Yep, it’s a religion

I have been concerned for years that dark matter was morphing from legitimate science into a cold, dark religion. I have been reluctant to put it that way, because there are lots of scientists who work on dark matter that have not fallen entirely down that rabbit hole and who continue to make valuable contributions working in that context. But a recent experience reminded me that my concerns were not misplaced, and there are plenty of scientists who have fallen irredeemably down this rabbit hole. No matter what answer the future holds to be correct, many current scientists will have gone to their graves in denial of it.

Where is the boundary between science and religion? It is hard to assess where the borderline is. But it is easy to see when people are far over the line – so far over that it doesn’t really matter where exactly the line is. One can attend any conference on the subject to find people who unabashedly assert that dark matter exists without question. Not just that acceleration discrepancies have been amply demonstrated empirically, but that the only possible interpretation is dark matter. If asked whether this invisible mass is in the room with us now, they will enthusiastically^# answer yes! Since dark matter has not been detected in the laboratory, this assertion is an expression of faith – the hallmark of religion – not of an established scientific fact. What we have established is that there are discrepancies between what we see and what we get when we assume Newtonian gravity (or GR, if needed). What we don’t know is whether the cause of these discrepancies is some form of invisible mass (dark matter) or if the equations we employ are inadequate (modified gravity [or more generally, dynamics]).

Indeed, these days many people will assert that dark matter has already been detected, usually citing astronomical evidence that used to be considered too feeble to merit a Nobel prize. Funny how repeating a mantra long enough morphs an aspiration into accepted reality. Modern physics is not providing a strong falsification of the supposition that science is a social construct.

A prominent example of an observation of the sky that is frequently cited as absolutely requiring cold dark matter is the acoustic power spectrum of the cosmic microwave background. Quoting clayton from a few years ago:

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. There is a stone-cold, qualitative, crystal clear prediction of CDM about the relative sizes of the second and third peaks that modified gravity profoundly and irredeemably gets wrong: it thinks the third peak should be relatively larger* than the second… whereas CDM thinks they should be about the same

I would accept that this were conclusive proof of dark matter if this were the unique prediction of dark matter: that there was no other way to do it, so all other approaches were indeed irredeemable. (Quite the strong language, eh?) The problem is that CDM is not the one unique was to fit these data. Skordis & Zlosnik showed that it is possible to write a modified gravity theory that also fits the CMB data:

*CMB power spectrum observed by Planck fit by AeST (Skordis & Zlosnik 2021).*

This does not prove the AeST theory of Skordis & Zlosnik is correct, but it does demonstrate that it is possible to write a modified gravity theory that does indeed do what it is frequently asserted to be impossible for a modified gravity theory to do. I’ve heard of a couple of other theories that can also do this (the relativistic Khronon theory of Blanchet and nonlocal MOND as discussed by Deffayet & Woodard), so clearly this success is not uniquely limited to cold dark matter, or even a particular modified gravity theory. The work of Skordis & Zlosnik (2021) was known and in the literature before clayton made the assertion above in late 2022, so either he wasn’t paying attention (likely) or is convinced that it is impossible so doesn’t even consider the possibility (also likely). The former just says we’re all too busy, but the latter is a mark of religious thinking: my god is the only god, thou shalt have no other hypotheses before^& me.

Many people are very impressed with the quality of the LCDM fit to the CMB. That is indeed very good, but there are enough free parameters that we were going to get a fit to any physically plausible power spectrum. If not, we’ve never been shy about making up new parameters. (Evolving dark energy, anyone? How about a running power spectrum? There’s a whole bag of possibilities!) What I’ve been more impressed with is the consistency of the fit to the CMB data with the many independent constraints on conventional cosmology. Or at least it was, until it wasn’t.

The Hubble tension has gotten steadily worse (in terms of statistical significance), and it really does not look like local measurements are to blame, nor is it the only tension. People seem to miss that it is the CMB-fitted value of the Hubble constant that has evolved over time to spoil the concordance that got us to believe in LCDM in the first place. But if the CMB is the cornerstone of your religion, all other data must inevitably be at fault and can be ignored: there is an entire community of cosmologists who choose to believe the best-fit Planck cosmology to the exclusion of all other data. It’s like the bad old days of the Hubble tension all over again, with the physics community choosing to believe the lower value of H₀ because it makes more sense for the aspects of cosmology that they care about while those in the astronomical community who actually measure H₀ find a persistently higher value.

A real tension in LCDM implies the need for new physics of the unknown variety. One doesn’t want to go there if it can be helped. I didn’t consider MOND until I was already concerned for the viability of dark matter. There are real problems for the paradigm that its more intense advocates simply deny, brush aside without real thought, or choose to remain ignorant of. When they are confronted with a problem, they are pretty creative about making stuff up on the spot. Anything to avoid having to confront the unspeakable – another hallmark of religion.

For example, cold dark matter is scale free. That’s foundational to the hypothesis. So the existence of an acceleration scale in the kinematic data is anathema to CDM. When I first pointed this contradiction out, there were a variety of assertions to the effect of “does too!” One example is provided by Kaplinghat & Turner, who claim to show “how Milgrom’s law comes about in the cold dark matter theory of structure formation.” That would, indeed, be ideal, and is a requirement for any theory to be successful.

Wee problem: they demonstrat no such thing. CDM is scale free, yet K&T claim that it explains Milgrom’s Law, which is predicated on the existence of an acceleration scale. Well, which is it? Is CDM scale free? Or does it explains the acceleration scale? We can’t have it both ways: their very premise is self-contradictory. It is absurd on its face.

The acceleration scale is defined by baryons, for which K&T have no model. To connect baryons with dark matter, they make a hand-waving argument about galaxies reaching a₀ at the edge of their disks. This is not even a concept of a model and does not begin to suffice as an explanation for many reasons, a prominent one being that low surface brightness galaxies have accelerations less than a₀ everywhere:

Centripetal acceleration curves color coded by galaxy surface brightness. Low surface brightness galaxies (blue colors) have low (sub-a₀) accelerations everywhere: there is no edge at which they reach a₀. (Adapted from McGaugh 2020.)

Milgrom pointed out this and many other shortcomings of their scenario, so I feel no need to elaborate further. Milgrom eviscerated their paper so thoroughly that the proper course of action would have been to retract it. Instead, they simply never acknowledge the criticism, and persist to this day in pushing it as some sort of valid scientific explanation. It is not; it does not withstand even mild critical scrutiny. But it doesn’t need to: it reassures the faithful that all is well. They hear what they want to hear without questioning its veracity. That’s another hallmark of religion.

I have refrained from saying these things in the past because I’m too nice. For example, a few years ago I started then abandoned the draft text below, which I simply cut & paste:

One of the things that attracted me to a career in science is the notion of objectivity. I grew up for a time in the bible belt, where people earnestly believed things that were obviously untrue, even to the eyes of a small child. On the occasions that I had the temerity to point out the obvious, the contradictions posed by facts never had an impact on their belief system. Rather, it inevitably earned me a warning that I was going to hell. No few of these people seemed to think it was their religious duty to send me there prematurely, or at least to make life on Earth a living hell.

Scientists eschew such behavior, but are also human, so often engage in it anyway. I’ve encountered it a lot. I get it; I went through the same denial, grief, and anger over the prospect of losing my good friend cold dark matter. The stages of grief never brought something back from the dead, but it has engendered a lot of blame-the-messenger.

Here’s an example, from a review by Mike Turner:

There is a lot of misinformation packed into this short paragraph.

The first clue is right there at the beginning, in red: the heading “False starts.” This is false framing, a classic tool of propagandists. It starts from the outset by asserting that the topic to be discussed is wrong at a level of knowledge so common it requires no justification. This is not the way one starts an objective discussion, much less a scientific one.

Turner then misconstrues what Milgrom did. He didn’t notice the scale a₀ in the data, for which there was scant evidence at the time. Rather, Milgrom made the obvious statement that the inference of dark matter relied on the assumption that dynamics, as encapsulated by the laws of inertia and gravity, is the same on the very different scales of galaxies as in the solar system where they were established, so we ought to consider if dynamics might change in some way. He quickly excluded a size dependence as a possibility. How he settled on acceleration is beyond the scope of this post, and not for me to say. Neither is it for Turner to say.

After a brief and incomplete description of what MOND is, Turner allows that “this one-parameter model fits all the rotation-curve data”. Even in making this admission, he chooses to call it a model rather than a theory. A model is something specific you build in the context of a theory, like a halo model in CDM. MOND is more than that.

Turner quickly moves on without contemplating any meaning that rotation curves might hold. Let’s pause to consider that.

First, I would not say that MOND fits all the rotation curve data. It fits most galaxies, but there are a minority of weird cases that are not well fit. The weird cases inevitably don’t make sense in terms of dark matter either, so on the whole I interpret this to be the usual price of dealing with astronomical data – some of it is just goofy. Setting such cases aside, I can and have fit the same data with all sorts of dark matter halo models. MOND requires fewer parameters, which is important, but the difference isn’t in the fitting. The difference is in predictive ability. I can use MOND to predict the dynamics of galaxies a priori, and have done so many times. I cannot use any flavor of dark matter theory to do the same, and it’s not for lack of trying.

The predictive power of MOND must be telling us something, even if it is something about the nature of dark matter or the process of galaxy formation. There are many papers written on this, some deep and profound, others absurd and banal. Turner cites none of them, nor displays any awareness that such work exists. I would venture to guess that is because acknowledging such work would imply that there is something to debate here, something he would apparently rather not admit.

That’s where I left off. It’s exhausting deciphering other people’s false assertions. Moreover, I just don’t like criticizing other people, no matter how richly they deserve it. (Turner has never refrained from criticizing me in ad hominem terms: on one occasion^$ he showed my picture to an audience and called me “the enemy.”) A large segment of the particle physics and cosmology community appears to think this way, and has succumbed to a scientific version of bible thumping in which you can assert any absurd thing so long as it falls within the framework of the holy LCDM. They really need to find something better to do.

I had hoped we were past this, but I heard a talk last week that was exactly in this mode. To paraphrase, the talk went

We’re sure dark matter exists. We have been sure about it for decades. In that time, we have been repeatedly proven wrong about what it is. Rather than re-think our paradigm in the face of these repeated failures, we double down yet again on the existence of this invisible, undetected mass, asserting aggressively^% that it must be true while eliding or misrepresenting the evidence that it is not. This enables us to make up a whole lot of exciting new possibilities for what the dark matter might be and conceive of ever more grandiose experiments to continue not to detect it. You must believe in dark matter!

This was not a science talk so much as an indoctrination session. It was as if I had stumbled into a revivalist tent where some hothead was preaching to the choir. This is the kind of talk that misled an entire generation into wasting their careers at the bottom of a mine shaft searching for WIMPs. At least WIMPs were a well-motivated hypothesis; this kind of talk could lead a new generation down an even greater variety of garden paths.

I am well aware that I might fall prey to this attitude myself. That’s why I set criteria by which I would change my mind: detect dark matter already, or at least provide a satisfactory explanation as to how MOND comes about. Neither of those criteria have been met. There are claims to do the latter, but so far these are just variations on models I tried and found to fail long ago. If I thought these could work, I would have said so. At the same time, I don’t see any dark matter advocates taking up the challenge to specify what would change their minds. When I ask them what could falsify dark matter, I get dumbfounded looks – the deer-in-the-headlight face one gets when the immediate response why would you even ask that? is checked by a distant memory that scientific theories are supposed to be falsifiable.

