Something that Sabine Hossenfelder noted recently on Twitter resonated with me:
This is a very real problem in academia, and I don’t doubt that it is a common feature of many human endeavors. Part of it is just that people don’t know enough to know what they don’t know. That is to say, so much has been written that it can be hard to find the right reference to put any given fever dream promptly to never-ending sleep. However, that’s not the real problem.
The problem is exactly what Sabine says it is. People keep pushing ideas that have been debunked. Why let facts get in the way of a fancy idea?
There are lots of examples of this in my own experience. Indeed, I’ve encountered it so often that I’ve concluded that there is no result so obvious that some bozo won’t conclude exactly the opposite.
I spent a lot of my early career working in the context of non-baryonic dark matter. For a long time, I was enthusiastic about it, but I’ve become skeptical. I continue to work on it, just in case. But I soured on it for good reasons, reasons I have explained repeatedly in exhaustive detail. Some people appreciate this level of detail, but most do not. This is the sort of thing Sabine is talking about. People don’t engage seriously with these problems.
Maybe I’m wrong to be skeptical of dark matter? I could accept that – one cannot investigate this wide universe in which we find ourselves without sometimes coming to the wrong conclusions. Has it been demonstrated that the concerns I raised were wrong? No. Rather than grapple with the problems raised, people have simply ignored them – or worse, assert that they aren’t problems at all without demonstrating anything of the sort. Heck, I’ve even seen people take lists of problems and spin them as virtues.
To give one very quick example, consider the physical interpretation of the Tully-Fisher relation. This has varied over time, and there are many flavors. But usually it is supposed that the luminosity is set by the stellar mass, and the rotation speed by the dark matter mass. If we (reasonably) presume that the stellar mass is proportional to the dark mass, viola – Tully-Fisher. This all sounds perfectly plausible, so most people don’t think any harder about it. No problem at al.
Well, one small problem: this explanation does not work. The velocity is not uniquely set by the dark matter halo. In the range of radii accessible to measurement, the contribution of the baryonic mass is non-negligible in high surface brightness galaxies. If that sounds a little technical, it is. One has to cope at this level to play in the sandbox.
Once we appreciate that we cannot just ignore the baryons, explaining Tully-Fisher becomes a lot harder – in particular, the absence of surface brightness residuals. Higher surface brightness galaxies should rotate faster at a given mass, but they don’t. The easy way to fix this is to suppose that the baryonic mass is indeed negligible, but this leads straight to a contradiction with the diversity of rotation curves following from the central density relation. The kinematics know about the shape of the baryonic mass distribution, not just its total. Solving all these problems simultaneously becomes a game of cosmic whack-a-mole: fixing one aspect of the problem makes another worse. All too often, people are so focused on one aspect of a problem that they don’t realize that their fix comes at the expense of something else. It’s like knocking a hole in one side of a boat to obtain material to patch a hole in the other side of the same boat.
Except they are sure. Problem solved! is what people want to hear, so that’s what they hear. Nobody bothers to double check whether the “right” answer in indeed right when it agrees with their preconceptions. And there is always someone willing to make that assertion.
Kuhn noted that as paradigms reach their breaking point, there is a divergence of opinions between scientists about what the important evidence is, or what even counts as evidence. This has come to pass in the debate over whether dark matter or modified gravity is a better interpretation of the acceleration discrepancy problem. It sometimes feels like we’re speaking about different topics in a different language. That’s why I split the diagram version of the dark matter tree as I did:
Evidence indicating acceleration discrepancies in the universe and various flavors of hypothesized solutions.
Astroparticle physicists seem to be well-informed about the cosmological evidence (top) and favor solutions in the particle sector (left). As more of these people entered the field in the ’00s and began attending conferences where we overlapped, I recognized gaping holes in their knowledge about the dynamical evidence (bottom) and related hypotheses (right). This was part of my motivation to develop an evidence-based course1 on dark matter, to try to fill in the gaps in essential knowledge that were obviously being missed in the typical graduate physics curriculum. Though popular on my campus, not everyone in the field has the opportunity to take this course. It seems that the chasm has continued to grow, though not for lack of attempts at communication.
Part of the problem is a phase difference: many of the questions that concern astroparticle physicists (structure formation is a big one) were addressed 20 years ago in MOND. There is also a difference in texture: dark matter rarely predicts things but always explains them, even if it doesn’t. MOND often nails some predictions but leaves other things unexplained – just a complete blank. So they’re asking questions that are either way behind the curve or as-yet unanswerable. Progress rarely follows a smooth progression in linear time.
I have become aware of a common construction among many advocates of dark matter to criticize “MOND people.” First, I don’t know what a “MOND person” is. I am a scientist who works on a number of topics, among them both dark matter and MOND. I imagine the latter makes me a “MOND person,” though I still don’t really know what that means. It seems to be a generic straw man. Users of this term consistently paint such a luridly ridiculous picture of what MOND people do or do not do that I don’t recognize it as a legitimate depiction of myself or of any of the people I’ve met who work on MOND. I am left to wonder, who are these “MOND people”? They sound very bad. Are there any here in the room with us?
I am under no illusions as to what these people likely say when I am out of ear shot. Someone recently pointed me to a comment on Peter Woit’s blog that I would not have come across on my own. I am specifically named. Here is a screen shot:
This concisely pinpoints where the field2 is at, both right and wrong. Let’s break it down.
let me just remind everyone that the primary reason to believe in the phenomenon of cold dark matter is the very high precision with which we measure the CMB power spectrum, especially modes beyond the second acoustic peak
This is correct, but it is not the original reason to believe in CDM. The history of the subject matters, as we already believed in CDM quite firmly before any modes of the acoustic power spectrum of the CMB were measured. The original reasons to believe in cold dark matter were (1) that the measured, gravitating mass density exceeds the mass density of baryons as indicated by BBN, so there is stuff out there with mass that is not normal matter, and (2) large scale structure has grown by a factor of 105 from the very smooth initial condition indicated initially by the nondetection of fluctuations in the CMB, while normal matter (with normal gravity) can only get us a factor of 103 (there were upper limits excluding this before there was a detection). Structure formation additionally imposes the requirement that whatever the dark matter is moves slowly (hence “cold”) and does not interact via electromagnetism in order to evade making too big an impact on the fluctuations in the CMB (hence the need, again, for something non-baryonic).
When cold dark matter became accepted as the dominant paradigm, fluctuations in the CMB had not yet been measured. The absence of observable fluctuations at a larger level sufficed to indicate the need for CDM. This, together with Ωm > Ωb from BBN (which seemed the better of the two arguments at the time), sufficed to convince me, along with most everyone else who was interested in the problem, that the answer had3 to be CDM.
This all happened before the first fluctuations were observed by COBE in 1992. By that time, we already believed firmly in CDM. The COBE observations caused initial confusion and great consternation – it was too much! We actually had a prediction from then-standard SCDM, and it had predicted an even lower level of fluctuations than what COBE observed. This did not cause us (including me) to doubt CDM (thought there was one suggestion that it might be due to self-interacting dark matter); it seemed a mere puzzle to accommodate, not an anomaly. And accommodate it we did: the power in the large scale fluctuations observed by COBE is part of how we got LCDM, albeit only a modest part. A lot of younger scientists seem to have been taught that the power spectrum is some incredibly successful prediction of CDM when in fact it has surprised us at nearly every turn.
As I’ve related here before, it wasn’t until the end of the century that CMB observations became precise enough to provide a test that might distinguish between CDM and MOND. That test initially came out in favor of MOND – or at least in favor of the absence of dark matter: No-CDM, which I had suggested as a proxy for MOND. Cosmologists and dark matter advocates consistently omit this part of the history of the subject.
I had hoped that cosmologists would experience the same surprise and doubt and reevaluation that I had experienced when MOND cropped up in my own data when it cropped up in theirs. Instead, they went into denial, ignoring the successful prediction of the first-to-second peak amplitude ratio, or, worse, making up stories that it hadn’t happened. Indeed, the amplitude of the second peak was so surprising that the first paper to measure it omitted mention of it entirely. Just didn’t talk about it, let alone admit that “Gee, this crazy prediction came true!” as I had with MOND in LSB galaxies. Consequently, I decided that it was better to spend my time working on topics where progress could be made. This is why most of my work on the CMB predates “modes beyond the second peak” just as our strong belief in CDM also predated that evidence. Indeed, communal belief in CDM was undimmed when the modes defining the second peak were observed, despite the No-CDM proxy for MOND being the only hypothesis to correctly predict it quantitatively a priori.
That said, I agree with clayton’s assessment that
CDM thinks [the second and third peak] should be about the same
That this is the best evidence now is both correct and a much weaker argument than it is made out to be. It sounds really strong, because a formal fit to the CMB data require a dark matter component at extremely high confidence – something approaching 100 sigma. This analysis assumes that dark matter exist. It does not contemplate that something else might cause the same effect, so all it really does, yet again, is demonstrate that General Relativity cannot explain cosmology when restricted to the material entities we concretely know to exist.
Given the timing, the third peak was not a strong element of my original prediction, as we did not yet have either a first or second peak. We hadn’t yet clearly observed peaks at all, so what I was doing was pretty far-sighted, but I wasn’t thinking that far ahead. However, the natural prediction for the No-CDM picture I was considering was indeed that the third peak should be lower than the second, as I’ve discussed before.
The No-CDM model (blue line) that correctly predicted the amplitude of the second peak fails to predict that of the third. Data from the Planck satellite; model line from McGaugh (2004); figure from McGaugh (2015).
In contrast, in CDM, the acoustic power spectrum of the CMB can do a wide variety of things:
Acoustic power spectra calculated for the CMB for a variety of cosmic parameters. From Dodelson & Hu (2002).
Given the diversity of possibilities illustrated here, there was never any doubt that a model could be fit to the data, provided that oscillations were observed as expected in any of the theories under consideration here. Consequently, I do not find fits to the data, though excellent, to be anywhere near as impressive as commonly portrayed. What does impress me is consistency with independent data.
What impresses me even more are a priori predictions. These are the gold standard of the scientific method. That’s why I worked my younger self’s tail off to make a prediction for the second peak before the data came out. In order to make a clean test, you need to know what both theories predict, so I did this for both LCDM and No-CDM. Here are the peak ratios predicted before there were data to constrain them, together with the data that came after:
The ratio of the first-to-second (left) and second-to-third peak (right) amplitude ratio in LCDM (red) and No-CDM (blue) as predicted by Ostriker & Steinhardt (1995) and McGaugh (1999). Subsequent data as labeled.
The left hand panel shows the predicted amplitude ratio of the first-to-second peak, A1:2. This is the primary quantity that I predicted for both paradigms. There is a clear distinction between the predicted bands. I was not unique in my prediction for LCDM; the same thing can be seen in other contemporaneous models. All contemporaneous models. I was the only one who was not surprised by the data when they came in, as I was the only one who had considered the model that got the prediction right: No-CDM.
The same No-CDM model fails to correctly predict the second-to-third peak ratio, A2:3. It is, in fact, way off, while LCDM is consistent with A2:3, just as Clayton says. This is a strong argument against No-CDM, because No-CDM makes a clear and unequivocal prediction that it gets wrong. Clayton calls this
a stone-cold, qualitative, crystal clear prediction of CDM
which is true. It is also qualitative, so I call it weak sauce. LCDM could be made to fit a very large range of A2:3, but it had already got A1:2 wrong. We had to adjust the baryon densityoutside the allowed range in order to make it consistent with the CMB data. The generous upper limit that LCDM might conceivably have predicted in advance of the CMB data was A1:2 < 2.06, which is still clearly less than observed. For the first years of the century, the attitude was that BBN had been close, but not quite right – preference being given to the value needed to fit the CMB. Nowadays, BBN and the CMB are said to be in great concordance, but this is only true if one restricts oneself to deuterium measurements obtained after the “right” answer was known from the CMB. Prior to that, practically all of the measurements for all of the important isotopes of the light elements, deuterium, helium, and lithium, all concurred that the baryon density Ωbh2 < 0.02, with the consensus value being Ωbh2 = 0.0125 ± 0.0005. This is barely half the value subsequently required to fit the CMB (Ωbh2 = 0.0224 ± 0.0001). But what’s a factor of two among cosmologists? (In this case, 4 sigma.)
Taking the data at face value, the original prediction of LCDM was falsified by the second peak. But, no problem, we can move the goal posts, in this case by increasing the baryon density. The successful prediction of the third peak only comes after the goal posts have been moved to accommodate the second peak. Citing only the comparable size of third peak to the second while not acknowledging that the second was too small elides the critical fact that No-CDM got something right, a priori, that LCDM did not. No-CDM failed only after LCDM had already failed. The difference is that I acknowledge its failure while cosmologists elide this inconvenient detail. Perhaps the second peak amplitude is a fluke, but it was a unique prediction that was exactly nailed and remains true in all subsequent data. That’s a pretty remarkable fluke4.
LCDM wins ugly here by virtue of its flexibility. It has greater freedom to fit the data – any of the models in the figure of Dodelson & Hu will do. In contrast. No-CDM is the single blue line in my figure above, and nothing else. Plausible variations in the baryon density make hardly any difference: A1:2 has to have the value that was subsequently observed, and no other. It passed that test with flying colors. It flunked the subsequent test posed by A2:3. For LCDM this isn’t even a test, it is an exercise in fitting the data with a model that has enough parameters5 to do so.
In those days, when No-CDM was the only correct a priori prediction, I would point out to cosmologists that it had got A1:2 right when I got the chance (which was rarely: I was invited to plenty of conferences in those days, but none on the CMB). The typical reaction was usually outright denial6 though sometimes it warranted a dismissive “That’s not a MOND prediction.” The latter is a fair criticism. No-CDM is just General Relativity without CDM. It represented MOND as a proxy under the ansatz that MOND effects had not yet manifested in a way that affected the CMB. I expected that this ansatz would fail at some point, and discussed some of the ways that this should happen. One that’s relevant today is that galaxies form early in MOND, so reionization happens early, and the amplitude of gravitational lensing effects is amplified. There is evidence for both of these now. What I did not anticipate was a departure from a damping spectrum around L=600 (between the second and third peaks). That’s a clear deviation from the prediction, which falsifies the ansatz but not MOND itself. After all, they were correct in noting that this wasn’t a MOND prediction per se, just a proxy. MOND, like Newtonian dynamics before it, is relativity adjacent, but not itself a relativistic theory. Neither can explain the CMB on their own. If you find that an unsatisfactory answer, imagine how I feel.
