. These items were sparked by a paper and a press release from Maryland astronomer Stacy McGaugh, with the rather more modest titles “A Novel Test of the Modified Newtonian Dynamics with Gas Rich Galaxies” and “Gas rich galaxies confirm prediction of modified gravity theory,” respectively.

I’m the first person to defend journalists against unfair attacks, and we all know that headlines are usually not written by the people who write the actual articles. But we can legitimately point fingers at a flawed system at work here: these articles are a tiny but very clear example of what is wrong wrong wrong about our current model for informing the public about science.

McGaugh’s new paper doesn’t give any evidence at all against dark matter. What it does is to claim that an alternative theory — MOND, which replaces dark matter with a modification of Newtonian dynamics — provides a good fit to a certain class of gas-rich galaxies. That’s an interesting result! Just not the result the headlines would have you believe.

It’s obvious what happens here. Nobody would read an article entitled “Gas rich galaxies confirm prediction of modified gravity theory” — or at least, most editors doubtless feel, fewer people would be interested in that than in evidence that went directly against dark matter. So let’s just spice up the story a bit by highlighting the most dramatic possible conclusion we can imagine drawing, and burying the caveats until the end. Net result: a few more people read the articles than otherwise would have, while many more people just read the headlines and are left with less understanding of modern cosmology than they started with. Scientists and journalists together have a responsibility to do a better job than this at making things clear, not just making things sound exciting.

But let me take this opportunity to lay out the problems with MOND. It’s a very clever idea, to start. In galaxies, dark matter seems to become important only when the force of gravity is not very strong. So maybe Newton’s famous inverse-square law, which tells us how the force of gravity falls off as a function of distance, needs to be modified when gravity is very weak. Miraculously, this simple idea does a really good job at accounting for the dynamics of galaxies, including — as this new result confirms — types of galaxies that weren’t yet observed back in 1983 when Mordehai Milgrom proposed the idea. Whether or not MOND is “true” as a replacement for dark matter, its phenomenological success at accounting for features of galaxies needs to be explained by whatever theory is true.

Which is an important point, because MOND is not true. That’s not an absolute statement; among its other shortcomings, MOND is not completely well-defined, so there’s a surprising amount of wriggle room available in fitting a variety of different observations. But to the vast majority of cosmologists, we have long since passed the point where MOND should be given up as a fundamental replacement for dark matter — it was a good idea that didn’t work. It happens sometimes. That’s not to say that gravity isn’t somehow modified in cosmology — you can always have very subtle effects that have yet to be discovered, and that’s a possibility well worth considering. But dark matter is real; any modification is on top of it, not instead of it.

Let’s look at the record:

  • MOND is ugly. Actually, that’s very generous. More accurately, MOND is not a theory; it’s only a phenomenological rule that’s supposed to apply in a limited regime. The question is, what is the more general theory? Jacob Bekenstein, in an heroic bit of theorizing, came up with his Tensor-Vector-Scalar (TeVeS) theory, which hopefully reduces to MOND in the appropriate limits. Here is the action for general relativity:

    And here is the action for TeVeS:

    Don’t worry about what it all means; the point is that the theory underlying MOND isn’t really simple at all, it’s an ungodly concatenation of random fields interacting in highly-specific but seemingly arbitrary ways. That doesn’t mean it’s not true, but the theory certainly doesn’t win any points for elegance.
  • MOND doesn’t fit clusters. Long ago, rotation curves of galaxies were the strongest evidence in favor of dark matter. Very long ago. We know better now, and a mature theory has a lot more hoops it needs to jump through. The nice thing about MOND is that, despite the ugliness above, when you get down to making predictions for large astrophysical objects, there really isn’t any wriggle room: you fit the data or you don’t. It works for galaxies, but when it comes to clusters — you don’t. Not close. Proponents of MOND understand this, of course, and they’ve come up with a clever workaround. It’s called “dark matter.” That’s right — even MOND’s biggest supporters admit that you need dark matter to explain galaxies. Let’s just emphasize that for those who find all this text kind of tedious:

    Even with MOND, you still need dark matter.