Personally, I found it humbling to encounter MOND in my own data. I too thought we understood the universe with dark matter. But who ordered this? Certainly not me: my own conventional, dark-matter based predictions were falsified. No one else working in the context of dark matter had got it right at the time either. Only Milgrom ordered this.

And what is this? There is a direct connection between what we see and what we get. Even in ignorance of MOND, the radial acceleration relation encodes a one-to-one relation between the distribution of baryons and the effective force. This is so direct that one can right down a single equation connecting the two:

g_{obs} = F(g_N/a_0)\,g_N.

The observed acceleration is a simple function of that predicted by Newton for the stars and gas that we see. There is no mention of unseen mass; everything is specified by what we can see is there.

I’ve sometimes heard astronomers complain about the reductionist ethos of physics, trying to cram all the complexity of the entire universe into a theory of everything. But here it is appropriate: there is a single, apparently universal force-law at work in galaxies. That’s telling us something profound. And yet if questioned about this, the physicists are the ones who will complain that galaxies are complicated, so they should be exempted from having to explain them. Galaxies should be complicated – in LCDM. But they’re observed not to be, in the sense that a single equation suffices to describe their kinematics. The problem isn’t that galaxies are inexplicably complicated, it’s that they should be but aren’t.

I am deeply disappointed that many scientists apparently lack the physical intuition to immediately recognize the import of the simple relation between what we see and what we get. It is the same sort of thing Newton noticed in the solar system: everything happens as if the gravitational force is proportional to the product of the masses and the inverse square of their separation. He didn’t understand why at the time, and was criticized for indulging in magical thinking: how can there be action at a distance? But that’s what the data were saying, and the same applies now. We might not yet understand the why, but that the data look as if MOND is what’s happening in this universe.

^#The framing has morphed over the years. A recent advent is that some people have started proactively asserting that invisible mass is in the room with us now in order to avoid having to answer it as a question that makes them sound like loonies.

*He means the third peak should be smaller than the second, not larger, if by “it” he means modified gravity with the baryon density expected from big bang nucleosynthesis, which was the hypothesis that correctly predicted the first-to-second peak ratio but does indeed get the second-to-third peak ratio wrong. Funny how the CMB community was able to completely ignore the successful prediction for several years, but were then suddenly all over the latter failure. The third peak falsifies the ansatz on which that particular prediction was built, not the entire concept of modified gravity. This would be like asserting that all possible forms of dark matter are excluded because we haven’t yet detected WIMPs. It is a classic failure of objectivity, which is another hallmark of faith-based argumentation: we know His name is [insert favorite deity], not [insert any other deity].

^&Or after me. Dark matter was my first hypothesis, and I’m here to tell you that True Believers do not suffer second hypotheses or those who stray from the fold. I guess that’s why so many scientists who are MOND-curious keep it on the down low. Wise, perhaps (that’s why tenure needs to be a thing), but hardly the ideal of the open and free exchange of scientific ideas.

^$I wasn’t there, but one audience member (not someone I knew) thought it was so over the top that he told me about it, sharing a link with a video. (I did not retain that link, and doubt the hosting conference website is still active.)

^%Argument weak here. RAISE VOICE!

Has dark matter been detected in the Milky Way?

If a title is posed as a question, the answer is usually

No.

There has been a little bit of noise that dark matter might have been detected near the center of the Milky Way. The chatter seems to have died down quickly, for, as usual, this claim is greatly exaggerated. Indeed, the claim isn’t even made in the actual paper so much as in the scuttlebutt^# related to it. The scientific claim that is made is that

The halo excess spectrum can be fitted by annihilation with a particle mass $m_{χ} \sim$ 0.5–0.8 TeV and cross section $⟨ σ υ ⟩ \sim$ (5–8) $\times 10^{- 25} {cm}^{3} s^{- 1}$ for the $b \bar{b}$ channel.

Totani (2025)

What the heck does that mean?

First, the “excess spectrum” refers to a portion of the gamma ray emission detected by the Fermi telescope that exceeds that from known astrophysical sources. This signal might be from a WIMP with a mass in the range of 500 – 800 GeV. That’s a bit heavier than originally anticipated (~100 GeV), but not ridiculous. The cross-section is the probability for an interaction with bottom quarks and anti-quarks. (The Higgs boson can decay into b quarks.)

Astrophysical sources at the Galactic center

There is a long-running issue with the interpretation of excess signals as dark matter. Most of the detected emission is from known astrophysical sources, hence the term “excess.” There being an excess implies that we understand all the sources. There are a lot of astrophysical sources at the Galactic center:

The center of the Milky Way as seen by the South African MeerKAT radio telescope with a close up from JWST. Image credit: NASA, ESA, CSA, STScI, SARAO, S. Crowe (UVA), J. Bally (CU), R. Fedriani (IAA-CSIC), I. Heywood (Oxford).

As you can see, the center of the Galaxy is a busy place. It is literally the busiest place in the Galaxy. Attributing any “excess” to non-baryonic dark matter is contingent on understanding all of the astrophysical sources so that they can be correctly subtracted off. Looking at the complexity of the image above, that’s a big if, which we’ll come back to later. But first, how does dark matter even come unto a discussion of emission from the Galactic center?

Indirect WIMP detection

Dark matter does not emit light – not directly, anyway. But WIMP dark matter is hypothesized to interact with Standard Model particles through the weak nuclear force, which is what provides a window to detect it in the laboratory. So how does that work? Here is the notional Feynman diagram:

Conceivable Interactions between WIMPs (X) and standard model particles (q). The diagram can be read left to right to represent WIMPs scattering off of atomic nuclei, top to bottom to represent WIMPs annihilating into standard model particles, or bottom to top to represent the production of dark matter particles in high energy collisions.

The devious brilliance of this Feynman diagram is that we don’t need to know how the interaction works. There are many possibilities, but that’s a detail – that central circle is where the magic happens; what exactly that magic is can remain TBD. All that matters is that it can happen (with some probability quantified by the interaction cross-section), so all the pathways illustrated above should be possible.

Direct detection experiments look for scattering of WIMPs off of nuclei in underground detectors. They have not seen anything. In principle, WIMPs could be created in sufficiently high-energy collisions of Standard Model particles. The LHC has more than adequate energy to produce dark matter particles in this way, but no such signal has been seen^$. The potential signal we’re discussing here is an example of indirect detection. There are a number of possibilities for this, but the most obvious^{^} one follows from WIMPs being their own anti-particles, so they occasionally meet in space and annihilate into Standard Model particles.

The most obvious product of WIMP annihilations is a pair of gamma rays, hence the potential for the Fermi gamma ray telescope to detect their decay products. Here is a simulated image of the gamma ray sky resulting from dark matter annihilations:

*Simulated image from the via Lactea II simultion (Fig. 1 of Kuhlen et al. 2008).*

The dark regions are the brightest, where the dark matter density is highest. That includes the center of the Milky Way (white circle) and also sub-halos that might contain dwarf satellite galaxies.

Since we don’t really know how the magic interaction happens, but have plenty of theoretical variations, many other things are also possible, some of which might be cosmic rays:

Fig. 3 of Topchiev et al. (2017) illustrating possible decay channels for WIMP annihilations. Gamma rays are one inevitable product, but other particles might also be produced. These would be born with energies much higher than their rest masses (~100 GeV, while electrons and positrons have masses of 0.5 MeV) so would be moving near the speed of light. In effect, dark matter could be a source of cosmic rays.

The upshot of all this is that the detection of an “excess” of unexpected but normal particles might be a sign of dark matter.

Sociology: different perspectives from different communities

A lot hinges on the confidence with which we can disentangle expected from unexpected. Once we’ve accounted for the sources we already knew about, there are always new sources to be discovered. That’s astronomy. So initially, the communal attitude was that we shouldn’t claim a signal was due to dark matter until all astrophysical signals had been thoroughly excluded. That never happened: we just kept discovering new astrophysical sources. But at some point, the communal attitude transformed into one of eager credulity. It was no longer embarrassing to make a wrong claim; instead, marginal and dubious claims were made eagerly in the hopes of claiming a Nobel prize. If it didn’t work out, oh well, just try again. And again and again and again. There is apparently no shame in claiming to see the invisible when you’re completely convinced it is there to be seen.

This switch in sociology happened in the mid to late ’00s as people calling themselves astroparticle^& physicists became numerous. These people were remarkably uninterested in astrophysics or astrophysical sources in their own right but very interested in dark matter. They were quick to claim that any and every quirk in data was a sign of dark matter. I can’t help but wonder if this behavior is inherited from the long drought in interesting particle collider results, which gradually evolved into a propensity for high energy particle phenomenologists to leap on every two-sigma blip as a sign of new physics, dumping hundreds of preprints on arXiv after each signal of marginal significance was announced. It is always a sprint to exercise the mental model-building muscles and make up some shit in the brief weeks before the signal inevitably goes away again.

Let’s review a few examples of previous indirect dark matter detection claims.

Cosmic rays from Kaluza-Klein dark matter – or not

This topic has a long and sordid history. In the late ’00s, there were numerous claims of an excess in cosmic rays – ATIC saw too many electrons for the astrophysical background, and and PAMELA saw an apparent rise in the positron fraction, perhaps indicating a source with a peak energy around 620 GeV. (If the signal is from dark matter, the rest mass of the WIMP is imprinted in the energy spectrum of its decay products.) The combination of excess electrons and extra positrons seemed fishy enough* to some to point to new physics: dark matter. There were of course more sober analyses, for example:

Fig. 3 from Aharonian et al. (2009): The energy spectrum E³ dN/dE of cosmic-ray electrons measured by H.E.S.S. and balloon experiments. Also shown are calculations for a Kaluza-Klein signature in the H.E.S.S. data with a mass of 620 GeV and a flux as determined from the ATIC data (dashed-dotted line), the background model fitted to low-energy ATIC and high-energy H.E.S.S. data (dashed line) and the sum of the two contributions (solid line). The shaded regions represent the approximate systematic error as in Fig. 2.

A few things to note about this plot: first, the data are noisy – science is hard. The ATIC and H.E.S.S. data are not really consistent – one shows an excess, the other does not. The excess is over a background model that is overly simplistic – the high energy astrophysicists I knew were shouting that the apparent signal could easily be caused by a nearby pulsar^##. The advocates for a detection in the astroparticle community simply ignored this point, or if pressed, asserted that it seemed unlikely.

One problem that arose with the dark matter interpretation was that there wasn’t enough of it. Space is big and the dark matter density is low, so it is hard to get WIMPs together to annihilate. Indeed, the expected signal scales as the square of the WIMP density, so is very sensitive to just how much dark matter is lurking about. The average density in the solar neighborhood needed to explain astronomical data is around 0.3 to 0.4 GeV cm^-3; this falls short of producing the observed signal (if real) by a factor of ~500.