The same people who complained then that No-CDM wasn’t a real MOND prediction now want to hold MOND to the No-CDM predicted power spectrum and nothing else. First it was the second peak isn’t a real MOND prediction! then when the third peak was observed it became no way MOND can do this! This isn’t just hypocritical, it is bad science. The obvious way to proceed would be to build on the theory that had the greater, if incomplete, predictive success. Instead, the reaction has consistently been to cherry-pick the subset of facts that precludes the need for serious rethinking.
This brings us to sociology, so let’s examine some more of what Clayton has to say:
Any talk I’ve ever seen by McGaugh (or more exotic modified gravity people like Verlinde) elides this fact, and they evade the questions when I put my hand up to ask. I have invited McGaugh to a conference before specifically to discuss this point, and he just doesn’t want to.
There is so much to unpack here, I hardly know where to start. By saying I “elide this fact” about the qualitatively equality of the second and third peak, Clayton is basically accusing me of lying by omission. This is pretty rich coming from a community that consistently elides the history I relate above, and never addresses the question raised by MOND’s predictive power.
Intellectual honesty is very important to me – being honest that MOND predicted what I saw in low surface brightness where my own prediction was wrong is what got me into this mess in the first place. It would have been vastly more convenient to pretend that I never heard of MOND (at first I hadn’t7) and act like that never happened. That would be an lie of omission. It would be a large lie, a lie that denies an important aspect of how the world works (what we’re supposed to uncover through science), the sort of lie that cleric Paul Gerhardt may have had in mind when he said
When a man lies, he murders some part of the world.
Clayton is, in essence, accusing me of exactly that by failing to mention the CMB in talks he has seen. That might be true – I give a lot of talks. He hasn’t been to most of them, and I usually talk about things I’ve done more recently than 2004. I’ve commented explicitly on this complaint before –
There’s only so much you can address in a half hour talk. [This is a recurring problem. No matter what I say, there always seems to be someone who asks “why didn’t you address X?” where X is usually that person’s pet topic. Usually I could do so, but not in the time allotted.]
– so you may appreciate my exasperation at being accused of dishonesty by someone whose complaint is so predictable that I’ve complained before about people who make this complaint. I’m only human – I can’t cover all subjects for all audiences every time all the time. Moreover, I do tend to choose to discuss subjects that may be news to an audience, not simply reprise the greatest hits they want to hear. Clayton obviously knows about the third peak; he doesn’t need to hear about it from me. This is the scientific equivalent of shouting Freebird!at a concert.
It isn’t like I haven’t talked about it. I have been rigorously honest about the CMB, and certainly have not omitted mention of the third peak. Here is a comment from February 2003 when the third peak was only tentatively detected:
Page et al. (2003) do not offer a WMAP measurement of the third peak. They do quote a compilation of other experiments by Wang et al. (2003). Taking this number at face value, the second to third peak amplitude ratio is A2:3 = 1.03 +/- 0.20. The LCDM expectation value for this quantity was 1.1, while the No-CDM expectation was 1.9. By this measure, LCDM is clearly preferable, in contradiction to the better measured first-to-second peak ratio.
the Boomerang data and the last credible point in the 3-year WMAP data both have power that is clearly in excess of the no-CDM prediction. The most natural interpretation of this observation is forcing by a mass component that does not interact with photons, such as non-baryonic cold dark matter.
There are lots like this, including my review for CJP and this talk given at KITP where I had been asked to explicitly take the side of MOND in a debate format for an audience of largely particle physicists. The CMB, including the third peak, appears on the fourth slide, which is right up front, not being elided at all. In the first slide, I tried to encapsulate the attitudes of both sides:
I did the same at a meeting in Stony Brook where I got a weird vibe from the audience; they seemed to think I was lying about the history of the second peak that I recount above. It will be hard to agree on an interpretation if we can’t agree on documented historical facts.
More recently, this image appears on slide 9 of this lecture from the cosmology course I just taught (Fall 2022):
I recognize this slide from talks I’ve given over the past five plus years; this class is the most recent place I’ve used it, not the first. On some occasions I wrote “The 3rd peak is the best evidence for CDM.” I do not recall which all talks I used this in; many of them were likely colloquia for physics departments where one has more time to cover things than in a typical conference talk. Regardless, these apparently were not the talks that Clayton attended. Rather than it being the case that I never address this subject, the more conservative interpretation of the experience he relates would be that I happened not to address it in the small subset of talks that he happened to attend.
But do go off, dude: tell everyone how I never address this issue and evade questions about it.
I have been extraordinarily patient with this sort of thing, but I confess to a great deal of exasperation at the perpetual whataboutism that many scientists engage in. It is used reflexively to shut down discussion of alternatives: dark matter has to be right for this reason (here the CMB); nothing else matters (galaxy dynamics), so we should forbid discussion of MOND. Even if dark matter proves to be correct, the CMB is being used an excuse to not address the question of the century: why does MOND get so many predictions right? Any scientist with a decent physical intuition who takes the time to rub two brain cells together in contemplation of this question will realize that there is something important going on that simply invoking dark matter does not address.
In fairness to McGaugh, he pointed out some very interesting features of galactic DM distributions that do deserve answers. But it turns out that there are a plurality of possibilities, from complex DM physics (self interactions) to unmodelable SM physics (stellar feedback, galaxy-galaxy interactions). There are no such alternatives to CDM to explain the CMB power spectrum.
Thanks. This is nice, and why I say it would be easier to just pretend to never have heard of MOND. Indeed, this succinctly describes the trajectory I was on before I became aware of MOND. I would prefer to be recognized for my own work – of whichthereisplenty – than an association with a theory that is not my own – an association that is born of honestly reporting a surprising observation. I find my reception to be more favorable if I just talk about the data, but what is the point of taking data if we don’t test the hypotheses?
I have gone to great extremes to consider all the possibilities. There is not a plurality of viable possibilities; most of these things do not work. The specific ideas that are cited here are known not work. SIDM apears to work because it has more free parameters than are required to describe the data. This is a common failing of dark matter models that simply fit some functional form to observed rotation curves. They can be made to fit the data, but they cannot be used to predict the way MOND can.
Feedback is even worse. Never mind the details of specific feedback models, and think about what is being said here: the observations are to be explained by “unmodelable [standard model] physics.” This is a way of saying that dark matter claims to explain the phenomena while declining to make a prediction. Don’t worry – it’ll work out! How can that be considered better than or even equivalent to MOND when many of the problems we invoke feedback to solve are caused by the predictions of MOND coming true? We’re just invoking unmodelable physics as a deus ex machina to make dark matter models look like something they are not. Are physicists straight-up asserting that it is better to have a theory that is unmodelable than one that makes predictions that come true?
Returning to the CMB, are there no “alternatives to CDM to explain the CMB power spectrum”? I certainly do not know how to explain the third peak with the No-CDM ansatz. For that we need a relativistic theory, like Beklenstein‘s TeVeS. This initially seemed promising, as it solved the long-standing problem of gravitational lensing in MOND. However, it quickly became clear that it did not work for the CMB. Nevertheless, I learned from this that there could be more to the CMB oscillations than allowed by the simple No-CDM ansatz. The scalar field (an entity theorists love to introduce) in TeVeS-like theories could play a role analogous to cold dark matter in the oscillation equations. That means that what I thought was a killer argument against MOND – the exact same argument Clayton is making – is not as absolute as I had thought.
Writing down a new relativistic theory is not trivial. It is not what I do. I am an observational astronomer. I only play at theory when I can’t get telescope time.
Comic from the Far Side by Gary Larson.
So in the mid-00’s, I decided to let theorists do theory and started the first steps in what would ultimately become the SPARC database (it took a decade and a lot of effort by Jim Schombert and Federico Lelli in addition to myself). On the theoretical side, it also took a long time to make progress because it is a hard problem. Thanks to work by Skordis & Zlosnik on a theory they [now] call AeST8, it is possible to fit the acoustic power spectrum of the CMB:
I consider this to be a demonstration, not necessarily the last word on the correct theory, but hopefully an iteration towards one. The point here is that it is possible to fit the CMB. That’s all that matters for our current discussion: contrary to the steady insistence of cosmologists over the past 15 years, CDM is not the only way to fit the CMB. There may be other possibilities that we have yet to figure out. Perhaps even a plurality of possibilities. This is hard work and to make progress we need a critical mass of people contributing to the effort, not shouting rubbish from the peanut gallery.
As I’ve done before, I like to take the language used in favor of dark matter, and see if it also fits when I put on a MOND hat:
As a galaxy dynamicist, let me just remind everyone that the primary reason to believe in MOND as a physical theory and not some curious dark matter phenomenology is the very high precision with which MOND predicts, a priori, the dynamics of low-acceleration systems, especially low surface brightness galaxies whose kinematics were practically unknown at the time of its inception. There is a stone-cold, quantitative, crystal clear prediction of MOND that the kinematics of galaxies follows uniquely from their observed baryon distributions. This is something CDM profoundly and irremediably gets wrong: it predicts that the dark matter halo should have a central cusp9 that is not observed, and makes no prediction at all for the baryon distribution, let alone does it account for the detailed correspondence between bumps and wiggles in the baryon distribution and those in rotation curves. This is observed over and over again in hundreds upon hundreds of galaxies, each of which has its own unique mass distribution so that each and every individual case provides a distinct, independent test of the hypothesized force law. In contrast, CDM does not even attempt a comparable prediction: rather than enabling the real-world application to predict that this specific galaxy will have this particular rotation curve, it can only refer to the statistical properties of galaxy-like objects formed in numerical simulations that resemble real galaxies only in the abstract, and can never be used to directly predict the kinematics of a real galaxy in advance of the observation – an ability that has been demonstrated repeatedly by MOND. The simple fact that the simple formula of MOND is so repeatably correct in mapping what we see to what we get is to me the most convincing way to see that we need a grander theory that contains MOND and exactly MOND in the low acceleration limit, irrespective of the physical mechanism by which this is achieved.
That is stronger language than I would ordinarily permit myself. I do so entirely to show the danger of being so darn sure. I actually agree with clayton’s perspective in his quote; I’m just showing what it looks like if we adopt the same attitude with a different perspective. The problems pointed out for each theory are genuine, and the supposed solutions are not obviously viable (in either case). Sometimes I feel like we’re up the proverbial creek without a paddle. I do not know what the right answer is, and you should be skeptical of anyone who is sure that he does. Being sure is the sure road to stagnation.
1It may surprise some advocates of dark matter that I barely touch on MOND in this course, only getting to it at the end of the semester, if at all. It really is evidence-based, with a focus on the dynamical evidence as there is a lot more to this than seems to be appreciated by most physicists*. We also teach a course on cosmology, where students get the material that physicists seem to be more familiar with.
*I once had a colleague who was is a physics department ask how to deal with opposition to developing a course on galaxy dynamics. Apparently, some of the physicists there thought it was not a rigorous subject worthy of an entire semester course – an attitude that is all too common. I suggested that she pointedly drop the textbook of Binney & Tremaine on their desks. She reported back that this technique proved effective.
2I do not know who clayton is; that screen name does not suffice as an identifier. He claims to have been in contact with me at some point, which is certainly possible: I talk to a lot of people about these issues. He is welcome to contact me again, though he may wish to consider opening with an apology.
3One of the hardest realizations I ever had as a scientist was that both of the reasons (1) and (2) that I believed to absolutely require CDM assumed that gravity was normal. If one drops that assumption, as one must to contemplate MOND, then these reasons don’t require CDM so much as they highlight that something is very wrong with the universe. That something could be MOND instead of CDM, both of which are in the category of who ordered that?
4In the early days (late ’90s) when I first started asking why MOND gets any predictions right, one of the people I asked was Joe Silk. He dismissed the rotation curve fits of MOND as a fluke. There were 80 galaxies that had been fit at the time, which seemed like a lot of flukes. I mention this because one of the persistent myths of the subject is that MOND is somehow guaranteed to magically fit rotation curves. Erwin de Blok and I explicitly showed that this was not true in a 1998 paper.
5I sometimes hear cosmologists speak in awe of the thousands of observed CMB modes that are fit by half a dozen LCDM parameters. This is impressive, but we’re fitting a damped and driven oscillation – those thousands of modes are not all physically independent. Moreover, as can be seen in the figure from Dodelson & Hu, some free parameters provide more flexibility than others: there is plenty of flexibility in a model with dark matter to fit the CMB data. Only with the Planck data do minortensions arise, the reaction to which is generally to add more free parameters, like decoupling the primordial helium abundance from that of deuterium, which is anathema to standard BBN so is sometimes portrayed as exciting, potentially new physics.
For some reason, I never hear the same people speak in equal awe of the hundreds of galaxy rotation curves that can be fit by MOND with a universal acceleration scale and a single physical free parameter, the mass-to-light ratio. Such fits are over-constrained, and every single galaxy is an independent test. Indeed, MOND can predict rotation curves parameter-free in cases where gas dominates so that the stellar mass-to-light ratio is irrelevant.
How should we weigh the relative merit of these very different lines of evidence?
6On a number of memorable occasions, people shouted “No you didn’t!” On smaller number of those occasions (exactly two), they bothered to look up the prediction in the literature and then wrote to apologize and agree that I had indeed predicted that.
7If you read this paper, part of what you will see is me being confused about how low surface brightness galaxies could adhere so tightly to the Tully-Fisher relation. They should not. In retrospect, one can see that this was a MOND prediction coming true, but at the time I didn’t know about that; all I could see was that the result made no sense in the conventional dark matter picture.