    Some people try to claim that the necessary dark matter could be neutrinos rather than some brand-new particle, and that’s supposed to be morally superior somehow. But there’s no two ways around the conclusion that dark matter is real.

  • MOND doesn’t even fit all galaxies. For almost twenty years now we’ve known that MOND fails for a certain type of galaxies known as “dwarf spheroidals.” These are small (thus the name) and hard to observe, so MONDians have come up with various schemes to explain away particular galaxies. That might even be okay — nobody said fitting the data would always be easy, even in the correct theory — except that it’s precisely this kind of extra work that is being scoffed at in the case of dark matter in these recent news items.
  • Gravity doesn’t always point in the direction of where the ordinary matter is. This is the lesson of the famous Bullet Cluster (and related observations). The evidence from gravitational lensing is absolutely unambiguous: to fit the data, you need to do better than just modifying the strength of Newtonian gravity. Once again, people try to wriggle out of this in TeVeS and other MONDian approaches. However, the way they do it is by imagining that other fields have energy, which warps spacetime, and therefore a gravitational field. We have a useful phrase to describe new fields whose energy warps spacetime: “dark matter.” MOND-like theories don’t replace dark matter so much as they make it much more complicated.
  • MOND doesn’t fit the cosmic microwave background. Saving my favorite for last. One of the coolest things about the temperature anisotropies in the cosmic microwave background is that they are sensitive to the existence of dark matter. In the early universe, dark matter just collapses under the pull of gravity, while ordinary matter also feels pressure, and therefore oscillates. As a result, the two components are out of phase in the even-numbered peaks in the CMB spectrum. In English: dark matter pushes up the first and third peak in the graph below, while suppressing the second and fourth peak. That would be extremely hard to mimic in a theory without dark matter; indeed, this was predicted before the third peak was precisely measured. But now it has been. And…

    See that dotted line? That’s the theory with dark matter, fitting all the data. See the solid line? That’s the MOND (really TeVeS) prediction, definitively inconsistent with the data. Can some clever theorist tweak things so that there’s a MOND version that actually fits? Probably. Or we could just accept what the data are telling us.

Having said all that, I’m glad that some people are still thinking about MOND-like approaches. You can still learn interesting things about galaxies, even if you’re not discovering a new law of nature. And dark matter, to be honest, isn’t established with 100% certainty; it’s really more like 99.9% certainty, and you never know.

What’s less admirable is people (mostly outside the professional community, but not all) hanging onto a theory because they want to believe it, no matter what new information comes along. Personally, I think it would be much cooler if gravity were modified, compared to the idea that it’s just some dumb new particle out there. I’ve put some thought into the prospect myself, which helped lead to some productive research ideas. But ultimately the universe doesn’t care what I prefer. Dark matter is real — gravity could also be modified, but there’s no reasonable doubt about the dark matter. So let’s try to figure it out.

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128 Responses to Dark Matter: Just Fine, Thanks

  1. Sam Gralla says:

    I thought the more interesting thing about that paper was the claim that CDM doesn’t reproduce the data without some extremely weird fine tuning of the mass to light ratio of the galaxies. At least I think that was the claim. I don’t have the paper in front of me.

  2. joe says:

    Is the wriggle room filled with gum?