An ordinary scientist might have taken this setback as a sign that he^$$ was barking up the wrong tree. Not to be discouraged, the extraordinary astroparticle physicists started talking about the “boost factor.” If there is a region of enhanced dark matter density, then the gamma ray/cosmic ray signal would be boosted, potentially by a lot given the density-squared dependence. This is not quite as crazy as it sounds, as cold dark matter halos are predicted to be lumpy: there should be lots of sub-halos within each halo (and many sub-sub halos within those, right the way down). So, what are the odds that we happen to live near enough to a subhalo that could result in the required boost factor?

The odds are small but nonzero. I saw someone at a conference in 2009 make a completely theoretical attempt to derive those odds. He took a merger tree from some simulation and calculated the chance that we’d be near one of these lumps. Then he expanded that to include a spectrum of plausible merger trees for Milky Way-mass dark matter halos. The noisier merger histories gave higher probabilities, as halos with more recent mergers tend to be lumpier, having had a fresh injection of subhalos that haven’t had time to erode away through dynamical friction into the larger central halo.

This was all very sensible sounding, in theory – and only in theory. We don’t live in any random galaxy. We live in the Milky Way and we know quite a bit about it. One of those things is that it has had a rather quiet merger history by the standards of simulated merger trees. To be sure, there have been some mergers, like the Gaia-Enceladus Sausage. But these are few and far between compared to the expectations of the simulations our theorist was considering. Moreover, we’d know if it weren’t, because mergers tend to heat the stellar disk and puff up its thickness. The spiral disk of the Milky Way is pretty cold dynamically, which places limits on how much mass has merged and when. Indeed, there is a whole subfield dedicated to the study of the thick disk, which seems to have been puffed up in an ancient event ~8 Gyr ago. Since then it has been pretty quiet, though more subtle things can and do happen.

The speaker did not mention any of that. He had a completely theoretical depiction of the probabilities unsullied by observational evidence, and was succeeding in persuading those who wanted to believe that the small probability he came up with was nevertheless reasonable. It was a mixed audience: along with the astroparticle physicists were astronomers like myself, including one of the world’s experts on the thick disk, Rosy Wyse. However, she was too polite to call this out, so after watching the discussion devolve towards accepting the unlikely as probable, I raise my hand to comment: “We know the Milky Way’s merger history isn’t as busy as the models that give a high probability.” This was met with utter incredulity. How could astronomy teach us anything about dark matter? It’s not like the evidence is 100% astronomical in nature, or… wait, it is. But no, no waiting or self-reflection was involved. It rapidly became clear that the majority of people calling themselves astroparticle physicists were ignorant of some relevant astrophysics that any astronomy grad student would be expected to know. It just wasn’t in their training or knowledge base. Consequently, it was strange and shocking^&& for them to learn about it this way. So the discussion trended towards denial, at which point Rosy spoke up to say yes, we know this. Duh. (I paraphrase.)

The interpretation of the excess cosmic ray signal as dark matter persisted a few years, but gradually cooler heads prevailed and the pulsar interpretation became widely accepted to be more plausible – as it always had been. Indeed, claiming cosmic rays were from dark matter became almost disreputable, as it richly deserved to be. So much so that when the AMS cosmic ray experiment joined the party late, it had essentially zero impact. I didn’t hear anyone advocating for it, even in whispers at workshops. It seemed more like its Nobel laureate PI just wanted a second Nobel prize, please and thank you, and even the astroparticle community felt embarrassed for him.

This didn’t preclude the same story from playing out repeatedly.

Gamma rays from WIMPs – or not

In the lead-up to a conference on dark matter hosted at Harvard in 2014, there were claims that the Fermi telescope – the same one that is again in the news – had seen a gamma ray line around 126 GeV that was attributed to dark matter. This claim had many red flags. The mass was close to the Higgs particle mass, which was kinda weird. The signal was primarily seen on the limb of the Earth, which is exactly where you’d expect garbage noise to creep in. Most telling, the Fermi team itself was not making this claim. It came from others who were analyzing their data. I am no fan of science by big teams – they tend to become bureaucratic behemoths that create red tape for their participants and often suppress internal dissent** – but one thing they do not do is leave Nobel prizes unanalyzed in their data. The Fermi team’s silence in this matter was deafening.

In short, this first claim of gamma rays from dark matter looked to be very much on the same trajectory as that from cosmic rays. So I was somewhat surprised when I saw the draft program for the Harvard conference, as it had an entire afternoon session devoted to this topic. I wrote the organizers to politely ask if they really thought this would still be a thing by the time the conference happened. One of them was an enthusiastic proponent, so yes.

Narrator: it was not.

By the time the conference happened, the related claims had all collapsed, and all the scientists invited to speak about it talked instead about something completely different, as if it had never been a thing at all.

X-rays from sterile neutrinos – or not

Later, there was the 3.5 keV line. If one squinted really hard at X-ray data, it looked like there might sorta kinda be an unidentified line. This didn’t look particularly convincing, and there are instances when new lines have been discovered in astronomical data rather than laboratory data (e.g., helium was first recognized in the spectrum of the sun, hence the name; also nebulium, which was later recognized to be ionized oxygen), so again, one needed to consider the astrophysical possibilities.

Of course, it was much more exciting to claim it was dark matter. Never mind that it was a silly energy scale, being far too low mass to be cold dark matter (people seem to have forgotten^*# the Lee-Weinberg limit, which requires m_X > 2 GeV); a few keV is rather less than a few GeV. No matter, we can always come up with an appropriate particle – in this case, sterile neutrinos^*$.

If you’ve read this far, you can see how this was going to pan out.

Gamma rays from WIMPs again, maybe maybe

So now we have a renewed claim that the Fermi excess is dark matter. Given the history related above, the reader may appreciate that my first reaction was Really? Are we doing this again?

This is different from the claim a decade ago. The claimed mass is different, and the signal is real, being part of the mess of emission from the Galactic center. The trick, as so often the case, is disentangling the dark matter signal from the plausible astrophysical sources.

Indeed, the signal is not new, only this particular fit with WIMP dark matter is. There had, of course, been discussion of all this before, but it faded out when it became clear that the Fermi signal was well explained by a population of millisecond pulsars. Astrophysics was again the more obvious interpretation^*%. Or perhaps not: I suppose if you’re part of a community convinced that dark matter exists who is spending an enormous amount of time and resources looking for a signal from dark matter and whose basic knowledge of astrophysics extends little beyond “astronomical data show dark matter exists but are messy so there’s always room to play” then maybe invoking an invisible agent from an unknown dark sector seems just as plausible as an obvious astrophysical source. Hmmm… that would have sounded crazy to me even back when, like them, I was sure that dark matter had to exist and be made of WIMPs, but here we are.

Looking around in the literature, I see there is still a somewhat active series of papers on this subject. They split between no way and maybe.

For example, Manconi et al. (2025) show that the excess signal has the same distribution on the sky as the light from old stars in the Galaxy. The distribution of stars is asymmetrical thanks to the Galactic bar, which we see at an angle somewhere around ~30 degrees, so one end is nearer to us than the other, creating a classic “X/peanut” shape seen in other edge-on barred spiral galaxies. So not only is the spectrum of the signal consistent with millisecond pulsars, it has the same distribution on the sky as the stars from which millisecond pulsars are born. So no way is this dark matter: it is clearly an astrophysical signal.

Not to be dissuaded by such a completely devastating combination of observations, Muru et al. (2025) argue that sure, the signal looks like the stars, but the dark matter could have exactly the same distribution as the stars. They cite the Hestia simulations of the Local Group as an example where this happens. Looking at those, they’re not as unrealistic as many simulations, but they appear to suffer the common affliction of too much dark mass near the center. That leaves the dark matter more room to be non-spherical so maybe be lumpy in the same was as the stars, and also provide a higher annihilation signal from the high density of dark matter. So they say maybe, calling the pulsar and dark matter interpretations “equally compelling.”

Returning to Totani’s sort-of claimed detection, he also says

This cross section is larger than the upper limits from dwarf galaxies and the canonical thermal relic value, but considering various uncertainties, especially the density profile of the MW halo, the dark matter interpretation of the 20 GeV “Fermi halo” remains feasible.

Totani (2025)

OK, so there’s a lot to break down in this one sentence.

The canonical thermal relic value is kinda central to the whole WIMP paradigm, so needing a value higher than that is a red flag reminiscent of the need for a boost factor for the cosmic ray signal. There aren’t really enough WIMPs there to do the job unless we juice their effectiveness at making gamma rays. The juice factor is an order of magnitude here: Steigman et al. (2012) give 2.2 x 10^-26 cm³s^-1 for what the thermal cross-section should be vs. the (5-8) x 10^-25 cm³s^-1 suggested by Totani (2025).

It is also worth noting that one point of Steigman’s paper is that as a well-posed hypothesis, the WIMP cross section can be calculated; it isn’t a free parameter to play with, so needing the cross-section to be larger than the upper limits from dwarf galaxies is another red flag. If this is indeed a dark matter signal from the Galactic center, then the subhalos in which dwarf satellites reside should also be visible, as in the simulated image from via Lactea above. They are not, despite having fewer messy astrophysical signals to compete with.

So “remains feasible” is doing a lot of work here. That’s the scientific way of saying “almost certainly wrong, but maybe? Because I’d really like for it to work out that way.”

The dark matter distribution in the Milky Way

One of the critical things here is the density of dark matter near the Galactic center, as the signal scales as the square of the density. Totani (2025) simply adopts the via Lactea simulation to represent the dark matter halo of the Galaxy in his calculations. This is a reasonable choice from a purely theoretical perspective, but it is not a conservative choice for the problem at hand.

What do we know empirically? The via Lactea simulation was dark matter only. There is no stellar disk, just a dark matter halo appropriate to the Milky Way. So let’s add that halo to a baryonic mass model of the Galaxy:

*The rotation curve of the via Lactea dark matter halo (red curve) combined with the Milky Way baryon distribution (light blue line). The total rotation (dark blue line) overshoots the data.*

The important part for the Galactic center signal is the region at small radius – the first kpc or two. Like most simulations, via Lactea has a cuspy central region of high dark matter density that is inconsistent with data. This overshoots the equivalent circular velocity curve from observed stellar motions. I could fix the fit above by reducing the stellar mass, but that’s not really an option in the Milky Way – we need a maximal stellar disk to explain the microlensing rate towards the center of the Galaxy. The “various uncertainties, especially the density profile of the MW halo” statement elides this inconvenient fact. Astronomical uncertainties are ever-present, but do not favor a dark matter signal here.

We can subtract the baryonic mass model from the rotation curve data to infer what the dark matter distribution needs to be. This is done in the plot below, where it is compared to the via Lactea halo:

*The empirical dark matter halo density profile of the Milky Way (blue line) compared to the via Lactea simulation (red line).*

The empirical dark matter density profile of the Milky Way does not continue to rise inwards as steeply as the simulation predicts. It shows the same proclivity for a shallower core as pretty much every other galaxy in the sky. This reduced density of dark matter in the central couple of kpc means the signal from WIMP annihilation should be much lower than calculated from the simulated distribution. Remember – the WIMP annihilation signal scales as the square of the dark matter density, so the turn-down seen at small radii in the log-log plot above is brutal. There isn’t enough dark matter there to do what it is claimed to be doing.

Cry wolf

There have now been so many claims to detect dark matter that have come and gone that it is getting to be like the fable of the boy who cried wolf. A long series of unpersuasive claims does not inspire confidence that the next will be correct. Indeed, it has the opposite effect: it is going to be really hard to take future claims seriously.