Some while after we published that paper, Bob Sanders, who was at the same institute as my collaborators, related to me that Milgrom had written to him and asked “Do you know these guys?”
8Initially they had called it RelMOND, or just RMOND. AeST stands for Aether-Scalar-Tensor, and is clearly a step along the lines that Bekenstein made with TeVeS.
In addition to fitting the CMB, AeST retains the virtues of TeVeS in terms of providing a lensing signal consistent with the kinematics. However, it is not obvious that it works in detail – Tobias Mistele has a brand new paper testing it, and it doesn’t look good at extremely low accelerations. With that caveat, it significantly outperforms extant dark matter models.
There is an oft-repeated fallacy that comes up any time a MOND-related theory has a problem: “MOND doesn’t work therefore it has to be dark matter.” This only ever seems to hold when you don’t bother to check what dark matter predicts. In this case, we should but don’t detect the edge of dark matter halos at higher accelerations than where AeST runs into trouble.
9Another question I’ve posed for over a quarter century now is what would falsify CDM? The first person to give a straight answer to this question was Simon White, who said that cusps in dark matter halos were an ironclad prediction; they had to be there. Many years later, it is clear that they are not, but does anyone still believe this is an ironclad prediction? If it is, then CDM is already falsified. If it is not, then what would be? It seems like the paradigm can fit any surprising result, no matter how unlikely a priori. This is not a strength, it is a weakness. We can, and do, add epicycle upon epicycle to save the phenomenon. This has been my concern for CDM for a long time now: not that it gets some predictions wrong, but that it can apparently never get a prediction so wrong that we can’t patch it up, so we can never come to doubt it if it happens to be wrong.
We are visual animals. What we see informs our perception of the world, so it often helps to make a sketch to help conceptualize difficult material. When first confronted with MOND phenomenology in galaxies that I had been sure were dark matter dominated, I made a sketch to help organize my thoughts. Here is a scan of the original dark matter tree that I drew on a transparency (pre-powerpoint!) in 1995:
The original dark matter tree.
At the bottom are the roots of the problem: the astronomical evidence for mass discrepancies. From these grow the trunk, which splits into categories of possible solutions, which in turn branch into ever more specific possibilities. Most of these items were already old news at the time: I was categorizing, not inventing. Indeed, some things have been rebranded over time without changing all that much, with strange nuggets now being known as macros (a generalization to describe dark matter candidates of nuclear density) and asymmetric gravity becoming MOG. The more things change, the more they stay the same.
I’ve used this picture many times in talks, both public and scientific. It helps to focus the mind. I updated it for the 2012 review Benoit Famaey wrote (see our Fig. 1), but I don’t think I really improved on the older version, which Don Lincoln had adapted for the cover illustration of an issue of Physics Teacher (circa 2013), with some embellishment by their graphic artists. That’s pretty good, but I prefer my original.
Though there are no lack of buds on the tree, there have certainly been more ideas for dark matter candidates over the past thirty years, so I went looking to see if someone had attempted a similar exercise to categorize or at least corral all the ideas people have considered. Tim Tait made one such figure, but you have to already be an expert to make any sense of it, it being a sort of Venn diagram of the large conceptual playground that is theoretical particle physics.
This is nice: well organized and pleasantly symmetric, and making good use of color to distinguish different types of possibilities. One can recognize many of the same names from the original tree like MACHOs and MOND, along with newer, related entities like Macros and TeVeS. Interestingly, WIMPs are not mentioned, despite dominating the history of the field. They are subsumed under supersymmetry, which is now itself just a sub-branch of weak-scale possibilities rather than the grand unified theory of manifest inevitability that it was once considered to be. It is a sign of how far we have come that the number one candidate, the one that remains the focus of dozens of large experiments, doesn’t even come up by name. It is also a sign of how far we have yet to go that it seems preferable to many to invent new dark matter candidates than take seriously alternatives that have had much greater predictive success.
A challenge one faces in doing this exercise is to decide which candidates deserve mention, and which are just specific details that should be grouped under some more major branch. As a practical matter, it is impossible to wedge everything in, nor does every wild idea we’ve ever thought up deserve equal mention: Kaluza-Klein dark matter is not a coequal peer to WIMPs. But how do we be fair about making that call? It may not be possible.
I wanted to see how the new diagram mapped to the old tree, so I chopped it up and grafted each piece onto the appropriate branch of the original tree:
New blossoms on the old dark matter tree.
This works pretty well. It looks like the tree has blossomed with more ideas, which it has. There are more possibilities along well-established branches, and entirely new branches that I could only anticipate with question marks that allowed for the possibility of things we had not yet thought up. The tree is getting bushy.
Ultimately, the goal is not to have an ever bushier tree, but rather the opposite: we want to find the right answer. As an experimentalist, one wants to either detect or exclude specific dark matter candidates. As an scientist, I want to apply the wealth of observational knowledge we have accumulated like a chainsaw in the hands of an overzealous gardener to hack off misleading branches until the tree has been pruned down to a single branch, the one (and hopefully only one) correct answer.
As much as I like Bertone & Tait’s hexagonal image, it is very focused on ideas in particle physics. Five of the six branches are various forms of dark matter, while the possibility of modified gravity is grudgingly acknowledged in only one. It is illustrated as a dull grey that is unlike the bright, cheerful colors granted to the various flavors of dark matter candidates. To be sure, there are more ideas for solutions to the mass discrepancy problem from the particle physics than anywhere else, but that doesn’t mean they all deserve equal mention. One looking at this diagram might get the impression that the odds of dark matter:modified gravity are 5:1, which seems at once both biased against the latter and yet considerably more generous than its authors likely intended.
There is no mention at all of the data at the roots of the problem. That is all subsumed in the central DARK MATTER, as if we’re looking down at the top of the tree and recognize that it must have a central trunk, but cannot see its roots. This is indeed an apt depiction of the division between physics and astronomy. Proposed candidates for dark matter have emerged primarily from the particle physics community, which is what the hexagon categorizes. It takes for granted the evidence for dark matter, which is entirely astronomical in nature. This is not a trivial point; I’ve often encountered particle physicists who are mystified that astronomers have the temerity of think they can contribute to the dark matter debate despite 100% (not 90%, nor 99%, nor even 99.9%, but 100%) of the evidence for mass discrepancies stemming from observations of the sky. Apparently, our job was done when we told them we needed something unseen, and we should remain politely quiet while the Big Brains figure it out.
For a categorization of solutions, I suppose it is tolerable if dangerous divorced from the origins of the problem to leave off the evidence. There is another problem with placing DARK MATTER at the center. This is a linguistic problem that raises deep epistemological issues that most scientists working in the field rarely bother to engage with. Words matter; the names we use frame how we think about the problem. By calling it the dark matter problem, we presuppose the answer. A more appropriate term might be mass discrepancy, which was in use for a while by more careful-minded people, but it seems to have fallen into disuse. Dark matter is easier to say and sounds way more cool.
Jacob Bekenstein pointed out that an even better term would be acceleration discrepancy. That’s what we measure, after all. The centripetal acceleration in spiral galaxies exceeds that predicted by the observed distribution of visible matter. Mass is an inference, and a sloppy one at that: dynamical data only constrain the mass enclosed by the last measured point. The total mass of a dark matter halo depends on how far it extends, which we never observe because the darn stuff is invisible. And of course we only infer the existence of dark matter by assuming that the force law is correct. That gravity as taught to us by Einstein and Newton should apply to galaxies seems like a pretty darn good assumption, but it is just that. By calling it the dark matter problem, we make it all about unseen mass and neglect the possibility that the inference might go astray with that first, basic assumption.
So I’ve made a new picture, placing the acceleration discrepancy at the center where it belongs. The astronomical observations that inform the problem are on the vertical axis while the logical possibilities for physics solutions are on the horizontal axis. I’ve been very spare in filling in both: I’m trying to trace the logical possibilities with a minimum of bias and clutter, so I’ve retained some ideas that are pretty well excluded.
For example, on the dark matter side, MACHOs are pretty well excluded at this point, as are most (all?) dark matter candidates composed of Standard Model particles. Normal matter just doesn’t cut it, but I’ve left that sector in as a logical possibility that was considered historically and shouldn’t be forgotten. On the dynamical side, one of the first thoughts is that galaxies are big so perhaps the force law changes at some appropriate scale much large than the solar system. At this juncture, we have excluded all modifications to the force law that are made at a specific length scale.
The acceleration discrepancy diagram.
There are too many lines of observational evidence to do justice to here. I’ve lumped an enormous amount of it into a small number of categorical bins. This is not ideal, but some key points are at least mentioned. I invite the reader to try doing the exercise with pencil and paper. There are serious limits imposed by what you can physically display in a font the eye can read with a complexity limited to that which does not make the head explode. I fear I may already be pushing both.
I have made a split between dynamical and cosmological evidence. These tend to push the interpretation one way or the other, as hinted by the colors. Which way one goes depends entirely on how one weighs rather disparate lines of evidence.
I’ve also placed the things that were known from the outset of the modern dark matter paradigm closer to the center than those that were not. That galaxies and clusters of galaxies needed something more than meets the eye was known, and informed the need for dark matter. That the dynamics of galaxies over a huge range of mass, size, surface brightness, gas fraction, and morphology are organized by a few simple empirical relations was not yet known. The Baryonic Tully-Fisher Relation (BTFR) and the Radial Acceleration Relation (RAR) are critical pieces of evidence that did not inform the construction of the current paradigm, and are not satisfactorily explained by it.
Similarly for cosmology, the non-baryonic cold dark matter paradigm was launched by the observation that the dynamical mass density apparently exceeds that allowed for normal matter by primordial nucleosynthesis. This, together with the need to grow the observed large scale structure from the very smooth initial condition indicated by the cosmic microwave background (CMB), convinced nearly everyone (including myself) that there must be some new form of non-baryonic dark matter particle outside the realm of the Standard Model. Detailed observations of the power spectra of both galaxies and the CMB are important corroborating observations that did not yet exist at the time the idea took hold. We also got our predictions for these things very wrong initially, hence the need to change from Standard CDM to Lambda CDM.
Most of the people I have met who work on dark matter candidates seem to be well informed of cosmological constraints. In contrast, their knowledge of galaxy dynamics often seems to start and end with “rotation curves are flat.” There is quite a lot more to it than that. But, by and large, they stopped listening at “therefore we need dark matter” and were off and running with ideas for what it could be. There is a need to reassess the viability of these ideas in the light of the BTFR and the RAR.
People who work on galaxy dynamics are concerned with the obvious connections between dynamics and the observed stars and are inclined to be suspicious of the cosmological inference requiring non-baryonic dark matter. Over the years, I have repeatedly been approached by eminent dynamicists who have related in hushed tones, less the cosmologists overhear, that the dark matter must be baryonic. I can understand their reticence, since I was, originally, one of those people who they didn’t want to have overhear. Baryonic dark mater was crazy – we need more mass than is allowed by big bang nucleosynthesis! I usually refrained from raising this issue, as I have plenty of reasons to sympathize, and try to be a sympathetic ear even when I don’t. I did bring it up in an extended conversation with Vera Rubin once, who scoffed that the theorists were too clever by half. She reckoned that if she could demonstrate that Ωm = 1 in baryons one day, that they would have somehow fixed nucleosynthesis by the next. Her attitude was well-grounded in experience.
A common attitude among advocates of non-baryonic dark matter is that the power spectrum of the CMB requires its existence. Fits to the data require a non-baryonic component at something like 100 sigma. That’s pretty significant evidence.
The problem with this attitude is that it assumes General Relativity (GR). That’s the theory in which the fits are made. There is, indeed, no doubt that the existence of cold dark matter is required in order to make the fits in the context of GR: it does not work without it. To take this as proof of the existence of cold dark mater is entirely circular logic. Indeed, that we have to invent dark matter as a tooth fairy to save GR might be interpreted as evidence against it, or at least as an indication that there might exist a still more general theory.
Nevertheless, I do have sympathy for the attitude that any idea that is going to work has to explain all the data – including both dynamical and cosmological evidence. Where one has to be careful is to assume that the explanation we currently have is unique – so unique that no other theory could ever conceivably explain it. By that logic, MOND is the only theory that uniquely predicted both the BTFR and the RAR. So if we’re being even-handed, cold dark matter is ruled out by the dynamical relations identified after its invention at least as much as its competitors are excluded by the detailed, later measurement of the power spectrum of the CMB.
If we believe all the data, and hold all theories to the same high standard, none survive. Not a single one. A common approach seems to be to hold one’s favorite theory to a lower standard. I will not dignify that with a repudiation. The challenge with data both astronomical and cosmological, is figuring out what to believe. It has gotten better, but you can’t rely on every measurement being right, or – harder to bear in mind – actually measure what you want it to measure. Do the orbits of gas clouds in spiral galaxies trace the geodesics of test particles in perfectly circular motion? Does the assumption of hydrostatic equilibrium in the intracluster medium (ICM) of clusters of galaxies provide the same tracer of the gravitational potential as dynamics? There is an annoying offset in the acceleration scale measured by the two distinct methods. Is that real, or some systematic? It seems to be real, but it is also suspicious for appearing exactly where the change in method occurs.
The characteristic acceleration scale in extragalactic systems as a function of their observed baryonic mass. This is always close to the ubiquitous scale of 10-10 m/s/s first recognized by Milgrom. There is a persistent offset for clusters of galaxies that occurs where we switch from dynamical to hydrostatic tracers of the potential (Fig. 48 from Famaey & McGaugh 2012).
One will go mad trying to track down every conceivable systematic. Trust me, I’ve done the experiment. So an exercise I like to do is to ask what theory minimizes the amount of data I have to ignore. I spent several years reviewing all the data in order to do this exercise when I first got interested in this problem. To my surprise, it was MOND that did best by this measure, not dark matter. To this date, clusters of galaxies remain the most problematic for MOND in having a discrepant acceleration scale – a real problem that we would not hesitate to sweep under the rug if dark matter suffered it. For example, the offset the EAGLE simulation requires to [sort of] match the RAR is almost exactly the same amplitude as what MOND needs to match clusters. Rather than considering this to be a problem, they apply the required offset and call it natural to have missed by this much.