  3. Ben says:

    Sean, everything that you say here is right, dark matter *DOES* exist, and even most MOND proponents fully agree with this. It might however depend on what dark matter precisely means. But what most MOND proponents try to say is “In spiral galaxies, MOND is right as a scaling relation, whatever dark matter is. And that IS right, and that IS amazing.” … What can be shocking for people working on galaxies is that cosmologists seem to deliberately ignore this fact, because they do not care about the details of messy astronomical systems such as galaxies… And this might be a big mistake. In short, as you say yourself, but as should sometimes be emphasized more, what the success of MOND might tell us about the nature of dark matter might really be fundamental… And how much you think the latter sentence is true depends on how far away from the galactic scale your main research interests lie. What strikes me is that when people say “MOND is wrong” or “MOND is right”, they dont necessarily mean the same thing, because some think it is a synonym for TeVeS (the equations you showed hereabove), and those people are mostly *NOT* working on galaxies (and obviously they are mostly finding problems with the whole modified gravity approach), while some others (mostly working on galaxies) just think it is the most awesome scaling relation to date, summarizing almost all scaling relations of both spiral and elliptical galaxies, let alone dwarf spheroidals, but including tidal dwarf galaxies that are much less well understood in the CDM context. And they simply think: “It works too well to be meaningless”. Again, this absolutely doesnt mean “dark matter doesnt exist”. There is a big difference between believing in dark matter, and believing in the current LambdaCDM model. As a conclusion, as Stacy points out, the success of MOND is just a huge fine-tuning problem that we need to understand, as there are many in physics. The problem right now is the vast majority of astronomers and cosmologists *completely* (and often deliberately) ignoring this fine-tuning problem just because they fear that they could give the wrong impression about what we actually know and what we actually dont. And that is, I think, not right. And that is why, for me, Stacy is right to point out what he does point out.

  4. Jake says:

    To be fair to the reporters the author seems to argue pretty hard for MOND over Dark Matter in the paper. For example claiming that the bullet cluster supports MOND “with equal vigor” as it does Dark matter. It seems to me (in my very non expert opinion) the easy solution would be to assume dark mater distributions are different in galaxies where the mass is dominated by gas instead of stars. I wouldn’t really consider that fine tuning.

  5. Shantanu says:

    do you think both MOND and lambdacdm are right? This is the pov advocated by Luc Blanchet
    starting with this paper.
    Somehow I don’t think these series of papers have been on the radar of cosmologists

  6. Sili says:

    I saw the BBC piece and swore at it when I got to the end without seeing any mention of the Bullet Cluster. Bloody waste of time.

  7. Joseph Smidt says:


    What a great write up! This is hands down the best written critique of MOND I have ever seen. I’ve known MOND has issues but I’ve never seen them written up so well. Thanks.

  8. Cosmonut says:

    This is off-topic, but:
    Which is an important point, because MOND is not true. That’s not an absolute statement; among its other shortcomings, MOND is not completely well-defined, so there’s a surprising amount of wriggle room available in fitting a variety of different observations.

    Does that (especially the second sentence), also describe the state of String Theory today ?
    Not trying to ask rhetorical questions, just genuinely curious.

    Great write-up on MOND. I knew the theory was ugly, but actually seeing the action was a revelation.

  9. Valatan says:

    Bekenstein claims that the coupling of the vector particle is chosen specifically to make the galactic cluster observations work out. Otherwise, according to him, you just need the scalar particle.

  10. dg says:

    Thanks Sean. I often come back to your explanations when I need a refresher on the full case for dark matter. Actually, for the benefit of everyone else, here’s a very nice talk where you explain the same thing:


  11. Great contribution to the public understanding of science. I also recall a similar article you wrote in Nature many years ago. I wonder if you too received similar headlines (Sean Carroll Kills Dark Energy) when you wrote that paper on modified gravity accounting for the cosmic acceleration?

    On a lighter note, I am sure Fritz Zwicky would have called those journalists ‘spherical bastards’!

  12. Shantanu says:

    Sili, The buller cluster also presents problems for Lambda -CDM.
    See this

  13. aa says:

    the action for GR is very nice, but we also know GR is wrong/incomplete.

  14. publius says:

    Great post, thank you for making the issue crystal clear.
    just a detail: it seems that the tilde over g in the Einstein-Hilbert action should not be there

  15. Capt. Galectro says:

    Dark matter does not exist people. It’s most matter, but gee we can’t detect it . Common sense people, common logic tells you something else is in play. What is in play is that all light from all galaxies is bent by the space-time warp of gravity. What we see, what we detect is all an illusion. http://bigbangabust.thecomicseries.com

  16. David George says:

    In your graph of the angular power spectrum of the CMB anisotropy, the left side of the graph is missing(90 degree anisotropy). In other reproductions of this graph, that “low l” is usually there, but it shows a data point that is not even within the range of “cosmic variance” (according to NASA, “cosmic variance” is “a measure of how likely random chance of our position relative to other matter in the universe is affecting the results”). It is too low even for random chance! But it is not on your graph. I can only assume you intentionally took it out. I seem to recall some years ago when the WMAP results came out, you said the task is to find the missing — (electrons?). Since the “low l” deficit is not shown, I imagine the “anomaly” remains unexplained. (I am not a physicist.)