It’s almost as if this invisible dark matter stuff doesn’t exist.

Note added: Jeff Grube points out in the comments that Wang & Duan (2025) have a recent paper showing that the dark matter signal discussed here also predicts an antiproton signal that is already excluded by AMS data. While I find this unsurprising, it is an excellent check. Indeed, it would have caused me to think again had the antiproton signal been there: independent corroboration from a separate experiment is how science is supposed to work.

^#It has become a pattern for advocates of dark matter to write a speculative paper for the journals that is fairly restrained in its claims, then hype it as an actual detection to the press. It’s like “Even I think this is probably wrong, but let’s make the claim on the off chance it pans out.”

^$Ironically, a detection from a particle collider would be a non-detection. The signature of dark matter produced in a collision would be an imbalance between the mass-energy that goes into the collision and that measured in detected particles coming out of it. The mass-energy converted into WIMPs would escape the detector undetected. This is analogous to how neutrinos were first identified, though Fermi was reluctant to make up an invisible, potentially undetectable particle – a conservative value system that modern particle physicists have abandoned. The 13,000 GeV collision energy of the LHC is more than adequate to make ~100 GeV WIMPs, so the failure of this detection mode is telling.

^{^}A less obvious possibility is spontaneous decay. This would happen if WIMPs are unstable and decay with a finite half-life. The shorter the half-life, the more decays, and the stronger the resulting signal. This implies some fine-tuning in the half-life – if it is much longer than a Hubble time, then it happens so seldom it is irrelevant; if it is shorter than a Hubble time, then dark matter halos evaporate and stable galaxies don’t exist.

^&Astroparticle physics, also known as particle astrophysics, is a relatively new field. It is also an oxymoron, being a branch of particle physics with only aspirational delusions of relevance to astrophysics. I say that to be rude to people who are rude to astronomers, but it is also true. Astrophysics is the physics of objects in the sky, and as such, requires all of physics. Physics is a broad field, so some aspects are more relevant than others. When I teach a survey course, it touches on gravity, electromagnetism, atomic and molecular quantum mechanics, nuclear physics, and with the discovery of exoplanets, increasingly on geophysics. Particle physics doesn’t come up. It’s just not relevant, except where it overlaps with nuclear physics. (As poorly as particle physicists think of astronomers, they seem to think even less of nuclear physicists, whom they consider to be failed particle physicists (if only they were smart enough!) and nuclear physicists hate them in return.) This new field of astroparticle physics seems to be all about dark matter as driven by early universe cosmology, with contempt for everything that happens in the 13 billion years following the production of the relic radiation seen as the microwave background. Anything later is dismissed as mere “gastrophysics” that is too complicated to understand so cannot possibly inform fundamental physics. I guess that’s true if one chooses to remain ignorant of it.

*Fishy results can also indicate something fishy with the data. I had a conversation with an instrument builder at the time who pointed out that PAMELA had chosen to fly without a particular discriminator in order to save weight; he suggested that its absence could explain the apparent upturn in positrons.

^##There is a relatively nearby pulsar that fits the bill. It has a name: Geminga. This illustrates the human tendency to see what we’re looking for. The astroparticle community was looking for dark matter, so that’s what many of them saw in the excess cosmic ray signal. High energy astrophysicists work on neutron stars, so the obvious interpretation to them was a pulsar. One I recall being particularly scornful of the dark matter interpretation when there was an obvious astrophysical source. I also remember the astroparticle people being quick to dismiss the pulsar interpretation because it seemed unlikely to them for one to be so close but really they hadn’t thought about it before: that pulsars could do this was news to them, and many preferred to believe the dark matter interpretation.

^$$All the people barking were men.

^&&This experience opened my eyes to the existence of an entire community of scientists who were working on dark matter in somewhat gratuitous ignorance of the astronomical evidence for dark matter. To them, the existence of the stuff had already been demonstrated; the interesting thing now was to find the responsible particle. But they were clearly missing many important ingredients – another example is disk stability, a foundational reason to invoke dark matter that seems to routinely come as a surprise to particle physicists. This disconnect is part of what motivated me to develop an entire semester course on dark matter, which I’ve taught every other year since 2013 and will teach again this coming semester. The first time I taught it, I worried that there wasn’t enough material for a whole semester. Now a semester isn’t enough time.

**I had a college friend (sadly now deceased) who was part of the team that discovered the Higgs. That was big business, to the extent that there were two experiments – one to claim the detection, and another on the same beam to do the confirmation. The first experiment exceeded the arbitrary 5σ threshold to claim a 5.2σ detection, but the second only reached 4.9σ. So, in all appropriateness, he asked in a meeting if they could/should really announce a detection. A Nobel prize was on the line, so the answer was straightforward: Do you want a detection or not? (His words.)

^*#Rather than forget, some choose to fiddle ways around the Lee-Weinberg limit. This has led to the sub-genre of “light dark matter” which means lightweight, not luminous. I’d say this was the worst name ever, but the same people talk about dark photons with a straight face, so irony continues to bleed out.

^*$Ironically, a sterile neutrino has also been invoked to address problems in MOND.

^*%I was amused once to see one of the more rabid advocates of dark matter signals of this type give an entire talk hyping the various possibilities only to mention pulsars at the end with a sigh, admitting that the Fermi signal looked exactly like that.

The fault in our stars: blame them, not the dark matter!

As discussed in recent posts, the appearance of massive galaxies in the early universe was predicted a priori by MOND (Sanders 1998, Sanders 2008, Eappen et al. 2022). This is problematic for LCDM. How problematic? That’s always the rub.

The data follow the evolutionary track of a monolithic model (purple line) rather than the track of the largest progenitor predicted by hierarchical LCDM (dotted lines leading to different final masses).

The problem that JWST observations pose for LCDM is that there is a population of galaxies in the high redshift universe that appear to evolve as giant monoliths rather than assembling hierarchically. Put that way, it is a fatal flaw: hierarchical assembly of mass is fundamental to the paradigm. But we don’t observe mass, we observe light. So the obvious “fix” is to adjust the mapping of observed light to predicted dark halo mass in order to match the observations. How plausible is this?

Merger trees from the Illustris-TNG50 simulation showing the hierarchical assembly of L* galaxies. The dotted lines in the preceding plot show the stellar mass growth of the largest progenitor, which is on the left of each merger tree. All progenitors were predicted to be tiny at z > 3, well short of what we observe.

Before trying to wriggle out of the basic result, note that doing so is not plausible from the outset. We need to make the curve of growth of the largest progenitors “look like” the monolithic model. They shouldn’t, by construction, so everything that follows is a fudge to try to avoid the obvious conclusion. But this sort of fudging has been done so many times before in so many ways (the “Frenk Principle” was coined nearly thirty years ago) that many scientists in the field have known nothing else. They seem to think that this is how science is supposed to work. This in turn feeds a convenient attitude that evades the duty to acknowledge that a theory is in trouble when it persistently has to be adjusted to make itself look like a competitor.

That noted, let’s wriggle!

Observational dodges

The first dodge is denial: somehow the JWST data are wrong or misleading. Early on, there were plausible concerns about the validity of some (some) photometric redshifts. There are enough spectroscopic redshifts now that this point is moot.

A related concern is that we “got lucky” with where we pointed JWST to start with, and the results so far are not typical of the universe at large. This is not quite as crazy as it sounds: the field of view of JWST is tiny, so there is no guarantee that the first snapshot will be representative. Moreover, a number of the first pointings intentionally targeted rich fields containing massive clusters, i.e., regions known to be atypical. However, as observations have accumulated, I have seen no indications of a reversal of our first impression, but rather lots of corroboration. So this hedge also now borders on reality denial.

A third observational concern that we worried a lot about in Franck & McGaugh (2017) is contamination by active galactic nuclei (AGN). Luminosity produced by accretion onto supermassive black holes (e.g., quasars) was more common in the early universe. Perhaps some of the light we are attributing to stars is actually produced by AGN. That’s a real concern, but long story short, AGN contamination isn’t enough to explain everything else away. Indeed, the AGN themselves are a problem in their own right: how do we make the supermassive black holes that power AGN so rapidly that they appear already in the early universe? Like the galaxies they inhabit, the black holes that power AGN should take a long time to assemble in the absence of the heavy seeds naturally provided by MOND but not dark matter.

An evergreen concern in astronomy is extinction by dust. Dust could play a role (Ferrara et al. 2023), but this would be a weird effect for it to have. Dust is made by stars, so we naively expect it to build up along with them. In order to explain high redshift JWST data with dust we have to do the opposite: make a lot of dust very early without a lot of stars, then eject it systematically from galaxies so that the net extinction declines with time – a galactic reveal sort of like a cosmic version of the dance of the seven veils. The rate of ejection for all galaxies must necessarily be fine-tuned to balance the barely evolving UV luminosity function with the rapidly evolving dark matter halo mass function. This evolution of the extinction has to coordinate with the dark matter evolution over a rather small window of cosmic time, there being only ∼10⁸ yr between z = 14 and 11. This seems like an implausible way to explain an unchanging luminosity density, which is more naturally explained by simply having stars form and be there for their natural lifetimes.

**Figure 5** from McGaugh et al. (2024): The UV luminosity function (left) observed by Donnan et al. (2024; points) compared to that predicted for ΛCDM by Yung et al. (2023; lines) as a function of redshift. Lines and points are color coded by redshift, with dark blue, light blue, green, orange, and red corresponding to z = 9, 10, 11, 12, and 14, respectively. There is a clear excess in the number density of galaxies that becomes more pronounced with redshift, ranging from a factor of ∼2 at z = 9 to an order of magnitude at z ≥ 11 (right). This excess occurs because the predicted number of sources declines with redshift while the observed numbers remain nearly constant with the data at z = 9, 10, and 11being right on top of each other.

The basic observation is that there is too much UV light produced by galaxies at all redshifts z > 9. What we’d rather have is the stellar mass function. JWST was designed to see optical light at the redshift of galaxy formation, but the universe surprised us and formed so many stars so early that we are stuck making inferences with the UV anyway. The relation of UV light to mass is dodgy, providing a knob to twist. So up next is the physics of light production.

In our discussion to this point, we have assumed that we know how to compute the luminosity evolution of a stellar population given a prescription for its star formation history. This is no small feat. This subject has a rich history with plenty of ups and downs, like most of astronomy. I’m not going to attempt to review all that here. I think we have this figured out well enough to do what we need to do for the purposes of our discussion here, but there are some obvious knobs to turn, so let’s turn ’em.

Blame the stars!

As noted above, we predict mass but observe light. So the program now is to squeeze more light out of less mass. Early dark matter halos too small? No problem; just make them brighter. More specifically, we need to make models in which the small dark matter halos that form first are better at producing photons from the small amount of baryons that they possess than are their low-redshift descendants. We have observational constraints on the latter; local star formation is inefficient, but maybe that wasn’t always the case. So the first obvious thing to try is to make star formation more efficient.