Most of the things we call evidence for dark matter are really evidence for the acceleration discrepancy. A mental hang up I had when I first came to the problem was that there’s so much evidence for dark matter. That is a misstatement stemming from the linguistic bias I noted earlier. There’s so much evidence for the acceleration discrepancy. I still see professionals struggle with this, often citing results as being contradictory to MOND that actually support it. They seem not to have bothered to check, as I have, and are content to repeat what they heard someone else assert. I sometimes wonder if the most lasting contribution to science made by the dark matter paradigm is as one giant Asch conformity experiment.
If we repeat today the exercise of minimizing the amount of data we have to disbelieve, the theory that fares best is the Aether Scalar Tensor (AeST) theory of Skordis & Zlosnik. It contains MOND in the appropriate limit while also providing an excellent fit to the power spectrum of galaxies and the CMB (see also the updated plots in their paper). Hybrid models struggle to do both while the traditional approach of simply adding mass in new particles does not provide a satisfactory explanation of the MOND phenomenology. They can be excluded unless we indulge in the special pleading that invokes feedback or other ad hoc auxiliary hypotheses. Similarly, more elaborate ideas like self-interacting dark matter were dead on arrival for providing a mechanism to solve the wrong problem: the cores inferred in dark matter halos are merely a symptom of the more general MONDian phenomenology; the proposed solution addresses the underlying disease about as much as a band-aid helps an amputation.
Does that mean AeST is the correct theory? Only in the sense that MOND was the best theory when I first did this exercise in the previous century. The needle has swung back and forth since then, so it might swing again. But I do hope that it is a step in a better direction.
In order to agree on an interpretation, we first have to agree on the facts. Even when we agree on the facts, the available set of facts may admit multiple interpretations. This was an obvious and widely accepted truth early in my career*. Since then, the field has decayed into a haphazardly conceived set of unquestionable absolutes that are based on a large but well-curated subset of facts that gratuitously ignores any subset of facts that are inconvenient.
Sadly, we seem to have entered a post-truth period in which facts are drowned out by propaganda. I went into science to get away from people who place faith before facts, and comfortable fictions ahead of uncomfortable truths. Unfortunately, a lot of those people seem to have followed me here. This manifests as people who quote what are essentially pro-dark matter talking points at me like I don’t understand LCDM, when all it really does is reveal that they are posers** who picked up on some common myths about the field without actually reading the relevant journal articles.
Indeed, a recent experience taught me a new psychology term: identity protective cognition. Identity protective cognition is the tendency for people in a group to selectively credit or dismiss evidence in patterns that reflect the beliefs that predominate in their group. When it comes to dark matter, the group happens to be a scientific one, but the psychology is the same: I’ve seen people twist themselves into logical knots to protect their belief in dark matter from being subject to critical examination. They do it without even recognizing that this is what they’re doing. I guess this is a human foible we cannot escape.
I’ve addressed these issues before, but here I’m going to start a series of posts on what I think some of the essential but underappreciated facts are. This is based on a talk that I gave at a conference on the philosophy of science in 2019, back when we had conferences, and published in Studies in History and Philosophy of Science. I paid the exorbitant open access fee (the journal changed its name – and publication policy – during the publication process), so you can read the whole thing all at once if you are eager. I’ve already written it to be accessible, so mostly I’m going to post it here in what I hope are digestible chunks, and may add further commentary if it seems appropriate.
Cosmic context
Cosmology is the science of the origin and evolution of the universe: the biggest of big pictures. The modern picture of the hot big bang is underpinned by three empirical pillars: an expanding universe (Hubble expansion), Big Bang Nucleosynthesis (BBN: the formation of the light elements through nuclear reactions in the early universe), and the relic radiation field (the Cosmic Microwave Background: CMB) (Harrison, 2000; Peebles, 1993). The discussion here will take this framework for granted.
The three empirical pillars fit beautifully with General Relativity (GR). Making the simplifying assumptions of homogeneity and isotropy, Einstein’s equations can be applied to treat the entire universe as a dynamical entity. As such, it is compelled either to expand or contract. Running the observed expansion backwards in time, one necessarily comes to a hot, dense, early phase. This naturally explains the CMB, which marks the transition from an opaque plasma to a transparent gas (Sunyaev and Zeldovich, 1980; Weiss, 1980). The abundances of the light elements can be explained in detail with BBN provided the universe expands in the first few minutes as predicted by GR when radiation dominates the mass-energy budget of the universe (Boesgaard & Steigman, 1985).
The marvelous consistency of these early universe results with the expectations of GR builds confidence that the hot big bang is the correct general picture for cosmology. It also builds overconfidence that GR is completely sufficient to describe the universe. Maintaining consistency with modern cosmological data is only possible with the addition of two auxiliary hypotheses: dark matter and dark energy. These invisible entities are an absolute requirement of the current version of the most-favored cosmological model, ΛCDM. The very name of this model is born of these dark materials: Λ is Einstein’s cosmological constant, of which ‘dark energy’ is a generalization, and CDM is cold dark matter.
Dark matter, on the other hand, plays an intimate and essential role in galaxy formation. The term ‘dark matter’ is dangerously crude, as it can reasonably be used to mean anything that is not seen. In the cosmic context, there are at least two forms of unseen mass: normal matter that happens not to glow in a way that is easily seen — not all ordinary material need be associated with visible stars — and non-baryonic cold dark matter. It is the latter form of unseen mass that is thought to dominate the mass budget of the universe and play a critical role in galaxy formation.
Cold Dark Matter
Cold dark matter is some form of slow moving, non-relativistic (‘cold’) particulate mass that is not composed of normal matter (baryons). Baryons are the family of particles that include protons and neutrons. As such, they compose the bulk of the mass of normal matter, and it has become conventional to use this term to distinguish between normal, baryonic matter and the non-baryonic dark matter.
The distinction between baryonic and non-baryonic dark matter is no small thing. Non-baryonic dark matter must be a new particle that resides in a new ‘dark sector’ that is completely distinct from the usual stable of elementary particles. We do not just need some new particle, we need one (or many) that reside in some sector beyond the framework of the stubbornly successful Standard Model of particle physics. Whatever the solution to the mass discrepancy problem turns out to be, it requires new physics.
The cosmic dark matter must be non-baryonic for two basic reasons. First, the mass density of the universe measured gravitationally (Ωm ≈ 0.3, e.g., Faber and Gallagher, 1979; Davis et al., 1980, 1992) clearly exceeds the mass density in baryons as constrained by BBN (Ωb ≈ 0.05, e.g., Walker et al., 1991). There is something gravitating that is not ordinary matter: Ωm > Ωb.
The second reason follows from the absence of large fluctuations in the CMB (Peebles and Yu, 1970; Silk, 1968; Sunyaev and Zeldovich, 1980). The CMB is extraordinarily uniform in temperature across the sky, varying by only ~ 1 part in 105 (Smoot et al., 1992). These small temperature variations correspond to variations in density. Gravity is an attractive force; it will make the rich grow richer. Small density excesses will tend to attract more mass, making them larger, attracting more mass, and leading to the formation of large scale structures, including galaxies. But gravity is also a weak force: this process takes a long time. In the long but finite age of the universe, gravity plus known baryonic matter does not suffice to go from the initially smooth, highly uniform state of the early universe to the highly clumpy, structured state of the local universe (Peebles, 1993). The solution is to boost the process with an additional component of mass — the cold dark matter — that gravitates without interacting with the photons, thus getting a head start on the growth of structure while not aggravating the amplitude of temperature fluctuations in the CMB.
Taken separately, one might argue away the need for dark matter. Taken together, these two distinct arguments convinced nearly everyone, including myself, of the absolute need for non-baryonic dark matter. Consequently, CDM became established as the leading paradigm during the 1980s (Peebles, 1984; Steigman and Turner, 1985). The paradigm has snowballed since that time, the common attitude among cosmologists being that CDM has to exist.
From an astronomical perspective, the CDM could be any slow-moving, massive object that does not interact with photons nor participate in BBN. The range of possibilities is at once limitless yet highly constrained. Neutrons would suffice if they were stable in vacuum, but they are not. Primordial black holes are a logical possibility, but if made of normal matter, they must somehow form in the first second after the Big Bang to not impair BBN. At this juncture, microlensing experiments have excluded most plausible mass ranges that primordial black holes could occupy (Mediavilla et al., 2017). It is easy to invent hypothetical dark matter candidates, but difficult for them to remain viable.
From a particle physics perspective, the favored candidate is a Weakly Interacting Massive Particle (WIMP: Peebles, 1984; Steigman and Turner, 1985). WIMPs are expected to be the lightest stable supersymmetric partner particle that resides in the hypothetical supersymmetric sector (Martin, 1998). The WIMP has been the odds-on favorite for so long that it is often used synonymously with the more generic term ‘dark matter.’ It is the hypothesized particle that launched a thousand experiments. Experimental searches for WIMPs have matured over the past several decades, making extraordinary progress in not detecting dark matter (Aprile et al., 2018). Virtually all of the parameter space in which WIMPs had been predicted to reside (Trotta et al., 2008) is now excluded. Worse, the existence of the supersymmetric sector itself, once seemingly a sure thing, remains entirely hypothetical, and appears at this juncture to be a beautiful idea that nature declined to implement.
In sum, we must have cold dark matter for both galaxies and cosmology, but we have as yet no clue to what it is.
* There is a trope that late in their careers, great scientists come to the opinion that everything worth discovering has been discovered, because they themselves already did everything worth doing. That is not a concern I have – I know we haven’t discovered all there is to discover. Yet I see no prospect for advancing our fundamental understanding simply because there aren’t enough of us pulling in the right direction. Most of the community is busy barking up the wrong tree, and refuses to be distracted from their focus on the invisible squirrel that isn’t there.
** Many of these people are the product of the toxic culture that Simon White warned us about. They wave the sausage of galaxy formation and feedback like a magic wand that excuses all faults while being proudly ignorant of how the sausage was made. Bitch, please. I was there when that sausage was made. I helped make the damn sausage. I know what went into it, and I recognize when it tastes wrong.
This expression exactly depicts the progression of the radial acceleration relation. Some people were ahead of this curve, others are still behind it, but it quite accurately depicts the mass sociology. This is how we react to startling new facts.
For quotation purists, I’m not sure exactly what the original phrasing was. I have paraphrased it to be succinct and have substituted orthodoxy for religion, because even scientists can have orthodoxies: holy cows that must not be slaughtered.
I might even add a precursor stage zero to the list above:
0. It goes unrecognized.
This is to say, that if a new fact is sufficiently startling, we don’t just disbelieve it (stage 1); at first we fail to see it at all. We lack the cognitive framework to even recognize how important it is. An example is provided by the 1941 detection of the microwave background by Andrew McKellar. In retrospect, this is as persuasive as the 1964 detection of Penzias and Wilson to which we usually ascribe the discovery. At the earlier time, there was simply no framework for recognizing what it was that was being detected. It appears to me that P&Z didn’t know what they were looking at either until Peebles explained it to them.
The radial acceleration relation was first posed as the mass discrepancy-acceleration relation. They’re fundamentally the same thing, just plotted in a slightly different way. The mass discrepancy-acceleration relation shows the ratio of total mass to that which is visible. This is basically the ratio of the observed acceleration to that predicted by the observed baryons. This is useful to see how much dark matter is needed, but by construction the axes are not independent, as both measured quantities are used in forming the ratio.
The radial acceleration relation shows independent observations along each axis: observed vs. predicted acceleration. Though measured independently, they are not physically independent, as the baryons contribute some to the total observed acceleration – they do have mass, after all. One can construct a halo acceleration relation by subtracting the baryonic contribution away from the total; in principle the remainders are physically independent. Unfortunately, the axes again become observationally codependent, and the uncertainties blow up, especially in the baryon dominated regime. Which of these depictions is preferable depends a bit on what you’re looking to see; here I just want to note that they are the same information packaged somewhat differently.
To the best of my knowledge, the first mention of the mass discrepancy-acceleration relation in the scientific literature is by Sanders (1990). Its existence is explicit in MOND (Milgrom 1983), but here it is possible to draw a clear line between theory and data. I am only speaking of the empirical relation as it appears in the data, irrespective of anything specific to MOND.
I met Bob Sanders, along with many other talented scientists, in a series of visits to the University of Groningen in the early 1990s. Despite knowing him and having talked to him about rotation curves, I was unaware that he had done this.
Stage 0: It goes unrecognized.
For me, stage one came later in the decade at the culmination of a several years’ campaign to examine the viability of the dark matter paradigm from every available perspective. That’s a long paper, which nevertheless drew considerable praise from many people who actually read it. If you go to the bother of reading it today, you will see the outlines of many issues that are still debated and others that have been forgotten (e.g., the fine-tuning issues).
Around this time (1998), the dynamicists at Rutgers were organizing a meeting on galaxy dynamics, and asked me to be one of the speakers. I couldn’t possibly discuss everything in the paper in the time allotted, so was looking for a way to show the essence of the challenge the data posed. Consequently, I reinvented the wheel, coming up with the mass discrepancy-acceleration relation. Here I show the same data that I had then in the form of the radial acceleration relation:
The Radial Acceleration Relation from the data in McGaugh (1999). Plot credit: Federico Lelli. (There is a time delay in publication: the 1998 meeting’s proceedings appeared in 1999.)
I recognize this version of the plot as having been made by Federico Lelli. I’ve made this plot many times, but this is version I came across first, and it is better than mine in that the opacity of the points illustrates where the data are concentrated. I had been working on low surface brightness galaxies; these have low accelerations, so that part of the plot is well populated.
The data show a clear correlation. By today’s standards, it looks crude. Going on what we had then, it was fantastic. Correlations practically never look this good in extragalactic astronomy, and they certainly don’t happen by accident. Low quality data can hide a correlation – uncertainties cause scatter – but they can’t create a correlation where one doesn’t exist.