    Is suppression of unwanted data on a public website such a great contribution to public understanding of science? It seems to me you are promoting some agenda – for example, “Big Bang cosmology is on the right track!”.

    As for “dark matter”, that label gives the impression that there is some matter that moves only according to gravitational influence, and so does not radiate light. Even though you would prefer some modification of theory, you say, “dark matter is real”. But it seems to me (I am not a physicist) that what is real is anomalous motion. So a more accurate phrase than “dark matter” would be “anomalous motion for which we have no explanation”. And what is alive and well is the lack of an explanation for the anomalous motion. But maybe public understanding of the progress of Big Bang cosmology would be harder to come by with such a longwinded phrase, so “Dark Matter” — that’s the ticket!

  17. Hi Sean,
    Thanks for noticing.

    I agree with much of what you have to say, but certainly not all.

    For example, I agree about the third peak of the CMB power spectrum. But you neglect to mention that I was the only person to correctly predict the amplitude of the second peak. That the third peak is high simply means ΛCDM survives this test, not that MOND fails it. For as you say, we need a proper covariant theory to do that, and it is not yet clear what that is, or indeed, if it is even possible to construct.

    The success of ΛCDM for the CMB hardly guarantees its success in galaxies. It too has its problems in dwarf spheroidals. The data in the particular paper you cite were really rather ambiguous. MOND does poorly in two cases (Draco and Ursa Minor) but does pretty well in the other five cases. So which is the forest, and which are the trees?

    More recently, I’ve looked into this very subject with Joe Wolf. The new “ultrafaint” dwarfs are much worse for MOND than Draco and Ursa Minor. I was ready to declare MOND dead myself because of this. Then I thought I should check the literature one last time, and discovered that Brada & Milgrom had in fact discussed how tidal effects (which are stronger in MOND) could plausibly cause the failing Joe and I were seeing. Indeed, they quantified the point at which the apparent failure should set in, and we found that is exactly where it does set in. So what I initially thought was a clear falsification is not.

    As for the press, it is a curious spin. In my initial submission to PRL all I said was “here is a specific prediction of a hypothesis, MOND, and geez, it works surprisingly well.” It wasn’t just the reporters who asked about the implications for dark matter, it was also (quite reasonably) the referees. As Ben notes above, that MOND works even to the extent it does poses a fine-tuning problem for dark matter models.

    Much of the evidence that we often point to for dark matter is ambiguous. More properly, we should say there is clear evidence for mass discrepancies. What you see plus Newton does not explain the data. So either there is dark matter, or we need to modify Newton. Like yourself and many other scientists, I am more comfortable with the former approach. I have noticed, however, that the universe does not seem too concerned about my personal comfort zone. If it were, it would stop handing me results that have MOND written all over them just as clearly as you say the CMB has dark matter written all over it.

    If we’re right about dark matter, why does MOND get any prediction right at all?
    I’m open to an explanation for this in the conventional context. Indeed, I have spent an enormous amount of my research time trying to come up with one myself. So far I have failed. That doesn’t mean it is impossible, but I can say it is a lot harder than most scientists seem to realize. Usually people invoke “feedback,” but this has become a code word for excusing anything we don’t understand. (Remember step 2 of that old cartoon “then a miracle occurs”?) Maybe it will. But please forgive me if I require a somewhat higher standard of proof than faith that what works at cosmological scales must inevitably work for galaxies.

    Indeed, you mention that it is not admirable to “hang onto a theory because [you] want to believe it.” I could not agree more! We must hold ourselves to very high standards of intellectual honesty. That’s how I got involved in this issue in the first place. I believed in cold dark matter as much as you obviously do. But MOND cropped up in my data. Should I deny that? Should I not report it?