Super Efficient Star Formation

First, note that stellar populations evolve pretty much as we expect for stars, so this is a bit tricky. We have to retain the evolution we understand well for most of cosmic time while giving a big boost at early times. One way to do that is to have two distinct modes of star formation: the one we think of as normal that persists to this day, and an additional mode of super-efficient star formation (SEFS) at play in the early universe. This way we retain the usual results while potentially giving us the extra boost that we need to explain the JWST data. We argue that this is the least implausible path to preserving LCDM. We’re trying to make it work, and anticipate the arguments Dr. Z would make.

This SESF mode of star formation needs to be very efficient indeed, as there are galaxies that appear to have converted essentially all of their available baryons into stars. Let’s pause to observe that this is pretty silly. Space is very empty; it is hard to get enough mass together to form stars at all: there’s good reason that it is inefficient locally! The early universe is a bit denser by virtue of being smaller; at z = 9 the expansion factor is only 1/(1+z) = 0.1 of what it is now, so the density is (1+z)³ = 1,000 times greater. ON AVERAGE. That’s not really a big boost when it comes to forming structures like stars since the initial condition was extraordinarily uniform. The lack of early structure by far outweighs the difference in density; that is precisely why we’re having a problem. Still, I can at least imagine that there are regions that experience a cascade of violent relaxation and SESF once some threshold in gas density is exceeded that differentiates the normal model of star formation from SESF. Why a threshold in the gas? Because there’s not anything obvious in the dark matter picture to distinguish the galaxies that result from one or the other mode. CDM itself is scale free, after all, so we have to imagine a scale set by baryons that funnels protogalaxies into one mode or the other. Why, physically, is there a particular gas density that makes that happen? That’s a great question.

There have been observational indications that local star formation is related to a gas surface density threshold, so maybe there’s another threshold that kicks it up another notch. That’s just a plausibility argument, but that’s the straw I’m clutching at to justify SESF as the least implausible option. We know there’s at least one way in which a surface density scale might matter to star formation.

Writing out the (1+z)³ argument for the density above tickled the memory that I’d seen something similar claimed elsewhere. Looking it up, indeed Boylan-Kolchin (2024) does this, getting an extra (1+z)³ [for a total of (1+z)⁶] by invoking a surface density Σ that follows from an acceleration scale g: Σ=g/(πG). Very MONDish, that. At any rate, the extra boost is claimed to lift a corner of dark matter halo parameter space into the realm of viability. So, sure. Why not make that step two.

However we do it, making stars super-efficiently is what the data appear to require – if we confine our consideration to the mass predicted by LCDM. It’s a way of covering the lack of mass with an surplus of stars. Any mechanism that makes stars more efficiently will boost the dotted lines in the M_*-z diagram above in the right direction. Do they map into the data (and the monolithic model) as needed? Unclear! All we’ve done so far is offer plausibility arguments that maybe it could be so, not demonstrate a model that works without fine-tuning that woulda coulda shoulda made the right prediction in the first place.

The ideas become less plausible from here.

Blame the IMF!

The next obvious idea after making more stars in total is to just make more of the high mass stars that produce UV photons. The IMF is a classic boogeyman to accomplish this. I discussed this briefly before, and it came up in a related discussion in which it was suggested that “in the end what will probably happen is that the IMF will be found to be highly redshift dependent.”

OK, so, first, what is the IMF? The Initial Mass Function is the spectrum of masses with which stars form: how many stars of each mass, ranging from the brown dwarf limit (0.08 M_☉) to the most massive stars formed (around 100 M_☉). The numbers of stars formed in any star forming event is a strong function of mass: low mass stars are common, high mass stars are rare. Here, though, is the rub: integrating over the whole population, low mass stars contain most of the mass, but high mass stars produce most of the light. This makes the conversion of mass to light quite sensitive to the IMF.

The number of UV photons produced by a stellar population is especially sensitive to the IMF as only the most massive and short-lived O and B stars produce them. This is low-hanging fruit for the desperate theorist: just a few more of those UV-bright, short-lived stars, please! If we adjust the IMF to produce more of these high mass stars, then they crank out lots more UV photons (which goes in the direction we need) but they don’t contribute much to the total mass. Better yet, they don’t live long. They’re like icicles as murder weapons in mystery stories: they do their damage then melt away, leaving no further evidence. (Strictly speaking that’s not true: they leave corpses in the form of neutron stars or stellar mass black holes, but those are practically invisible. They also explode as supernovae, boosting the production of metals, but the amount is uncertain enough to get away with murder.)

There is a good plausibility argument for a variable IMF. To form a star, gravity has to overcome gas pressure to induce collapse. Gas pressure depends on temperature, and interstellar gas can cool more efficiently when it contains some metals (here I mean metals in the astronomy sense, which is everything in the periodic table that’s not hydrogen or helium). It doesn’t take much; a little oxygen (one of the first products of supernova explosions) goes a long way to make cooling more efficient than a primordial gas composed of only hydrogen and helium. Consequently, low metallicity regions have higher gas temperatures, so it makes sense that gas clouds would need more gravity to collapse, leading to higher mass stars. The early universe started with zero metals, and it takes time for stars to make them and to return them to the interstellar medium, so voila: metallicity varies with time so the IMF varies with redshift.

This sound physical argument is simple enough to make that it can be done in a small part of a blog post. This has helped it persist in our collective astronomical awareness for many decades. Unfortunately, it appears to have bugger-all to do with reality.

If metalliticy plays a strong role in determining the IMF, we would expect to see it in stellar populations of different metallicity. We measure the IMF for solar metallicity stars in the solar neighborhood. Globular clusters are composed of stars formed shortly after the Big Bang and have low metallicities. So following this line of argument, we anticipate that they would have a different IMF. There is no evidence that this is the case. Still, we only really need to tweak the high-mass end of the IMF, and those stars died a long time ago, so maybe this argument applies for them if not for the long-lived, low-mass stars that we observe today.

In addition to counting individual stars, we can get a constraint on the galaxy-wide average IMF from the scatter in the Tully-Fisher relation. The physical relation depends on mass, but we rely on light to trace that. So if the IMF varies wildly from galaxy to galaxy, it will induce scatter in Tully-Fisher. This is not observed; the amount of intrinsic scatter that we see is consistent with that expected for stochastic variations in the star formation history for a fixed IMF. That’s a pretty strong constraint, as it doesn’t take much variation in the IMF to cause a lot of scatter that we don’t see. This constraint applies to entire galaxies, so it tolerates variations in the IMF in individual star forming events, but whatever is setting the IMF apparently tends to the same result when averaged over the many star forming events it takes to build a galaxy.

Variation in the IMF has come up repeatedly over the years because it provides so much convenient flexibility. Early in my career, it was commonly invoked to explain the variation in spectral hardness with metallicity. If one looks at the spectra of HII regions (interstellar gas ionized by hot young stars), there is a trend for lower metallicity HII regions to be ionized by hotter stars. The argument above was invoked: clearly the IMF tended to have more high mass stars in low metallicity environments. However, the light emitted by stars also depends on metallicity; low metallicity stars are bluer than their high metallicity equivalents because there are few UV absorption lines from iron in their atmospheres. Taking care to treat the stars and interstellar gas self-consistentlty and integrating over a fixed IMF, I showed that the observed variation in spectral hardness was entirely explained by the variation in metallicity. There didn’t need to be more high mass stars in low metallicity regions, the stars were just hotter because that’s what happens in low metallicity stars. (I didn’t set out to do this; I was just trying to calibrate an abundance indicator that I would need for my thesis.)

Another example where excess high mass stars were invoked was to explain the apparently high optical depth to the surface of last scattering reported by WMAP. If those words don’t mean anything to you, don’t worry – all it means is that a couple of decades ago, we thought we needed lots more UV photons at high redshift (z ~ 17) than CDM naturally provided. The solution was, you guessed it, an IMF rich in high mass stars. Indeed, this result launched a thousand papers on supermassive Population III stars that didn’t pan out for reasons that were easily anticipated at the time. Nowadays, analysis to the Planck data suggest a much lower optical depth than initially inferred by WMAP, but JWST is observing too many UV photons at high redshift to remain consistent with Plank. This apparent tension for LCDM is a natural consequence of early structure formation in MOND; indeed, it is another thing that was specifically predicted (see section 3.1 of McGaugh 2004).

I relate all these stories of encounters with variations in the high mass end of the IMF because they’ve never once panned out. Maybe this time will be different.

Stochastic Star Formation

What else can we think up? There’s always another possibility. It’s a big universe, after all.

One suggestion I haven’t discussed yet is that high redshift galaxies appear overly bright from stochastic fluctuations in their early star formation. This again invokes the dubious relation between stellar mass and UV light, but in a more subtle way than simply stocking the IMF with a bunch more high mass stars. Instead, it notes that the instantaneous star formation rate is stochastic. The massive stars that produces all the UV light are short-lived, so the number present will fluctuate up and down. Over time, this averages out, but there hasn’t been much time yet in the early universe. So maybe the high redshift galaxies that seem to be over-luminous are just those that happen to be near a peak in the ups and downs of star formation. Galaxies will be brightest and most noticeable in this peak phase, so the real mass is less than it appears – albeit there must be a lot of galaxies in the off phase for every one that we see in the on phase.

One expects a lot of scatter in the inferred stellar mass in the early universe due to stochastic variations in the star formation rate. As time goes on, these average out and the inferred stellar mass becomes steady. That’s pretty much what is observed (data). The data track the monolithic model (purple line) and sometimes exceed it in the early, stochastic phase. The data bear no resemblance to hierarchical LCDM (orange line).

This makes a lot of sense to me. Indeed, it should happen at some level, especially in the chaotic early universe. It is also what I infer to be going on to explain why some measurements scatter above the monolithic line. That is the baseline star formation history for this population, with some scatter up and down at early times. Simply scattering from the orange LCDM line isn’t going to look like the purple monolithic line. The shape is wrong and the amplitude difference is too great to overcome in this fashion.

What else?

I’m sure we’ll come up with something, but I think I’ve covered everything I’ve heard so far. Indeed, most of these possibilities are obvious enough that I thought them up myself and wrote about them in McGaugh et al (2024). I don’t see anything in the wide-ranging discussion at KITP that wasn’t already in my paper.

I note this because I want to point out that we are following a well-worn script. This is the part where I tick off all the possibilities for more complicated LCDM models and point out their shortcomings. I expect the same response:

That’s too long to read. Dr. Z says it works, so he must be right since we already know that LCDM is correct.
Triton Station, 8 February 2022

People will argue about which of these auxiliary hypotheses is preferable. MOND is not an auxiliary hypothesis, but an entirely different paradigm, so it won’t be part of the discussion. After some debate, one of the auxiliaries (SESF not IMF!) will be adopted as the “standard” picture. This will be repeated until it becomes familiar, and once it is familiar it will seem that it was always so, and then people will assert that there was never a problem, indeed, that we expected it all along. This self-gaslighting reminds me of Feynman’s warning:

The first principle is that you must not fool yourself and you are the easiest person to fool.
Richard Feynman

What is persistently lacking in the community is any willingness to acknowledge, let alone engage with, the deeper question of why we have to keep invoking ad hoc patches to somehow match what MOND correctly predicted a priori. The sociology of invoking arbitrary auxiliary hypotheses to make these sorts of excuses for LCDM has been so consistently on display for so long that I wrote this parody a year ago:

It always seems to come down to special pleading:

Please don’t falsify LCDM! I ran out of computer time. I had a disk crash. I didn’t have a grant for supercomputer time. My simulation data didn’t come back from the processing center. A senior colleague insisted on a rewrite. Someone stole my laptop. There was an earthquake, a terrible flood, locusts! It wasn’t my fault! I swear to God!