I showed the same result later that year (1998) at a meeting on the campus of the University of Maryland where I was a brand new faculty member. It was a much shorter presentation, so I didn’t have time to justify the context or explain much about the data. Contrary to the reception at Rutgers where I had adequate time to speak, the hostility of the audience to the result was palpable, their stony silence eloquent. They didn’t want to believe it, and plenty of peoplegot busyquestioning the data.
Stage 1: It is not true.
I spent the next five years expanding and improving the data. More rotation curves became available thanks to the work of many, particularly Erwin de Blok, Marc Verheijen, and Rob Swaters. That was great, but the more serious limitation was how well we could measure the stellar mass distribution needed to predict the baryonic acceleration.
The mass models we could build at the time were based on optical images. A mass model takes the observed light distribution, assigns a mass-to-light ratio, and makes a numerical solution of the Poisson equation to obtain the the gravitational force corresponding to the observed stellar mass distribution. This is how we obtain the stellar contribution to the predicted baryonic force; the same procedure is applied to the observed gas distribution. The blue part of the spectrum is the best place in which to observe low contrast, low surface brightness galaxies as the night sky is darkest there, at least during new moon. That’s great for measuring the light distribution, but what we want is the stellar mass distribution. The mass-to-light ratio is expected to have a lot of scatter in the blue band simply from the happenstance of recent star formation, which makes bright blue stars that are short-lived. If there is a stochastic uptick in the star formation rate, then the mass-to-light ratio goes down because there are lots of bright stars. Wait a few hundred million years and these die off, so the mass-to-light ratio gets bigger (in the absence of further new star formation). The time-integrated stellar mass may not change much, but the amount of blue light it produces does. Consequently, we expect to see well-observed galaxies trace distinct lines in the radial acceleration plane, even if there is a single universal relation underlying the phenomenon. This happens simply because we expect to get M*/L wrong from one galaxy to the next: in 1998, I had simply assumed all galaxies had the same M*/L for lack of any better prescription. Clearly, a better prescription was warranted.
In those days, I traveled through Tucson to observe at Kitt Peak with some frequency. On one occasion, I found myself with a few hours to kill between coming down from the mountain and heading to the airport. I wandered over to the Steward Observatory at the University of Arizona to see who I might see. A chance meeting in the wild west: I encountered Eric Bell and Roelof de Jong, who were postdocs there at the time. I knew Eric from his work on the stellar populations of low surface brightness galaxies, an interest closely aligned with my own, and Roelof from my visits to Groningen.
As we got to talking, Eric described to me work they were doing on stellar populations, and how they thought it would be possible to break the age-metallicity degeneracy using near-IR colors in addition to optical colors. They were mostly focused on improving the age constraints on stars in LSB galaxies, but as I listened, I realized they had constructed a more general, more powerful tool. At my encouragement (read their acknowledgements), they took on this more general task, ultimately publishing the classic Bell & de Jong (2001). In it, they built a table that enabled one to look up the expected mass-to-light ratio of a complex stellar population – one actively forming stars – as a function of color. This was a big step forward over my educated guess of a constant mass-to-light ratio: there was now a way to use a readily observed property, color, to improve the estimated M*/L of each galaxy in a well-calibrated way.
Combining the new stellar population models with all the rotation curves then available, I obtained an improved mass discrepancy-acceleration relation:
The Radial Acceleration Relation from the data in McGaugh (2004); version using Bell’s stellar population synthesis models to estimate M*/L (see Fig. 5 for other versions). Plot credit: Federico Lelli.
Again, the relation is clear, but with scatter. Even with the improved models of Bell & de Jong, some individual galaxies have M*/L that are wrong – that’s inevitable in this game. What you cannot know is which ones! Note, however, that there are now 74 galaxies in this plot, and almost all of them fall on top of each other where the point density is large. There are some obvious outliers; those are presumably just that: the trees that fall outside the forest because of the expected scatter in M*/L estimates.
I tried a variety of prescriptions for M*/L in addition to that of Bell & de Jong. Though they differed in texture, they all told a consistent story. A relation was clearly present; only its detailed form varied with the adopted prescription.
The prescription that minimized the scatter in the relation was the M*/L obtained in MOND fits. That’s a tautology: by construction, a MOND fit finds the M*/L that puts a galaxy on this relation. However, we can generalize the result. Maybe MOND is just a weird, unexpected way of picking a number that has this property; it doesn’t have to be the true mass-to-light ratio in nature. But one can then define a ratio Q
Equation 21 of McGaugh (2004).
that relates the “true” mass-to-light ratio to the number that gives a MOND fit. They don’t have to be identical, but MOND does return M*/L that are reasonable in terms of stellar populations, so Q ~ 1. Individual values could vary, and the mean could be a bit more or less than unity, but not radically different. One thing that impressed me at the time about the MOND fits (most of which were made by Bob Sanders) was how well they agreed with the stellar population models, recovering the correct amplitude, the correct dependence on color in different bandpasses, and also giving the expected amount of scatter (more in the blue than in the near-IR).
Fig. 7 of McGaugh (2004). Stellar mass-to-light ratios of galaxies in the blue B-band (top) and near-IR K-band (bottom) as a function of B–V color for the prescription of maximum disk (left) and MOND (right). Each point represents one galaxy for which the requisite data were available at the time. The line represents the mean expectation of stellar population synthesis models from Bell et al. (2003). These lines are completely independent of the data: neither the normalization nor the slope has been fit to the dynamical data. The red points are due to Sanders & Verheijen (1998); note the weak dependence of M*/L on color in the near-IR.
The obvious interpretation is that we should take seriously a theory that obtains good fits with a single free parameter that checks out admirably well with independent astrophysical constraints, in this case the M*/L expected for stellar populations. But I knew many people would not want to do that, so I defined Q to generalize to any M*/L in any (dark matter) context one might want to consider.
Indeed, Q allows us to write a general expression for the rotation curve of the dark matter halo (essentially the HAR alluded to above) in terms of that of the stars and gas:
The stars and the gas are observed, and μ is the MOND interpolation function assumed in the fit that leads to Q. Except now the interpolation function isn’t part of some funny new theory; it is just the shape of the radial acceleration relation – a relation that is there empirically. The only fit factor between these data and any given model is Q – a single number of order unity. This does leave some wiggle room, but not much.
I went off to a conference to describe this result. At the 2006 meeting Galaxies in the Cosmic Web in New Mexico, I went out of my way at the beginning of the talk to show that even if we ignore MOND, this relation is present in the data, and it provides a strong constraint on the required distribution of dark matter. We may not know why this relation happens, but we can use it, modulo only the modest uncertainty in Q.
Having bent over backwards to distinguish the data from the theory, I was disappointed when, immediately at the end of my talk, prominent galaxy formation theorist Anatoly Klypin loudly shouted
“We don’t have to explain MOND!”
It stinks of MOND!
But you do have to explain the data. The problem was and is that the data look like MOND. It is easy to conflate one with the other; I have noticed that a lot of people have trouble keeping the two separate. Just because you don’t like the theory doesn’t mean that the data are wrong. What Anatoly was saying was that
2. It is contrary to orthodoxy.
Despite phrasing the result in a way that would be useful to galaxy formation theorists, they did not, by and large, claim to explain it at the time – it was contrary to orthodoxy so didn’t need to be explained. Looking at the list of papers that cite this result, the early adopters were not the target audience of galaxy formation theorists, but rather others citing it to say variations of “no way dark matter explains this.”
At this point, it was clear to me that further progress required a better way to measure the stellar mass distribution. Looking at the stellar population models, the best hope was to build mass models from near-infrared rather than optical data. The near-IR is dominated by old stars, especially red giants. Galaxies that have been forming stars actively for a Hubble time tend towards a quasi-equilibrium in which red giants are replenished by stellar evolution at about the same rate they move on to the next phase. One therefore expects the mass-to-light ratio to be more nearly constant in the near-IR. Not perfectly so, of course, but a 2 or 3 micron image is as close to a map of the stellar mass of a galaxy as we’re likely to get.
Around this time, the University of Maryland had begun a collaboration with Kitt Peak to build a big infrared camera, NEWFIRM, for the 4m telescope. Rob Swaters was hired to help write software to cope with the massive data flow it would produce. The instrument was divided into quadrants, each of which had a field of view sufficient to hold a typical galaxy. When it went on the telescope, we developed an efficient observing method that I called “four-shooter”, shuffling the target galaxy from quadrant to quadrant so that in processing we could remove the numerous instrumental artifacts intrinsic to its InSb detectors. This eventually became one of the standard observing modes in which the instrument was operated.
NEWFIRM in the lab in Tucson. Most of the volume is for cryogenics: the IR detectors are helium–cooled to 30 K. Partial student for scale.
I was optimistic that we could make rapid progress, and at first we did. But despite all the work, despite all the active cooling involved, we were still on the ground. The night sky was painfully bright in the IR. Indeed, the thermal component dominated, so we could observe during full moon. To an observer of low surface brightness galaxies attuned to any hint of scattered light from so much as a crescent moon, I cannot describe how discombobulating it was to walk outside the dome and see the full fricking moon. So bright. So wrong. And that wasn’t even the limiting factor: the thermal background was.
We had hit a surface brightness wall, again. We could do the bright galaxies this way, but the LSBs that sample the low acceleration end of the radial acceleration relation were rather less accessible. Not inaccessible, but there was a better way.
The Spitzer Space Telescope was active at this time. Jim Schombert and I started winning time to observe LSB galaxies with it. We discovered that space is dark. There was no atmosphere to contend with. No scattered light from the clouds or the moon or the OH lines that afflict that part of the sky spectrum. No ground-level warmth. The data were fantastic. In some sense, they were too good: the biggest headache we faced was blotting out all the background galaxies that shown right through the optically thin LSB galaxies.
Still, it took a long time to collect and analyze the data. We were starting to get results by the early-teens, but it seemed like it would take forever to get through everything I hoped to accomplish. Fortunately, when I moved to Case Western, I was able to hire Federico Lelli as a postdoc. Federico’s involvement made all the difference. After many months of hard, diligent, and exacting work, he constructed what is now the SPARC database. Finally all the elements were in place to construct an empirical radial acceleration relation with absolutely minimal assumptions about the stellar mass-to-light ratio.
In parallel with the observational work, Jim Schombert had been working hard to build realistic stellar population models that extended to the 3.6 micron band of Spitzer. Spitzer had been built to look redwards of this, further into the IR. 3.6 microns was its shortest wavelength passband. But most models at the time stopped at the K-band, the 2.2 micron band that is the reddest passband that is practically accessible from the ground. They contain pretty much the same information, but we still need to calculate the band-specific value of M*/L.
Being a thorough and careful person, Jim considered not just the star formation history of a model stellar population as a variable, and not just its average metallicity, but also the metallicity distribution of its stars, making sure that these were self-consistent with the star formation history. Realistic metallicity distributions are skewed; it turn out that this subtle effect tends to counterbalance the color dependence of the age effect on M*/L in the near-IR part of the spectrum. The net results is that we expect M*/L to be very nearly constant for all late type galaxies.
This is the best possible result. To a good approximation, we expected all of the galaxies in the SPARC sample to have the same mass-to-light ratio. What you see is what you get. No variable M*/L, no equivocation, just data in, result out.
We did still expect some scatter, as that is an irreducible fact of life in this business. But even that we expected to be small, between 0.1 and 0.15 dex (roughly 25 – 40%). Still, we expected the occasional outlier, galaxies that sit well off the main relation just because our nominal M*/L didn’t happen to apply in that case.
One day as I walked past Federico’s office, he called for me to come look at something. He had plotted all the data together assuming a single M*/L. There… were no outliers. The assumption of a constant M*/L in the near-IR didn’t just work, it worked far better than we had dared to hope. The relation leapt straight out of the data:
The Radial Acceleration Relation from the data in McGaugh et al. (2016). Plot credit: Federico Lelli.
Over 150 galaxies, with nearly 2700 resolved measurements within each galaxy, each with their own distinctive mass distribution, all pile on top of each other without effort. There was plenty of effort in building the database, but once it was there, the result appeared, no muss, no fuss. No fitting or fiddling. Just the measurements and our best estimate of the mean M*/L, applied uniformly to every individual galaxy in the sample. The scatter was only 0.12 dex, within the range expected from the population models.
No MOND was involved in the construction of this relation. It may look like MOND, but we neither use MOND nor need it in any way to see the relation. It is in the data. Perhaps this is the sort of result for which we would have to invent MOND if it did not already exist. But the dark matter paradigm is very flexible, and many papers have since appeared that claim to explain the radial acceleration relation. We have reached
3. We knew it all along.
On the one hand, this is good: the community is finally engaging with a startling fact that has been pointedly ignored for decades. On the other hand, many of the claims to explain the radial acceleration relation are transparently incorrecton their face, being nothing more than elaborations of models I considered and discarded as obviously unworkable long ago. They do not provide a satisfactory explanation of the predictive power of MOND, and inevitably fail to address important aspects of the problem, like disk stability. Rather than grapple with the deep issues the new and startling fact poses, it has become fashionable to simply assert that one’s favorite model explains the radial acceleration relation, and does so naturally.
There is nothing natural about the radial acceleration relation in the context of dark matter. Indeed, it is difficult to imagine a less natural result – hence stages one and two. So on the one hand, I welcome the belated engagement, and am willing to consider serious models. On the other hand, if someone asserts that this is natural and that we expected it all along, then the engagement isn’t genuine: they’re just fooling themselves.
Early Days. This was one of Vera Rubin’s favorite expressions. I always had a hard time with it, as many things are very well established. Yet it seems that we have yet to wrap our heads around the problem. Vera’s daughter, Judy Young, once likened the situation to the parable of the blind men and the elephant. Much is known, yes, but the problem is so vast that each of us can perceive only a part of the whole, and the whole may be quite different from the part that is right before us.
So I guess Vera is right as always: these remain Early Days.