    What I should do is consider the other evidence. I was already familiar with dark matter, but I had to learn a lot about MOND. I have. I’ve written lengthy reviews about it, long ago addressing many of the points above – though not always favorably to either theory. I can tell the story from either side, both positive and negative, warts and all. Indeed, I decided that to be fair, I had to work as hard on behalf of MOND as I work on behalf of ΛCDM.

    Have you tried that?

  18. Sean says:

    Hi Stacy–

    Thanks for responding. I’m not sure what it means to “work on behalf” of a theory. I’ve certainly tried to be as fair as I can be in evaluating the theories. But I haven’t spent as much time thinking about MOND as I have thinking about dark matter, since one theory is ruled out by the data and the other is not.

    I’m very happy to point to the circumstances in which the MOND phenomenology is successful, and argue that we should try to understand it. People are working on that. But the time is long past when we should take seriously the idea that MOND replaces dark matter. It’s the implication otherwise in the news stories that I was objecting to.

    Nobody says you shouldn’t report on what you find; that’s just a straw man.

    It would have been great if, in your press release, there had been something along the lines of “of course we have more than sufficient evidence to conclude that dark matter exists, we’re just trying to understand how it works and what else might be going on.”

  19. onymous says:

    Is there any nice place for a particle physicist without a lot of astrophysics background to read a little about the “fine-tuning problem” that some in this thread claim that MOND phenomenology poses for dark matter models? This has something to do with the physics of galaxy formation, right? Naively I would think that different kinds of plausible dark matter (WIMPs, axions, gravitinos, etc) could have different effects on galaxy formation, and that surely people would have tried to study this and see if consistency with “MOND phenomenology” (meaning, what, things like the Tully-Fisher relation?) prefers some models over others. But if such things exist, it at least doesn’t seem to be part of the folklore among particle physicists. Can it really be the case that any realistic dark matter candidate (regardless of mass, interactions, etc) is equally tuned with respect to the phenomenological facts that fit MOND?

  20. Sean says:

    onymous — Roughly speaking, most viable DM models are astrophysically equivalent. They’re cold, they’re non-interacting, and their perturbations are adiabatic. As far as galaxy formation and dynamics are concerned, they’re indistinguishable.

    The “fine-tuning problems” are (perfectly reasonable) questions about the relationship between the dark matter distribution and the baryon distribution. They have nothing to do with particle properties.

    Of course you can consider interacting dark matter models as well, but they’re less minimal, and the evidence in favor of them is sketchy. (It’s very likely that DM has some non-gravitational interactions, but they may or may not be relevant for astrophysics.)

  21. Pingback: Kort astronieuws van de afgelopen week | Astroblogs

  22. Shantanu says:

    onymous, see this paper. esp figure 4 (and also fig2)
    Also the only papers which discuss about differences in effects of WIMP vs axion dark matter is
    http://arxiv.org/abs/astro-ph/0211325 (and you can references to it)

  23. Bud says:

    Until they can fit dark matter into Einstein’s relativity it will remain an unproven speculation, not even a scientific theory.
    All matter must be convertible to energy, else it is not matter.
    Let’s all play by the rules
    James E Gambrell

  24. TimG says:

    Bud (post #23), you have no idea what you’re talking about. Dark matter is in no way in conflict with the theory of relativity. Moreover, what Einstein said was that the mass of a body is equal to its energy content, not that matter is “convertible into energy” as if energy is some sort of special substance. Energy is a property of matter and radiation, and no one doubts that whatever interactions dark matter experiences, these will produce matter and radiation with an equivalent energy content to the dark matter you started with — this is just conservation of energy.

    The fact that Sean can list multiple empirical observations in support of dark matter and you respond by calling it “unproven speculation” suggests you haven’t even been paying attention.

  25. Bud says:

    TimG, I respect your right to have an opinion and to express it but until you understand that energy is the first cause of all that is you will be one of the blind that is being led by the blind.