And the community loves LCDM, so we fall for it every time.

PS – to appreciate the paraphrased quotes here, you need to hear it as it would be spoken by the pictured actors. So if you do not instantly recognize this scene from the Blues Brothers, you need to correct this shortcoming in your cultural education to get the full effect of the reference.

What if we never find dark matter?

Some people have asked me to comment on the Scientific American article What if We Never Find Dark Matter? by Slatyer & Tait. For the most part, I find it unobjectionable – from a certain point of view. It is revealing to examine this point of view, starting with the title, which frames the subject in a way that gives us permission to believe in dark matter while never finding it. This framing is profoundly unscientific, as it invites a form of magical thinking that could usher in a thousand years of dark epicycles (feedback being the modern epicycle) on top of the decades it has already sustained.

The article does recognize that a modification of gravity is at least a logical possibility. The mere mention of this is progress, if grudging and slow. They can’t bring themselves to name a specific theory: they never say MOND and only allude obliquely to a single relativistic theory as if saying its name out loud would bring a curse^% upon their house.

Of course, they mention modified gravity merely to dismiss it:

A universe without dark matter would require striking modifications to the laws of gravity… [which] seems exceptionally difficult.

Yes it is. But it has also proven exceptionally difficult to detect dark matter. That hasn’t stopped people from making valiant efforts to do so. So the argument is that we should try really hard to accomplish the exceptionally difficult task of detecting dark matter, but we shouldn’t bother trying to modify gravity because doing so would be exceptionally difficult.

This speaks to motivations – is one idea better motivated? In the 1980s, cold dark matter was motivated by both astronomical observations and physical theory. Absent the radical thought of modifying gravity, we had a clear need for unseen mass. Some of that unseen mass could simply have been undetected normal matter, but most of it needed to be some form of non-baryonic dark matter that exceeded the baryon density allowed by Big Bang Nucleosynthesis and did not interact directly with photons. That meant entirely new physics from beyond the Standard Model of particle physics: no particle in the known stable of particles suffices. This new physics was seen as a good thing, because particle physicists already had the feeling that there should be something more than the Standard Model. There was a desire for Grand Unified Theories (GUTs) and supersymmetry (SUSY). SUSY naturally provides a home for particles that could be the dark matter, in particular the Weakly Interacting Massive Particles (WIMPs) that are the prime target for the vast majority of experiments that are working to achieve the exceptionally difficult task of detecting them. So there was a confluence of reasons from very different perspectives to make the search for WIMPs very well motivated.

That was then. Fast forward a few decades, and the search for WIMPs has failed. Repeatedly. Continuing to pursue it is an example of the sunk cost fallacy. We keep doing it because we’ve already done so much of it that surely we should keep going. So I feel the need to comment on this seemingly innocuous remark:

although many versions of supersymmetry predict WIMP dark matter, the converse isn’t true; WIMPs are viable dark matter candidates even in a universe without supersymmetry.

Strictly speaking, this is correct. It is also weak sauce. The neutrino is an example of a weakly interacting particle that has some mass. We know neutrinos exist, and they reside in the Standard Model – no need for supersymmetry. We also know that they cannot be the dark matter, so it would be disingenuous to conflate the two. Beyond that, it is possible to imagine a practically infinite variety of particles that are weakly interacting by not part of supersymmetry. That’s just throwing mud at the wall. SUSY WIMPs were extraordinarily well motivated, with the WIMP miracle being the beautiful argument that launched a thousand experiments. But lacking SUSY – which seems practically dead at this juncture – WIMPS as originally motivated are dead along with it. The motivation for more generic WIMPs is lacking, so the above statement is nothing more than an assertion that runs interference for the fact that we no longer have good reason to expect WIMPs at all.

There is also an element of disciplinary-centric thinking: if you’re a particle physicist, you can build a dark matter detector and maybe make a major discovery or at least get great gobs of grants in the effort to do so. If instead what is going on is really a modification of gravity, then your expertise is irrelevant and there is no reason to keep shoveling money into your field. Worse, a career spent at the bottom of a mine shaft working on dark matter detectors is a waste of effort. I can understand why people don’t want to hear that message, but that just brings us back to the sunk cost fallacy.

Speaking of money, I occasionally get scientists who come up to me Big Mad that grant money gets spent on MOND research, as that would be a waste of taxpayer money. I can assure them that no government dollars have been harmed in the pursuit of MOND research. Certainly not in the U.S., at any rate. But lots and lots of tax dollars have been burned in the search for dark matter, and the article we’re discussing advocates spending a whole lot more to search for dark matter candidates that are nowhere near as well motivated as WIMPs were. That’s why I keep asking: how do we know when to stop? I don’t expect other scientists to agree to my interpretation of the data, but I do expect them to have a criterion whereby they would accede that dark matter is incorrect. If we lack any notion of how we could figure out that we are wrong, then we’ve made the leap from science to religion. So far, such criteria are sadly lacking, and I see precious little evidence of people rising to the challenge. Indeed, I frequently get the opposite, as other scientists have frequently asserted to me that they would only consider MOND as a last resort. OK, when does that happen? There’s always another particle we can think up, so the answer seems to be “never.”

I wrote long ago that “After WIMPs, the next obvious candidate is axions.” Sure enough, this article spills a lot of ink discussing axions. Rather than dwell on this different doomed idea for dark matter, let’s take a gander at the remarkable art made to accompany the article, because we are visual animals and graphical representations are important.

Where to start? Right in the center is a scroll of an old-timey star chart. On top of that are several depictions of what I guess are meant to be galaxies*. Around those is an ethereal dragon representing the unknown dark matter. The depiction of dark matter as an unfathomable monster is at once both spot on and weirdly anthropomorphic. Is this a fabled beast the adventurous hero is supposed to seek out and slay? or befriend? or maybe it is a tale in which he grows during the journey to realize he has been on the wrong path the whole time? I love the dragon as art, but as a representation of a scientific subject it imparts an aura of teleological biology to something that is literally out of this world, residing in a dark sector that is not part of our daily experience and may be entirely inaccessible to our terrestrial experimentation. Off the edge of the map and on into extra dimensions: here there be monsters.

The representations here are fantastic. There is the coffee mug and the candle to represent the hard work of those of us who burn the candle at both ends wrestling with the dark matter problem. There’s a magnifying glass to represent how hard the experimentalists have looked for the dark matter. Scattered around are various totems, like the Polaroid-style picture at right depicting the gravitational lensing around a black hole. This is cool, but has squat to do with the missing mass problem. It’s more a nod to General Relativity and the Faith we have therein, albeit in a regime many orders of magnitude removed from the one that concerns us here. On the left is an old newspaper article about WIMPs, complete with a sketch of a Feynman diagram that depicts how we might detect them. And at the top, peeking out of a book, as it were a thought made long ago now seeking new relevance, a note saying Axions!

I can save everyone a lot of time, effort, and expense. It ain’t WIMPs and it ain’t axions. Nor is the dark matter any of the plethora of other ideas illustrated in the eye-watering depiction of the landscape of particle possibilities in the article. These simply add mass while providing no explanation of the observed MOND phenomenology. This phenomenology is fundamental to the problem, so any approach that ignores it is doomed to failure. I’m happy to consider explanations based on dark matter, but these need to have a direct connection to baryons baked-in to be viable. None of the ideas they discuss meet this minimum criterion.

Of course it could be that MOND – either as modified gravity or modified inertia, an important possibility that usually gets overlooked – is essentially correct and that’s why it keeps having predictions come true. That’s what motivates considering it now: repeated and sustained predictive success, particularly for phenomena that dark matter does not provide a satisfactory explanation for.

Of course, this article advocating dark matter is at pains to dismiss modified gravity as a possibility:

The changes [of modified gravity] would have to mimic the effects of dark matter in astrophysical systems ranging from giant clusters of galaxies to the Milky Way’s smallest satellite galaxies. In other words, they would need to apply across an enormous range of scales in distance and time, without contradicting the host of other precise measurements we’ve gathered about how gravity works. The modifications would also need to explain why, if dark matter is just a modification to gravity—which is universally associated with all matter—not all galaxies and clusters appear to contain dark matter. Moreover, the most sophisticated attempts to formulate self-consistent theories of modified gravity to explain away dark matter end up invoking a type of dark matter anyway, to match the ripples we observe in the cosmic microwave background, leftover light from the big bang.

That’s a lot, so let’s break it down. First, that modified gravity “would have to mimic the effects of dark matter” gets it exactly backwards. It is dark matter that has to mimic the effects of MOND. That’s an easy call: dark matter plus baryons could combine in a large variety of ways that might bear no resemblance to MOND. Indeed, they should do that: the obvious prediction of LCDM-like theories is an exponential disk in an NFW halo. In contrast, there is one and only one thing that can happen in MOND since there is a single effective force law that connects the dynamics to the observed distribution of baryons. Galaxies didn’t have to do that, shouldn’t do that, but remarkably they do. The uniqueness of this relation poses a problem for dark matter that has been known since the previous century:

*Reluctant conclusions from McGaugh & de Blok (1998). As we said at the time, “This result surprised the bejeepers out of us, too.”*

This basic conclusion has not changed over the years, only gotten stronger. The equation coupling dark to luminous matter I wrote down in all generality in McGaugh (2004) and again in McGaugh et al. (2016). The latter paper is published in Physical Review Letters, arguably the most prominent physics journal, and is in the top percentile of citation rates, so it isn’t some minuscule detail buried in an obscure astronomical journal that might have eluded the attention of particle physicists. It is the implication that conclusion [1] could be correct that bounces off a protective shell of cognitive dissonance so hard that the necessary corollary [2] gets overlooked.

OK, that’s just the first sentence. Let’s carry on with “[the modification] would need to apply across an enormous range of scales in distance and time, without contradicting the host of other precise measurements we’ve gathered about how gravity works.” Well, duh. That’s the first thing I checked. Thoroughly and repeatedly. I’ve written many reviews on the subject. They’re either unaware of some well-established results, or choose to ignore them.

The reason MOND doesn’t contradict the host of other constraints about how gravity works is simple. It happens in the low acceleration regime, where the only test of gravity is provided by the data that evince the mass discrepancy. If we had posed galaxy observations as a test of GR, we would have concluded that it fails at low accelerations. Of course we didn’t do that; we observed galaxies because we were interested in how they worked, then inferred the need for dark matter when gravity as we currently know it failed to explain the data. Other tests, regardless how precise, are irrelevant if they probe accelerations higher than Milgrom’s constant (1.2 x 10^-10 m/s/s).

Continuing on, there is the complaint that “modifications would also need to explain why… not all galaxies and clusters appear to contain dark matter.” Yep, you gotta explain all the data. That starts with the vast majority of the data that do follow the radial acceleration relation, which is not satisfactorily explained by dark matter. They skip⁺ past that part, preferring to ignore the forest in order to complain about a few outlying trees. There are some interesting cases, to be sure, but this complaint about objects lacking dark matter is misplaced for deeper reasons. It makes no sense in terms of dark matter that there are objects without dark matter. That shouldn’t happen in LCDM any more than in MOND^$. One winds up invoking non-equilibrium effects, which we can do in MOND just as we do in dark matter. It is not satisfactory in either case, but it is weird to complain about it for one theory while not for the other. This line of argument is perilously close to the a priori fallacy.