It’s early in the new year, so what better time to violate my own resolutions? I prefer to be forward-looking and not argue over petty details, or chase wayward butterflies. But sometimes the devil is in the details, and the occasional butterfly can be entertaining if distracting. Today’s butterfly is the galaxy AGC 114905, which has recently been in the news.
There are a couple of bandwagons here: one to rebrand very low surface brightness galaxies as ultradiffuse, and another to get overly excited when these types of galaxies appear to lack dark matter. The nomenclature is terrible, but that’s normal for astronomy so I would overlook it, except that in this case it gives the impression that there is some new population of galaxies behaving in an unexpected fashion, when instead it looks to me like the opposite is the case. The extent to which there are galaxies lacking dark matter is fundamental to our interpretation of the acceleration discrepancy (aka the missing mass problem), so bears closer scrutiny. The evidence for galaxies devoid of dark matter is considerably weaker than the current bandwagon portrays.
If it were just one butterfly (e.g., NGC 1052-DF2), I wouldn’t bother. Indeed, it was that specific case that made me resolve to ignore such distractions as a waste of time. I’ve seen this movie literally hundreds of times, I know how it goes:
Observations of this one galaxy falsify MOND!
Hmm, doing the calculation right, that’s what MOND predicts.
OK, but better data shrink the error bars and now MOND falsified.
Are you sure about…?
Yes. We like this answer, let’s stop thinking about it now.
As the data continue to improve, it approaches what MOND predicts.
Over and over again. DF44 is another example that has followed this trajectory, and there are many others. This common story is not widely known – people lose interest once they get the answer they want. Irrespective of whether we can explain this weird case or that, there is a deeper story here about data analysis and interpretation that seems not to be widely appreciated.
My own experience inevitably colors my attitude about this, as it does for us all, so let’s start thirty years ago when I was writing a dissertation on low surface brightness (LSB) galaxies. I did many things in my thesis, most of them well. One of the things I tried to do then was derive rotation curves for some LSB galaxies. This was not the main point of the thesis, and arose almost as an afterthought. It was also not successful, and I did not publish the results because I didn’t believe them. It wasn’t until a few years later, with improved data, analysis software, and the concerted efforts of Erwin de Blok, that we started to get a handle on things.
The thing that really bugged me at the time was not the Doppler measurements, but the inclinations. One has to correct the observed velocities by the inclination of the disk, 1/sin(i). The inclination can be constrained by the shape of the image and by the variation of velocities across the face of the disk. LSB galaxies presented raggedy images and messy velocity fields. I found it nigh on impossible to constrain their inclinations at the time, and it remains a frequent struggle to this day.
Here is an example of the LSB galaxy F577-V1 that I find lurking around on disk from all those years ago:
The LSB galaxy F577-V1 (B-band image, left) and the run of the eccentricity of ellipses fit to the atomic gas data (right).
A uniform disk projected on the sky at some inclination will have a fixed corresponding eccentricity, with zero being the limit of a circular disk seen perfectly face-on (i = 0). Do you see a constant value of the eccentricity in the graph above? If you say yes, go get your eyes checked.
What we see in this case is a big transition from a fairly eccentric disk to one that is more nearly face on. The inclination doesn’t have a sudden warp; the problem is that the assumption of a uniform disk is invalid. This galaxy has a bar – a quasi-linear feature that is common in many spiral galaxies that is supported by non-circular orbits. Even face-on, the bar will look elongated simply because it is. Indeed, the sudden change in eccentricity is one way to define the end of the bar, which the human eye-brain can do easily by looking at the image. So in a case like this, one might adopt the inclination from the outer points, and that might even be correct. But note that there are spiral arms along the outer edge that is visible to the eye, so it isn’t clear that even these isophotes are representative of the shape of the underlying disk. Worse, we don’t know what happens beyond the edge of the data; the shape might settle down at some other level that we can’t see.
This was so frustrating, I swore never to have anything to do with galaxy kinematics ever again. Over 50 papers on the subject later, all I can say is D’oh! Repeatedly.
Bars are rare in LSB galaxies, but it struck me as odd that we saw any at all. We discovered unexpectedly that they were dark matter dominated – the inferred dark halo outweighs the disk, even within the edge defined by the stars – but that meant that the disks should be stable against the formation of bars. My colleague Chris Mihos agreed, and decided to look into it. The answer was yes, LSB galaxies should be stable against bar formation, at least internally generated bars. Sometimes bars are driven by external perturbations, so we decided to simulate the close passage of a galaxy of similar mass – basically, whack it real hard and see what happens:
Simulation of an LSB galaxy during a strong tidal encounter with another galaxy. Closest approach is at t=24 in simulation units (between the first and second box). A linear bar does not form, but the model galaxy does suffer a strong and persistent oval distortion: all these images are shown face-on (i=0). From Mihos et al (1997).
This was a conventional simulation, with a dark matter halo constructed to be consistent with the observed properties of the LSB galaxy UGC 128. The results are not specific to this case; it merely provides numerical corroboration of the more general case that we showed analytically.
Consider the image above in the context of determining galaxy inclinations from isophotal shapes. We know this object is face-on because we can control our viewing angle in the simulation. However, we would not infer i=0 from this image. If we didn’t know it had been perturbed, we would happily infer a substantial inclination – in this case, easily as much as 60 degrees! This is an intentionally extreme case, but it illustrates how a small departure from a purely circular shape can be misinterpreted as an inclination. This is a systematic error, and one that usually makes the inclination larger than it is: it is possible to appear oval when face-on, but it is not possible to appear more face-on than perfectly circular.
Around the same time, Erwin and I were making fits to the LSB galaxy data – with both dark matter halos and MOND. By this point in my career, I had deeply internalized that the data for LSB galaxies were never perfect. So we sweated every detail, and worked through every “what if?” This was a particularly onerous task for the dark matter fits, which could do many different things if this or that were assumed – we discussed all the plausible possibilities at the time. (Subsequently, a rich literature sprang up discussing many unreasonable possibilities.) By comparison, the MOND fits were easy. They had fewer knobs, and in 2/3 of the cases they simply worked, no muss, no fuss.
For the other 1/3 of the cases, we noticed that the shape of the MOND-predicted rotation curves was usually right, but the amplitude was off. How could it work so often, and yet miss in this weird way? That sounded like a systematic error, and the inclination was the most obvious culprit, with 1/sin(i) making a big difference for small inclinations. So we decided to allow this as a fit parameter, to see whether a fit could be obtained, and judge how [un]reasonable this was. Here is an example for two galaxies:
UGC 1230 (left) and UGC 5005 (right). Ovals show the nominally measured inclination (i=22o for UGC 1230 and 41o for UGC 5005, respectively) and the MOND best-fit value (i=17o and 30o). From de Blok & McGaugh (1998).
The case of UGC 1230 is memorable to me because it had a good rotation curve, despite being more face-on than widely considered acceptable for analysis. And for good reason: the difference between 22 and 17 degrees make a huge difference to the fit, changing it from way off to picture perfect.
Rotation curve fits for UGC 1230 (top) and UGC 5005 (bottom) with the inclination fixed (left) and fit (right). From de Blok & McGaugh (1998).
What I took away from this exercise is how hard it is to tell the difference between inclination values for relatively face-on galaxies. UGC 1230 is obvious: the ovals for the two inclinations are practically on top of each other. The difference in the case of UGC 5005 is more pronounced, but look at the galaxy. The shape of the outer isophote where we’re trying to measure this is raggedy as all get out; this is par for the course for LSB galaxies. Worse, look further in – this galaxy has a bar! The central bar is almost orthogonal to the kinematic major axis. If we hadn’t observed as deeply as we had, we’d think the minor axis was the major axis, and the inclination was something even higher.
I remember Erwin quipping that he should write a paper on how to use MOND to determine inclinations. This was a joke between us, but only half so: using the procedure in this way would be analogous to using Tully-Fisher to measure distances. We would simply be applying an empirically established procedure to constrain a property of a galaxy – luminosity from line-width in that case of Tully-Fisher; inclination from rotation curve shape here. That we don’t understand why this works has never stopped astronomers before.
Systematic errors in inclination happen all the time. Big surveys don’t have time to image deeply – they have too much sky area to cover – and if there is follow-up about the gas content, it inevitably comes in the form of a single dish HI measurement. This is fine; it is what we can do en masse. But an unresolved single dish measurement provides no information about the inclination, only a pre-inclination line-width (which itself is a crude proxy for the flat rotation speed). The inclination we have to take from the optical image, which would key on the easily detected, high surface brightness central region of the image. That’s the part that is most likely to show a bar-like distortion, so one can expect lots of systematic errors in the inclinations determined in this way. I provided a long yet still incomplete discussion of these issues in McGaugh (2012). This is both technical and intensely boring, so not even the pros read it.
This brings us to the case of AGC 114905, which is part of a sample of ultradiffuse galaxies discussed previously by some of the same authors. On that occasion, I kept to the code, and refrained from discussion. But for context, here are those data on a recent Baryonic Tully-Fisher plot. Spoiler alert: that post was about a different sample of galaxies that seemed to be off the relation but weren’t.
Baryonic Tully-Fisher relation showing the ultradiffuse galaxies discussed by Mancera Piña et al. (2019) as gray circles. These are all outliers from the relation; AGC 114905 is highlighted in orange. Placing much meaning in the outliers is a classic case of missing the forest for the trees. The outliers are trees. The Tully-Fisher relation is the forest.
On the face of it, these ultradiffuse galaxies (UDGs) are all very serious outliers. This is weird – they’re not some scatter off to one side, they’re just way off on their own island, with no apparent connection to the rest of established reality. By calling them a new name, UDG, it makes it sound plausible that these are some entirely novel population of galaxies that behave in a new way. But they’re not. They are exactly the same kinds of galaxies I’ve been talking about. They’re all blue, gas rich, low surface brightness, fairly isolated galaxies – all words that I’ve frequently used to describe my thesis sample. These UDGs are all a few billion solar mass is baryonic mass, very similar to F577-V1 above. You could give F577-V1 a different name, slip into the sample, and nobody would notice that it wasn’t like one of the others.
The one slight difference is implied by the name: UDGs are a little lower in surface brightness. Indeed, once filter transformations are taken into account, the definition of ultradiffuse is equal to what I arbitrarily called very low surface brightness in 1996. Most of my old LSB sample galaxies have central stellar surface brightnesses at or a bit above 10 solar masses per square parsec while the UDGs here are a bit under this threshold. For comparison, in typical high surface brightness galaxies this quantity is many hundreds, often around a thousand. Nothing magic happens at the threshold of 10 solar masses per square parsec, so this line of definition between LSB and UDG is an observational distinction without a physical difference. So what are the odds of a different result for the same kind of galaxies?
Indeed, what really matters is the baryonic surface density, not just the stellar surface brightness. A galaxy made purely of gas but no stars would have zero optical surface brightness. I don’t know of any examples of that extreme, but we came close to it with the gas rich sample of Trachternach et al. (2009) when we tried this exact same exercise a decade ago. Despite selecting that sample to maximize the chance of deviations from the Baryonic Tully-Fisher relation, we found none – at least none that were credible: there were deviant cases, but their data were terrible. There were no deviants among the better data. This sample is comparable or even extreme than the UDGs in terms of baryonic surface density, so the UDGs can’t be exception because they’re a genuinely new population, whatever name we call them by.
The key thing is the credibility of the data, so let’s consider the data for AGC 114905. The kinematics are pretty well ordered; the velocity field is well observed for this kind of beast. It ought to be; they invested over 40 hours of JVLA time into this one galaxy. That’s more than went into my entire LSB thesis sample. The authors are all capable, competent people. I don’t think they’ve done anything wrong, per se. But they do seem to have climbed aboard the bandwagon of dark matter-free UDGs, and have talked themselves into believing smaller error bars on the inclination than I am persuaded is warranted.
AGC 114905 in stars (left) and gas (right). The contours of the gas distribution are shown on top of the stars in white. Figure 1 from Mancera Piña et al. (2021).
This messy morphology is typical of very low surface brightness galaxies – hence their frequent classification as Irregular galaxies. Though messier, it shares some morphological traits with the LSB galaxies shown above. The central light distribution is elongated with a major axis that is not aligned with that of the gas. The gas is raggedy as all get out. The contours are somewhat boxy; this is a hint that something hinky is going on beyond circular motion in a tilted axisymmetric disk.
The authors do the right thing and worry about the inclination, checking to see what it would take to be consistent with either LCDM or MOND, which is about i=11o in stead of the 30o indicated by the shape of the outer isophote. They even build a model to check the plausibility of the smaller inclination:
Contours of models of disks with different inclinations (lines, as labeled) compared to the outer contour of the gas distribution of AGC 114905. Figure 7 from Mancera Piña et al. (2021).
Clearly the black line (i=30o) is a better fit to the shape of the gas distribution than the blue dashed line (i=11o). Consequently, they “find it unlikely that we are severely overestimating the inclination of our UDG, although this remains the largest source of uncertainty in our analysis.” I certainly agree with the latter phrase, but not the former. I think it is quite likely that they are overestimating the inclination. I wouldn’t even call it a severe overestimation; more like par for the course with this kind of object.
As I have emphasized above and elsewhere, there are many things that can go wrong in this sort of analysis. But if I were to try to put my finger on the most important thing, here it would be the inclination. The modeling exercise is good, but it assumes “razor-thin axisymmetric discs.” That’s a reasonable thing to do when building such a model, but we have to bear in mind that real disks are neither. The thickness of the disk probably doesn’t matter too much for a nearly face-on case like this, but the assumption of axisymmetry is extraordinarily dubious for an Irregular galaxy. That’s how they got the name.
It is hard to build models that are not axisymmetric. Once you drop this simplifying assumption, where do you even start? So I don’t fault them for stopping at this juncture, but I can also imagine doing as de Blok suggested, using MOND to set the inclination. Then one could build models with asymmetric features by trial and error until a match is obtained. Would we know that such a model would be a better representation of reality? No. Could we exclude such a model? Also no. So the bottom line is that I am not convinced that the uncertainty in the inclination is anywhere near as small as the adopted ±3o.
That’s very deep in the devilish details. If one is worried about a particular result, one can back off and ask if it makes sense in the context of what we already know. I’ve illustrated this process previously. First, check the empirical facts. Every other galaxy in the universe with credible data falls on the Baryonic Tully-Fisher relation, including very similar galaxies that go by a slightly different name. Hmm, strike one. Second, check what we expect from theory. I’m not a fan of theory-informed data interpretation, but we know that LCDM, unlike SCDM before it, at least gets the amplitude of the rotation speed in the right ballpark (Vflat ~ V200). Except here. Strike two. As much as we might favor LCDM as the standard cosmology, it has now been extraordinarily well established that MOND has considerable success in not just explaining but predicting these kind of data, with literally hundreds of examples. One hundred was the threshold Vera Rubin obtained to refute excuses made to explain away the first few flat rotation curves. We’ve crossed that threshold: MOND phenomenology is as well established now as flat rotation curves were at the inception of the dark matter paradigm. So while I’m open to alternative explanations for the MOND phenomenology, seeing that a few trees stand out from the forest is never going to be as important as the forest itself.
This brings us to a physical effect that people should be aware of. We touched on the bar stability above, and how a galaxy might look oval even when seen face on. This happens fairly naturally in MOND simulations of isolated disk galaxies. They form bars and spirals and their outer parts wobble about. See, for example, this simulation by Nils Wittenburg. This particular example is a relatively massive galaxy; the lopsidedness reminds me of M101 (Watkins et al. 2017). Lower mass galaxies deeper in the MOND regime are likely even more wobbly. This happens because disks are only marginally stable in MOND, not the over-stabilized entities that have to be hammered to show a response as in our early simulation of UGC 128 above. The point is that there is good reason to expect even isolated face-on dwarf Irregulars to look, well, irregular, leading to exactly the issues with inclination determinations discussed above. Rather than being a contradiction to MOND, AGC 114905 may illustrate one of its inevitable consequences.
I don’t like to bicker at this level of detail, but it makes a profound difference to the interpretation. I do think we should be skeptical of results that contradict well established observational reality – especially when over-hyped. God knows I was skeptical of our own results, which initially surprised the bejeepers out of me, but have been repeatedlycorroborated by subsequent observations.
I guess I’m old now, so I wonder how I come across to younger practitioners; perhaps as some scary undead monster. But mates, these claims about UDGs deviating from established scaling relations are off the edge of the map.
An important issue in science is what’s right and what’s wrong. Another is who gets credit for what. The former issue is scientific while the second is social. It matters little to the progress of science who discovers what. It matters a lot to the people who do it. We like to get credit where due.
discovered by me but contested by masses of unbelievers, [who asserted] that there exist no bona fide clusters of stable or stationary clusters of galaxies.
Zwicky, CSCGPEG
Were Zwicky alive today, a case could be made that he deserves the Nobel Prize in physics for the discovery of dark matter. However, Zwicky was not the first or only person to infer the existence of dark matter early on. Jan Oort was concerned that dark mass was necessary to explain the accelerations of stars perpendicular to the plane of the Milky Way as early as 1932. Where Zwicky’s discrepancy was huge, over a factor of 100, Oort’s was a more modest factor of 2. Oort was taken seriously at the time while Zwicky was largely ignored.
The reasons for this difference in response are many and varied. I wasn’t around at the time, so I will refrain from speculating too much. But in many ways, this divide reflects the difference in cultures between physics and astronomy. Oort was thoroughly empirical and immaculately detailed in his observational work and conservative in its interpretation, deeply impressing his fellow astronomers. Zwicky was an outsider and self-described lone wolf, and may have come across as a wild-eyed crackpot. That he had good reason for that didn’t alter the perception. That he is now posthumously recognized as having been basically correct does nothing to aid him personally, only our memory of him.
Nowadays, nearly every physicist I hear talk about the subject credits Zwicky with the discovery of dark matter. When I mention Oort, most have never heard of him, and they rarely seem prepared to share the credit. This is how history gets rewritten, by oversimplification and omission: Oort goes unmentioned in the education of physicists, the omission gets promulgated by those who never heard of him, then it becomes fact since an omission so glaring cannot possibly be correct. I’m doing that myself here by omitting mention of Opik and perhaps others I haven’t heard of myself.
Zwicky got that treatment in real time, leading to some of the best published rants in all of science. I’ll let him speak for himself, quoting from the CSCGPEG. One of his great resentments was his exclusion from premiere observational facilities:
I myself was allowed the use of the 100-inch telescope only in 1948, after I was fifty years of age, and of the 200-inch telescope on Palomar Mountain only after I was 54 years old, although I had built and successfully operated the 18-inch Schmidt telescope in 1936, and had been professor of physics and of astrophysics at the California Institute of Technology since 1927 and 1942 respectively.
Zwicky, in the introduction to the CSCGPEG
For reference, I have observed many hundreds of nights at various observatories. Only a handful of those nights have been in my fifties. Observing is mostly a young person’s occupation.
I do not know why Zwicky was excluded. Perhaps there is a book on the subject; there should be. Maybe it was personal, as he clearly suspects. Applying for telescope time can be highly competitive, even within one’s own institution, which hardly matters if it crossed departmental lines. Perhaps his proposals lacked grounding in the expectations of the field, or some intangible quality that made them less persuasive than those of his colleagues. Maybe he simply didn’t share their scientific language, a perpetual problem I see at the interface between physics and astronomy. Perhaps all these things contributed.
More amusing if inappropriate are his ad hominem attacks on individuals:
a shining example of a most deluded individual we need only quote the high pope of American Astronomy, one Henry Norris Russell…
Zwicky, CSCGPEG
or his more generalized condemnation of the entire field:
Today’s sycophants and plain thieves seem to be free, in American Astronomy in particular, to appropriate discoveries and inventions made by lone wolves and non-conformists, for whom there is never any appeal to the hierarchies and for whom even the public Press is closed, because of censoring committees within the scientific institutions.
Zwicky, CSCGPEG
or indeed, of human nature:
we note that again and again scientists and technical specialists arrive at stagnation points where they think they know it all.
Zwicky, CSCGPEG, emphasis his.
He’s not wrong.
I have heard Zwicky described as a “spherical bastard”: a bastard viewed from any angle. You can see why from these quotes. But you can also see why he might have felt this way. The CSCGPEG was published about 35 years after his pioneering work on clusters of galaxies. That’s a career-lifetime lacking recognition for what would now be consider Nobel prize worthy work. Dark matter would come to prominence in the following decade, by which time he was dead.
I have also heard that “spherical bastard” was a phrase invented by Zwicky to apply to others. I don’t know who was the bigger bastard, and I am reluctant to attribute his lack of popularity in his own day to his personality. The testimony I am aware of is mostly from those who disagreed with him, and may themselves have been spherical bastards. Indeed, I strongly suspect those who sing his praises most loudly now would have been among his greatest detractors had they been contemporaries.
I know from my own experience that people are lousy at distinguishing between a scientific hypothesis that they don’t like and the person who advocates it. Often they are willing and eager to attribute a difference in scientific judgement to a failure of character: “He disagrees with me, therefore he is a bastard.” Trash talk by mediocre wannabes is common, and slander works wonders to run down a reputation. I imagine Zwicky was a victim of this human failing.
Of course, the correctness of a scientific hypothesis has nothing to do with how likeable its proponents might be. Indeed, a true scientist has an obligation to speak the facts, even if they are unpopular, as Zwicky reminded us with a quote of his own in the preface to the CSCGPEG:
The more things change, the more they stay the same.
I read somewhere – I don’t think it was Kuhn himself, but someone analyzing Kuhn – that there came a point in the history of science where there was a divergence between scientists, with different scientists disagreeing about what counts as a theory, what counts as a test of a theory, what even counts as evidence. We have reached that point with the mass discrepancy problem.
For many years, I worried that if the field ever caught up with me, it would zoom past. That hasn’t happened. Instead, it has diverged towards a place that I barely recognize as science. It looks more like the Matrix – a simulation – that is increasingly sophisticated yet self-contained, making only parsimonious contact with observational reality and unable to make predictions that apply to real objects. Scaling relations and statistical properties, sure. Actual galaxies with NGC numbers, not so much. That, to me, is not science.
I have found it increasingly difficult to communicate across the gap built on presumptions buried so deep that they cannot be questioned. One obvious one is the existence of dark matter. This has been fueled by cosmologists who take it for granted and particle physicists eager to discover it who repeat “we know dark matter exists*; we just need to find it” like a religious mantra. This is now ingrained so deeply that it has become difficult to convey even the simple concept that what we call “dark matter” is really just evidence of a discrepancy: we do not know whether it is literally some kind of invisible mass, or a breakdown of the equations that lead us to infer invisible mass.
I try to look at all sides of a problem. I can say nice things about dark matter (and cosmology); I can point out problems with it. I can say nice things about MOND; I can point out problems with it. The more common approach is to presume that any failing of MOND is an automatic win for dark matter. This is a simple-minded logical fallacy: just because MOND gets something wrong doesn’t mean dark matter gets it right. Indeed, my experience has been that cases that don’t make any sense in MOND don’t make any sense in terms of dark matter either. Nevertheless, this attitude persists.
I made this flowchart as a joke in 2012, but it persists in being an uncomfortably fair depiction of how many people who work on dark matter approach the problem.
I don’t know what is right, but I’m pretty sure this attitude is wrong. Indeed, it empowers a form of magical thinking: dark matter has to be correct, so any data that appear to contradict it are either wrong, or can be explained with feedback. Indeed, the usual trajectory has been denial first (that can’t be true!) and explanation later (we knew it all along!) This attitude is an existential threat to the scientific method, and I am despondent in part because I worry we are slipping into a post-scientific reality, where even scientists are little more than priests of a cold, dark religion.
*If we’re sure dark matter exists, it is not obvious that we need to be doing expensive experiments to find it.
It often happens that data are ambiguous and open to multiple interpretations. The evidence for dark matter is an obvious example. I frequently hear permutations on the statement
We know dark matter exists; we just need to find it.
This is said in all earnestness by serious scientists who clearly believe what they say. They mean it. Unfortunately, meaning something in all seriousness, indeed, believing it with the intensity of religious fervor, does not guarantee that it is so.
The way the statement above is phrased is a dangerous half-truth. What the data show beyond any dispute is that there is a discrepancy between what we observe in extragalactic systems (including cosmology) and the predictions of Newton & Einstein as applied to the visible mass. If we assume that the equations Newton & Einstein taught us are correct, then we inevitably infer the need for invisible mass. That seems like a very reasonable assumption, but it is just that: an assumption. Moreover, it is an assumption that is only tested on the relevant scales by the data that show a discrepancy. One could instead infer that theory fails this test – it does not work to predict observed motions when applied to the observed mass. From this perspective, it could just as legitimately be said that
A more general theory of dynamics must exist; we just need to figure out what it is.
That puts an entirely different complexion on exactly the same problem. The data are the same; they are not to blame. The difference is how we interpret them.
Neither of these statements are correct: they are both half-truths; two sides of the same coin. As such, one risks being wildly misled. If one only hears one, the other gets discounted. That’s pretty much where the field is now, and has it been stuck there for a long time.
That’s certainly where I got my start. I was a firm believer in the standard dark matter interpretation. The evidence was obvious and overwhelming. Not only did there need to be invisible mass, it had to be some new kind of particle, like a WIMP. Almost certainly a WIMP. Any other interpretation (like MACHOs) was obviously stupid, as it violated some strong constraint, like Big Bang Nucleosynthesis (BBN). It had to be non-baryonic cold dark matter. HAD. TO. BE. I was sure of this. We were all sure of this.
What gets us in trouble is not what we don’t know. It’s what we know for sure that just ain’t so.
Josh Billings
I realized in the 1990s that the above reasoning was not airtight. Indeed, it has a gaping hole: we were not even considering modifications of dynamical laws (gravity and inertia). That this was a possibility, even a remote one, came as a profound and deep shock to me. It took me ages of struggle to admit it might be possible, during which I worked hard to save the standard picture. I could not. So it pains me to watch the entire community repeat the same struggle, repeat the same failures, and pretend like it is a success. That last step follows from the zeal of religious conviction: the outcome is predetermined. The answer still HAS TO BE dark matter.
So I asked myself – what if we’re wrong? How could we tell? Once one has accepted that the universe is filled with invisible mass that can’t be detected by any craft available known to us, how can we disabuse ourselves of this notion should it happen to be wrong?
One approach that occurred to me was a test in the power spectrum of the cosmic microwave background. Before any of the peaks had been measured, the only clear difference one expected was a bigger second peak with dark matter, and a smaller one without it for the same absolute density of baryons as set by BBN. I’ve written about the lead up to this prediction before, and won’t repeat it here. Rather, I’ll discuss some of the immediate fall out – some of which I’ve only recently pieced together myself.
The first experiment to provide a test of the prediction for the second peak was Boomerang. The second was Maxima-1. I of course checked the new data when they became available. Maxima-1 showed what I expected. So much so that it barely warranted comment. One is only supposed to write a scientific paper when one has something genuinely new to say. This didn’t rise to that level. It was more like checking a tick box. Besides, lots more data were coming; I couldn’t write a new paper every time someone tacked on an extra data point.
There was one difference. The Maxima-1 data had a somewhat higher normalization. The shape of the power spectrum was consistent with that of Boomerang, but the overall amplitude was a bit higher. The latter mattered not at all to my prediction, which was for the relative amplitude of the first to second peaks.
Systematic errors, especially in the amplitude, were likely in early experiments. That’s like rule one of observing the sky. After examining both data sets and the model expectations, I decided the Maxima-1 amplitude was more likely to be correct, so I asked what offset was necessary to reconcile the two. About 14% in temperature. This was, to me, no big deal – it was not relevant to my prediction, and it is exactly the sort of thing one expects to happen in the early days of a new kind of observation. It did seem worth remarking on, if not writing a full blown paper about, so I put it in a conference presentation (McGaugh 2000), which was published in a journal (IJMPA, 16, 1031) as part of the conference proceedings. This correctly anticipated the subsequent recalibration of Boomerang.