The last line, “the most sophisticated attempts to formulate self-consistent theories of modified gravity to explain away dark matter end up invoking a type of dark matter anyway, to match the ripples we observe in the cosmic microwave background” actually has some merit. The theory they’re talking about is Aether-Scalar-Tensor (AeST) theory, which I guess earns the badge of “most sophisticated” because it fits the power spectrum of the cosmic microwave background (CMB).

I’ve discussed the CMB in detail before, so won’t belabor it here. I will note that the microwave background is only one piece of many lines of evidence, and the conclusion one reaches depends on how one chooses to weigh the various incommensurate evidence. That they choose to emphasize this one thing while entirely eliding the predictive successes of MOND is typical, but does not encourage me to take this as a serious argument, especially when I had more success predicting important aspects of the microwave background than did the entire community that persistently cites the microwave background to the exclusion of all else.

It is also a bit strange to complain that AeST “explain[s] away dark matter [but] end[s] up invoking a type of dark matter.” I think what they mean here is true at the level of quantum field theory where all particles are fields and all fields are particles, but beyond that, they aren’t the same thing at all. It is common for modified gravity theories to invoke scalar fields^#, and this is an important degree of freedom that enables AeST to fit the CMB. TeVeS also added a scalar and tensor field, but could not fit the CMB, so this approach isn’t guaranteed to work. But are these a type of dark matter? Or are our ideas of dark matter mimicking a scalar field? It seems like this argument could cut either way, and we’re just granting dark matter priority as a concept because we thought of it first. I don’t think nature cares about the order of our thoughts.

None of this addresses the question of the year. Why does MOND get any predictions right? Just saying “dark matter does it” is not sufficient. Until scientists engage seriously with this question, they’re doomed to chasing phantoms that aren’t there to catch.

^%From what I’ve seen, they’re probably right to fear the curses of their colleagues for such blasphemy. Very objective, very scientific.

*Galaxies are nature’s artwork; human imitations never seem adequate. These look more like fried eggs to me. On the whole, this art is exceptionally well informed by science, or at least by particle physics, but not so much by astronomy. And therein lies the greater problem: there is a whole field of physics devoted to dark matter that is entirely motivated by astronomical observations yet its practitioners are, by and large, remarkably ignorant of anything more than the most rudimentary aspects of the data that motivate their field’s existence.

⁺There seems to be a common misconception that anything we observe is automatically explained by dark matter. That’s only true at the level of inference: any excess gravity is attributable to unseen mass. That’s why a hypothesis is only as good as its prior; a mere inference isn’t science, you have to make a prediction. Once you do that, you find dark matter might do lots of things that are not at all like the MONDian phenomenology that we observe. While I would hope the need for predictions is obvious, many scientists seem to conflate observation with prediction – if we observe it, that’s what dark matter must predict!

^$The discrepancy should only appear below the critical acceleration scale in MOND. So strictly speaking, MOND does predict that there should be objects without dark matter: systems that are high acceleration. The central regions of globular clusters and elliptical galaxies are such regions, and MOND fares well there. In contrast, it is rather hard to build a sensible dark matter model that is as baryon dominated as observed. So this is an example of MOND explaining the absence of dark matter better than dark matter theory. This is related to the observation that the apparent need for dark matter only appears at low accelerations, at a scale that dark matter knows nothing about.

^#I, personally, am skeptical of this approach, as it seems too generic (let’s add some new freedom!) when it feels like we’re missing something fundamental, perhaps along the lines of Mach’s Principle. However, I also recognize that this is a feeling on my part; it is outside my training to have a meaningful opinion.

A Nobel prize in physics for something that is not physics

When I wrote about Nobel prizes a little while back, I did not expect to return to the subject. I assumed the prize this year would be awarded for some meritorious advance in laboratory physics, like last year’s prize “for experimental methods that generate attosecond pulses of light for the study of electron dynamics in matter.” Instead, we find that the 2024 prize has been awarded to John Hopfield and Geoffrey Hinton “for foundational discoveries and inventions that enable machine learning with artificial neural networks.” This is the Nobel prize in physics we’re talking about.

One small issue: that’s not physics.

I’ve been concerned for a long time with the interface between astronomy and physics – where they are distinct fields and where they overlap. One of the reasons I left physics as a grad student was because the string theorists were taking over. They were talking about phenomena that were tens of orders of magnitude beyond any conceivable experimental test. That sort of theoretical speculation is often fun, sometimes important, and very rarely relevant to physical reality. Lacking exposure to experimental tests or observational consequences, to my mind it was just that: speculation, not physics.

Nearly forty years on, my concerns about string theory have not been misplaced. And while, in the strictest sense, I don’t think it qualifies as physics – it’s more of a physics-adjacent branch of mathematics – it is at least attempting to be physical theory. But machine learning is not physics. It’s computer science. Computers are a useful tool, to be sure. But programming them is no more physics than teaching a horse to count.

I’m not sure we should even consider machine learning to be meritorious. It can be useful, but it is also a gateway drug to artificial intelligence (AI). I remember the more earnest proponents of early AI propounding on the virtues of LISP and how it would bring us AI – in the 1980s. All it brought us then was dystopian fantasies about killer robots nuking the world. Despite the current hype, we have not now developed intelligent machines – what we’re calling AI is certainly artificial but not at all intelligent. It uses machine “learning” to reprocess existing information into repackaged forms. There is zero original thought, nothing resembling intelligence. Modern AI is, in essence, a bullshit generator. Now, we can all think of people who qualify as organic bullshit generators, but that begs the question:

Why is the Nobel prize in physics being awarded for something that is clearly not physics?

Maybe it has something to do with the hype around AI. I don’t know what the decision process was, but I do know that I am not the only scientist to have this reaction.

Myself, I’m not mad, just disappointed. I’m not unique in feeling that physics has lost its way. This just emphasizes how far it has strayed.

Apparently the Nobel committee is sensing the blow-back, as this poll currently appears on the award page:

I… don’t think this helps their case. Did you know that molecules are made of atoms? Ergo all of chemistry is just applied atomic physics. I mean, it is a long-standing trope that physicists think every other science is just a lesser, applied form of physics. At the level of being based on the equations of physics, that’s almost kinda if not really true. So asserting that machine learning models are based on physics equations comes nowhere near to making machine learning into physics. It’s fancy programming, not physics.

Well, there will be complaints about this one for a while, so I won’t pile on more. I guess if you give out 118 prizes since 1901, one of them has to rank 118th.

Sociology in the hunt for dark matter

Who we give prizes to is more a matter of sociology than science. Good science is a prerequisite, but after that it is a matter of which results we value in the here and now. Results that are guaranteed to get a Nobel prize, like the detection of dark matter, attract many suitors who pursue them vigorously. Results that come as a surprise can be more important than the expected results, but it takes a lot longer to recognize and appreciate them.

When there are expected results with big stakes, sociology kicks into hyperdrive. Let’s examine the attitudes in some recent quotes:

In Science, Hunt for dark matter particles bags nothing—again (24 Aug 2024): Chamkaur Ghag says

If WIMPs were there, we have the sensitivity to have seen them

which is true. WIMP detection experiments have succeeded in failing. They have explored the predicted parameter space. But in the same paragraph, it is said that it is too early to “give up hope of detecting WIMPs.” That is a pretty vague assertion, and is precisely why I’ve been asking other scientists to define a criterion by which we could agree that enough was enough already. How do we know when to stop looking?

The same paragraph ends with

This is our first real foray into discovery territory

which is not true. We’ve explored the region in which WIMPs were predicted to reside over and over and over again. This was already excruciatingly old news when I wrote about it in 2008. The only way to spin this as a factual statement is to admit that the discovery territory is practically infinite, in which case we can assert that every foray is our first “real” foray because we’ll never get anywhere relative to infinity. It sounds bad when put that way, which is the opposite of the positivity the spokespeople for huge experiments are appointed to project.

And that’s where the sociology kicks in. The people who do the experiments want to keep doing the experiments until they discover dark matter and win the Nobel prize. It’s disappointing that this hasn’t happened already, but it is an expected result. It’s what they do, so it’s natural to want to keep at it.

On the one hand, I’d like to see these experiments continue until they reach the neutrino fog, at which point they will provide interesting astrophysical information. Says Michael Murra (in Science News, 25 July 2024)

It’s very cool to see that we can turn this detector into a neutrino observatory

Yes, it is. But that wasn’t the point, was it?

On the other hand, I do not expect these experiments to ever detect dark matter. That’s because I understand that the astronomical data contain self-contradictions to their interpretation in terms of dark matter. Any particle physicist will tell you that astronomical data require dark matter. But they’re not experts on that topic, I am. I’ve talked to enough of them at this point to conclude that the typical physicist working on dark matter has only a cartoonish understanding of the data that motivates their whole field. After all,

It is difficult to get a man to understand something, when his salary depends on his not understanding it.

Upton Sinclair

Nobel prizes that were, that might have been, and others that have not yet come to pass

The time is approaching when Nobel prizes are awarded. This inevitably leads to a lot of speculation and chattering rumor. Last year one publication, I think it was Physics Today, went so far as to publish a list of things various people thought should be recognized. This aspirational list was led, of course, by dark matter. It was even formatted the way prize awards are phrased, saying something like “the prize goes to [blank] for the discovery of dark matter.” This would certainly be a prize-worthy discovery, if made. So far it hasn’t been, and I expect it never will be: blank will remain blank forever. I’d be happy to be proved wrong, as forever is a long time to wait for corroboration of this prediction.

While the laboratory detection of dark matter is a slam-dunk for a Nobel prize, there are plenty of discoveries that drive the missing mass problem that are already worthy of this recognition. The issue is too big for a single prize. Laboratory detection would be the culmination of a search that has been motivated by astronomical observations. The Nobel prize in physics has sometimes been awarded for astronomical discoveries – and should be, for those that impact fundamental physics or motivate entire fields like the search for dark matter – so let’s think about what those might be.

An obvious historical example would be Kepler’s Laws. Kepler predates Nobel by a few centuries, but there is no doubt that his identification of the eponymous laws of planetary motion impacted fundamental physics, being one of the key set of facts that led Newton to his universal law of gravity. Whether Tycho Brahe should also be named as the person who made the observations on which Kepler’s work is based is the sort of question the prize committee has to wrestle with. I would say yes: the prize is for “the person who shall have made the most important discovery or invention within the field of physics.” In this case, the discovery that led to gravity was a set of rules – how the orbits of planets behave – that required both observational work (Brahe’s) and numerical analysis (Kepler’s) to achieve.

One could of course also give a prize to Newton some decades later, though theories are not generally considered discoveries. The line can be hazy. For example, the Nobel Prize in Physics 1921 was awarded to Albert Einstein “for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect.” The “especially” is reserved for the empirical law, not relativity, though I guess “services to theoretical physics” is doing a lot of work there.