The figure from McGaugh (2000) is below. Basically, I said “gee, looks like the Boomerang calibration needs to be adjusted upwards a bit.” This has been done in the figure. The amplitude of the second peak remained consistent with the prediction for a universe devoid of dark matter. In fact, if got better (see Table 4 of McGaugh 2004).
Plot from McGaugh (2000): The predictions of LCDM (left) and no-CDM (right) compared to Maxima-1 data (open points) and Boomerang data (filled points, corrected in normalization). The LCDM model shown is the most favorable prediction that could be made prior to observation of the first two peaks; other then-viable choices of cosmic parameters predicted a higher second peak. The no-CDM got the relative amplitude right a priori, and remains consistent with subsequent data from WMAP and Planck.
This much was trivial. There was nothing new to see, at least as far as the test I had proposed was concerned. New data were pouring in, but there wasn’t really anything worth commenting on until WMAP data appeared several years later, which persisted in corroborating the peak ratio prediction. By this time, the cosmological community had decided that despite persistent corroborations, my prediction was wrong.
That’s right. I got it right, but then right turned into wrong according to the scuttlebutt of cosmic gossip. This was a falsehood, but it took root, and seems to have become one of the things that cosmologists know for sure that just ain’t so.
How did this come to pass? I don’t know. People never asked me. My first inkling was 2003, when it came up in a chance conversation with Marv Leventhal (then chair of Maryland Astronomy), who opined “too bad the data changed on you.” This shocked me. Nothing relevant in the data had changed, yet here was someone asserting that it had like it was common knowledge. Which I suppose it was by then, just not to me.
Over the years, I’ve had the occasional weird conversation on the subject. In retrospect, I think the weirdness stemmed from a divergence of assumed knowledge. They knew I was right then wrong. I knew the second peak prediction had come true and remained true in all subsequent data, but the third peak was a different matter. So there were many opportunities for confusion. In retrospect, I think many of these people were laboring under the mistaken impression that I had been wrong about the second peak.
I now suspect this started with the discrepancy between the calibration of Boomerang and Maxima-1. People seemed to be aware that my prediction was consistent with the Boomerang data. Then they seem to have confused the prediction with those data. So when the data changed – i.e., Maxima-1 was somewhat different in amplitude, then it must follow that the prediction now failed.
This is wrong on many levels. The prediction is independent of the data that test it. It is incredibly sloppy thinking to confuse the two. More importantly, the prediction, as phrased, was not sensitive to this aspect of the data. If one had bothered to measure the ratio in the Maxima-1 data, one would have found a number consistent with the no-CDM prediction. This should be obvious from casual inspection of the figure above. Apparently no one bothered to check. They didn’t even bother to understand the prediction.
Understanding a prediction before dismissing it is not a hard ask. Unless, of course, you already know the answer. Then laziness is not only justified, but the preferred course of action. This sloppy thinking compounds a number of well known cognitive biases (anchoring bias, belief bias, confirmation bias, to name a few).
I mistakenly assumed that other people were seeing the same thing in the data that I saw. It was pretty obvious, after all. (Again, see the figure above.) It did not occur to me back then that other scientists would fail to see the obvious. I fully expected them to complain and try and wriggle out of it, but I could not imagine such complete reality denial.
The reality denial was twofold: clearly, people were looking for any excuse to ignore anything associated with MOND, however indirectly. But they also had no clear prior for LCDM, which I did establish as a point of comparison. A theory is only as good as its prior, and all LCDM models made before these CMB data showed the same thing: a bigger second peak than was observed. This can be fudged: there are ample free parameters, so it can be made to fit; one just had to violate BBN (as it was then known) by three or four sigma.
In retrospect, I think the very first time I had this alternate-reality conversation was at a conference at the University of Chicago in 2001. Andrey Kravtsov had just joined the faculty there, and organized a conference to get things going. He had done some early work on the cusp-core problem, which was still very much a debated thing at the time. So he asked me to come address that topic. I remember being on the plane – a short ride from Cleveland – when I looked at the program. Nearly did a spit take when I saw that I was to give the first talk. There wasn’t a lot of time to organize my transparencies (we still used overhead projectors in those days) but I’d given the talk many times before, so it was enough.
I only talked about the rotation curves of low surface brightness galaxies in the context of the cusp-core problem. That was the mandate. I didn’t talk about MOND or the CMB. There’s only so much you can address in a half hour talk. [This is a recurring problem. No matter what I say, there always seems to be someone who asks “why didn’t you address X?” where X is usually that person’s pet topic. Usually I could do so, but not in the time allotted.]
About halfway through this talk on the cusp-core problem, I guess it became clear that I wasn’t going to talk about things that I hadn’t been asked to talk about, and I was interrupted by Mike Turner, who did want to talk about the CMB. Or rather, extract a confession from me that I had been wrong about it. I forget how he phrased it exactly, but it was the academic equivalent of “Have you stopped beating your wife lately?” Say yes, and you admit to having done so in the past. Say no, and you’re still doing it. What I do clearly remember was him prefacing it with “As a test of your intellectual honesty” as he interrupted to ask a dishonest and intentionally misleading question that was completely off-topic.
Of course, the pretext for his attack question was the Maxima-1 result. He phrased it in a way that I had to agree that those disproved my prediction, or be branded a liar. Now, at the time, there were rumors swirling that the experiment – some of the people who worked on it were there – had detected the third peak, so I thought that was what he was alluding to. Those data had not yet been published and I certainly had not seen them, so I could hardly answer that question. Instead, I answered the “intellectual honesty” affront by pointing to a case where I had said I was wrong. At one point, I thought low surface brightness galaxies might explain the faint blue galaxy problem. On closer examination, it became clear that they could not provide a complete explanation, so I said so. Intellectual honesty is really important to me, and should be to all scientists. I have no problem admitting when I’m wrong. But I do have a problem with demands to admit that I’m wrong when I’m not.
To me, it was obvious that the Maxima-1 data were consistent with the second peak. The plot above was already published by then. So it never occurred to me that he thought the Maxima-1 data were in conflict with what I had predicted – it was already known that it was not. Only to him, it was already known that it was. Or so I gather – I have no way to know what others were thinking. But it appears that this was the juncture in which the field suffered a psychotic break. We are not operating on the same set of basic facts. There has been a divergence in personal realities ever since.
Arthur Kosowsky gave the summary talk at the end of the conference. He told me that he wanted to address the elephant in the room: MOND. I did not think the assembled crowd of luminary cosmologists were mature enough for that, so advised against going there. He did, and was incredibly careful in what he said: empirical, factual, posing questions rather than making assertions. Why does MOND work as well as it does?
The room dissolved into chaotic shouting. Every participant was vying to say something wrong more loudly than the person next to him. (Yes, everyone shouting was male.) Joel Primack managed to say something loudly enough for it to stick with me, asserting that gravitational lensing contradicted MOND in a way that I had already shown it did not. It was just one of dozens of superficial falsehoods that people take for granted to be true if they align with one’s confirmation bias.
The uproar settled down, the conference was over, and we started to disperse. I wanted to offer Arthur my condolences, having been in that position many times. Anatoly Klypin was still giving it to him, keeping up a steady stream of invective as everyone else moved on. I couldn’t get a word in edgewise, and had a plane home to catch. So when I briefly caught Arthur’s eye, I just said “told you” and moved on. Anatoly paused briefly, apparently fathoming that his behavior, like that of the assembled crowd, was entirely predictable. Then the moment of awkward self-awareness passed, and he resumed haranguing Arthur.
Before we can agree on the interpretation of a set of facts, we have to agree on what those facts are. Even if we agree on the facts, we can differ about their interpretation. It is OK to disagree, and anyone who practices astrophysics is going to be wrong from time to time. It is the inevitable risk we take in trying to understand a universe that is vast beyond human comprehension. Heck, some people have made successful careers out of being wrong. This is OK, so long as we recognize and correct our mistakes. That’s a painful process, and there is an urge in human nature to deny such things, to pretend they never happened, or to assert that what was wrong was right all along.
This happens a lot, and it leads to a lot of weirdness. Beyond the many people in the field whom I already know personally, I tend to meet two kinds of scientists. There are those (usually other astronomers and astrophysicists) who might be familiar with my work on low surface brightness galaxies or galaxy evolution or stellar populations or the gas content of galaxies or the oxygen abundances of extragalactic HII regions or the Tully-Fisher relation or the cusp-core problem or faint blue galaxies or big bang nucleosynthesis or high redshift structure formation or joint constraints on cosmological parameters. These people behave like normal human beings. Then there are those (usually particle physicists) who have only heard of me in the context of MOND. These people often do not behave like normal human beings. They conflate me as a person with a theory that is Milgrom’s. They seem to believe that both are evil and must be destroyed. My presence, even the mere mention of my name, easily destabilizes their surprisingly fragile grasp on sanity.
One of the things that scientists-gone-crazy do is project their insecurities about the dark matter paradigm onto me. People who barely know me frequently attribute to me motivations that I neither have nor recognize. They presume that I have some anti-cosmology, anti-DM, pro-MOND agenda, and are remarkably comfortably about asserting to me what it is that I believe. What they never explain, or apparently bother to consider, is why I would be so obtuse? What is my motivation? I certainly don’t enjoy having the same argument over and over again with their ilk, which is the only thing it seems to get me.
The only agenda I have is a pro-science agenda. I want to know how the universe works.
This agenda is not theory-specific. In addition to lots of other astrophysics, I have worked on both dark matter and MOND. I will continue to work on both until we have a better understanding of how the universe works. Right now we’re very far away from obtaining that goal. Anyone who tells you otherwise is fooling themselves – usually by dint of ignoring inconvenient aspects of the evidence. Everyone is susceptible to cognitive dissonance. Scientists are no exception – I struggle with it all the time. What disturbs me is the number of scientists who apparently do not. The field is being overrun with posers who lack the self-awareness to question their own assumptions and biases.
So, I feel like I’m repeating myself here, but let me state my bias. Oh wait. I already did. That’s why it felt like repetition. It is.
The following bit of this post is adapted from an old web page I wrote well over a decade ago. I’ve lost track of exactly when – the file has been through many changes in computer systems, and unix only records the last edit date. For the linked page, that’s 2016, when I added a few comments. The original is much older, and was written while I was at the University of Maryland. Judging from the html style, it was probably early to mid-’00s. Of course, the sentiment is much older, as it shouldn’t need to be said at all.
I will make a few updates as seem appropriate, so check the link if you want to see the changes. I will add new material at the end.
Long standing remarks on intellectual honesty
The debate about MOND often degenerates into something that falls well short of the sober, objective discussion that is suppose to characterize scientific debates. One can tell when voices are raised and baseless ad hominem accusations made. I have, with disturbing frequency, found myself accused of partisanship and intellectual dishonesty, usually by people who are as fair and balanced as Fox News.
Let me state with absolute clarity that intellectual honesty is a bedrock principle of mine. My attitude is summed up well by the quote
When a man lies, he murders some part of the world.
This is a great quote for science, as the intent is clear. We don’t get to pick and choose our facts. Outright lying about them is antithetical to science.
I would extend this to ignoring facts. One should not only be honest, but also as complete as possible. It does not suffice to be truthful while leaving unpleasant or unpopular facts unsaid. This is lying by omission.
I “grew up” believing in dark matter. Specifically, Cold Dark Matter, presumably a WIMP. I didn’t think MOND was wrong so much as I didn’t think about it at all. Barely heard of it; not worth the bother. So I was shocked – and angered – when it its predictions came true in my data for low surface brightness galaxies. So I understand when my colleagues have the same reaction.
Nevertheless, Milgrom got the prediction right. I had a prediction, it was wrong. There were other conventional predictions, they were also wrong. Indeed, dark matter based theories generically have a very hard time explaining these data. In a Bayesian sense, given the prior that we live in a ΛCDM universe, the probability that MONDian phenomenology would be observed is practically zero. Yet it is. (This is very well established, and has been for some time.)
So – confronted with an unpopular theory that nevertheless had some important predictions come true, I reported that fact. I could have ignored it, pretended it didn’t happen, covered my eyes and shouted LA LA LA NOT LISTENING. With the benefit of hindsight, that certainly would have been the savvy career move. But it would also be ignoring a fact, and tantamount to a lie.
In short, though it was painful and protracted, I changed my mind. Isn’t that what the scientific method says we’re suppose to do when confronted with experimental evidence?
That was my experience. When confronted with evidence that contradicted my preexisting world view, I was deeply troubled. I tried to reject it. I did an enormous amount of fact-checking. The people who presume I must be wrong have not had this experience, and haven’t bothered to do any fact-checking. Why bother when you already are sure of the answer?
Willful Ignorance
I understand being skeptical about MOND. I understand being more comfortable with dark matter. That’s where I started from myself, so as I said above, I can empathize with people who come to the problem this way. This is a perfectly reasonable place to start.
To give an example of disinformation, I still hear said things like “MOND fits rotation curves but nothing else.” This is not true. The first thing I did was check into exactly that. Years of fact-checking went into McGaugh & de Blok (1998), and I’ve done plenty more since. It came as a great surprise to me that MOND explained the vast majority of the data as well or better than dark matter. Not everything, to be sure, but lots more than “just” rotation curves. Yet this old falsehood still gets repeated as if it were not a misconception that was put to rest in the previous century. We’re stuck in the dark ages by choice.
It is not a defensible choice. There is no excuse to remain ignorant of MOND at this juncture in the progress of astrophysics. It is incredibly biased to point to its failings without contending with its many predictive successes. It is tragi-comically absurd to assume that dark matter provides a better explanation when it cannot make the same predictions in advance. MOND may not be correct in every particular, and makes no pretense to be a complete theory of everything. But it is demonstrably less wrong than dark matter when it comes to predicting the dynamics of systems in the low acceleration regime. Pretending like this means nothing is tantamount to ignoring essential facts.
Even a lie of omission murders a part of the world.
Triton Station 