Reading up on that I was mildly surprised to learn that the committee had a hard time finding deserving recipients, initially skipping 1918 and 1921 but awarding those prizes in the subsequent year to Planck and Einstein, respectively. I wonder if they struggled with the definition of discovery: need it be experimental? For many, the answer is yes. A theory by itself, untethered from experimental or observational corroboration, does not a discovery make.

I don’t think they need to skip years any more, as the list of plausible nominees has grown so long that deserving people die waiting to be recognized: the Nobel prize is not awarded posthumously. The story is that this is what happened to both Henrietta Leavitt (who discovered the Cepheid period-luminosity relation) and Edwin Hubble (who used Leavitt’s relation for Cepheids to measure distances to other galaxies, thereby changing the course of cosmology). There is also the issue of what counts as physics. At the time, these were very astronomical discoveries. In retrospect, it is obvious that the impact Hubble had on cosmology counts as physics as well.

The same can be said for the discovery of flat rotation curves. I have made the case before that Vera Rubin and Albert Bosma (and arguably others) deserve the Nobel prize for this discovery. Note that I do not say the discovery of dark matter, because (1) that’s not what they did*, and (2) flat rotation curves are enough. Flat rotation curves are a de facto law of nature. That’s enough, every bit as much as Einstein’s “discovery of the law of the photoelectric effect.” A laboratory detection of dark matter would be another discovery worthy of a Nobel prize, but we already missed out on recognizing Rubin for this one.

Conflating discoveries with their interpretation has precluded recognition of other important astronomical discoveries – discoveries that implicate basic physics regardless of their ultimate interpretation, be it cold dark matter or MOND or something else we have yet to figure out. So, what are some others?

One obvious one is the Tully-Fisher relation. This is another de facto law of nature. Tully has been recognized for his work with the Gruber prize, so it’s not like it hasn’t been recognized. What remains lacking is recognition that this is a fundamental law of physics, at least the baryonic version when flat rotation speeds are measured.

Philip Mannheim pointed out to me that Milgrom deserves the prize for the discovery of the acceleration scale a₀. This is a new constant of nature. That’s enough.

Milgrom went further, developing the whole MOND paradigm around this new scale. But that is extra credit material that needn’t be correct. Unfortunately, the controversial nature of MOND, deserved or not, serves to obscure that there is a new constant of nature whose discovery is analogous to Planck’s discovery of his eponymous constant. People argue over whether a₀ is a single constant (it is) or whether it evolves over cosmic time (not so far as I can tell). The latter objection could be raised for Planck’s constant or Newton’s constant; these were established when it wasn’t possible to test whether their values might have varied over cosmic time. Now that we can, we do check! and so far, no: h, G, and a₀ all appear to be constants of nature, to the extent we are able to perceive.

The above discoveries are all worthy of recognition by a Nobel prize. They are all connected by the radial acceleration relation, which is another worthy observational discovery in its own right. This is one that clearly transgresses the boundaries of physics and astronomy, as the early versions (Sanders 1990, McGaugh 1999, 2004) appeared in the astronomical literature, but more recent ones in the physics literature (McGaugh et al. 2016, Mistele et al. 2024). Sadly, the community seems perpetually stuck looping through the stages of Louis Agassiz‘s progression of responses to scientific discoveries. It shouldn’t be: this is an empirical relation that has long been well established and repeatedly confirmed. It suffers from association with MOND, but no reference to MOND is made in the construction of the observed relation. It’s right there in the data:

The radial acceleration relation as traced by both early (red) and late (cyan) type galaxies via both kinematics and gravitational lensing. The low acceleration behavior maps smoothly onto the Newtonian behavior seen in the solar system at higher accelerations. If Newton’s discovery of the inverse square force law would warrant a Nobel prize, as surely it would had the prize existed in Newton’s time, then so does the discovery of a systematically new behavior.

*Rubin and Bosma both argued, sensibly, that the interpretation of flat rotation curves required dark matter. That’s an interpretation, not a discovery. That rotation curves were flat, over and over again in every galaxy examined, to indefinitely large radii, was the observational discovery.

Decision Trees & Philosophical Blunders

Given recent developments in the long-running hunt for dark matter and the difficulty interpreting what this means, it seems like a good juncture to re-up* this:

The history of science is a decision tree. Vertices appear where we must take one or another branching. Sometimes, we take the wrong road for the right reasons.

A good example is the geocentric vs. heliocentric cosmology. The ancient Greeks knew that in many ways it made more sense for the earth to revolve around the sun than vice-versa. Yet they were very clever. Ptolemy and others tested for the signature of the earth’s orbit in the seasonal wobbling in the positions of stars, or parallax. If the earth is moving around the sun, nearby stars should appear to move on the sky as the earth moves from one side of the sun to the other. Try blinking back and forth between your left and right eyes to see this effect, noting how nearby objects appear to move relative to distant ones.

Problem is, Ptolemy did not find the parallax. Quite reasonably, he inferred that the earth stayed put. We know now that this was the wrong branch to choose, but it persisted as the standard world view for many centuries. It turns out that even the nearest stars are so distant that their angular parallax is tiny (the angle of parallax is inversely proportional to distance). Precision sufficient for measuring the parallax was not achieved until the 19th century, by which time astronomers were already convinced it must happen.

Ptolemy was probably aware of this possibility, though it must have seemed quite unreasonable to conjecture at that time that the stars could be so very remote. The fact was that parallax was not observed. Either the earth did not move, or the stars were ridiculously distant. Which sounds more reasonable to you?

So, science took the wrong branch. Once this happened, sociology kicked in. Generation after generation of intelligent scholars confirmed the lack of parallax until the opposing branch seemed so unlikely that it became heretical to even discuss. It is very hard to reverse back up the decision tree and re-assess what seems to be such a firm conclusion. It took the Copernican revolution to return to that ancient decision branch and try the other one.

Cosmology today faces a similar need to take a few steps back on the decision tree. The problem now is the issue of the mass discrepancy, typically attributed to dark matter. When it first became apparent that things didn’t add up when one applied the usual Law of Gravity to the observed dynamics of galaxies, there was a choice. Either lots of matter is present which happens to be dark, or the Law of Gravity has to be amended. Which sounds more reasonable to you?

Having traveled down the road dictated by the Dark Matter decision branch, cosmologists find themselves trapped in a web of circular logic entirely analogous to the famous Ptolemaic epicycles. Not many of them realize it yet, much less admit that this is what is going on. But if you take a few steps back up the decision branch, you find a few attempts to alter the equations of gravity. Most of these failed almost immediately, encouraging cosmologists down the dark matter path just as Ptolemy wisely chose a geocentric cosmology. However, one of these theories is not only consistent with the data, it actually predicts many important new results. This theory is known as MOND (MOdified Newtonian Dynamics). It was introduced in 1983 by Moti Milgrom of the Weizmann Institute in Israel.

MOND accurately describes the effective force law in galaxies based only on the observed stars and gas. What this means is unclear, but it clearly means something! It is conceivable that dark and luminous matter somehow interact to mimic the behavior stipulated by MOND. This is not expected, and requires a lot of epicyclic thinking to arrange. The more straightforward interpretation is that MOND is correct, and we took the wrong branch of the decision tree back in the ’70s.

MOND has dire implications for much modern cosmological thought which has developed symbiotically with dark matter. As yet, no one has succeeded in writing down a theory which encompasses both MOND and General Relativity. This leaves open many questions in cosmology that were thought to be solved, such as the expansion history of the universe. There is nothing a scientist hates to do more than unlearn what was thought to be well established. It is this sociological phenomenon that makes it so difficult to climb back up the decision tree to the faulty branching.

Once one returns and takes the correct branch, the way forward is not necessarily obvious. The host of questions which had been assigned seemingly reasonable explanations along the faulty branch must be addressed anew. And there will always be those incapable of surrendering the old world view irrespective of the evidence.

In my opinion, the new successes of MOND can not occur by accident. They are a strong sign that we are barking up the wrong tree with dark matter. A grander theory encompassing both MOND and General Relativity must exist, even if no one has as yet been clever enough to figure it out (few have tried).

These all combine to make life as a cosmologist interesting. Sometimes it is exciting. Often it is frustrating. Most of the time, “interesting” takes on the meaning implied by the old Chinese curse:

MAY YOU LIVE IN INTERESTING TIMES

Like it or not, we do.

*I wrote this in 2000. I leave it to the reader to decide how much progress has been made since then.

Discussion of Dark Matter and Modified Gravity

To start the new year, I provide a link to a discussion I had with Simon White on Phil Halper’s YouTube channel:

In this post I’ll say little that we don’t talk about, but will add some background and mildly amusing anecdotes. I’ll also try addressing the one point of factual disagreement. For the most part, Simon & I entirely agree about the relevant facts; what we’re discussing is the interpretation of those facts. It was a perfectly civil conversation, and I hope it can provide an example for how it is possible to have a positive discussion about a controversial topic⁺ without personal animus.

First, I’ll comment on the title, in particular the “vs.” This is not really Simon vs. me. This is a discussion between two scientists who are trying to understand how the universe works (no small ask!). We’ve been asked to advocate for different viewpoints, so one might call it “Dark Matter vs. MOND.” I expect Simon and I could swap sides and have an equally interesting discussion. One needs to be able to do that in order to not simply be a partisan hack. It’s not like MOND is my theory – I falsified my own hypothesis long ago, and got dragged reluctantly into this business for honestly reporting that Milgrom got right what I got wrong.

For those who don’t know, Simon White is one of the preeminent scholars working on cosmological computer simulations, having done important work on galaxy formation and structure formation, the baryon fraction in clusters, and the structure of dark matter halos (Simon is the W in NFW halos). He was a Reader at the Institute of Astronomy at the University of Cambridge where we overlapped (it was my first postdoc) before he moved on to become the director of the Max Planck Institute for Astrophysics where he was mentor to many people now working in the field.

That’s a very short summary of a long and distinguished career; Simon has done lots of other things. I highlight these works because they came up at some point in our discussion. Davis, Efstathiou, Frenk, & White are the “gang of four” that was mentioned; around Cambridge I also occasionally heard them referred to as the Cold Dark Mafia. The baryon fraction of clusters was one of the key observations that led from SCDM to LCDM.

The subject of galaxy formation runs throughout our discussion. It is always a fraught issue how things form in astronomy. It is one thing to understand how stars evolve, once made; making them in the first place is another matter. Hard as that is to do in simulations, galaxy formation involves the extra element of dark matter in an expanding universe. Understanding how galaxies come to be is essential to predicting anything about what they are now, at least in the context of LCDM^*. Both Simon and I have worked on this subject our entire careers, in very much the same framework if from different perspectives – by which I mean he is a theorist who does some observational work while I’m an observer who does some theory, not LCDM vs. MOND.

When Simon moved to Max Planck, the center of galaxy formation work moved as well – it seemed like he took half of Cambridge astronomy with him. This included my then-office mate, Houjun Mo. At one point I refer to the paper Mo & I wrote on the clustering of low surface brightness galaxies and how I expected them to reside in late-forming dark matter halos^**. I often cite Mo, Mao, & White as a touchstone of galaxy formation theory in LCDM; they subsequently wrote an entire textbook about it. (I was already warning them then that I didn’t think their explanations of the Tully-Fisher relation were viable, at least not when combined with the effect we have subsequently named the diversity of rotation curve shapes.)

When I first began to worry that we were barking up the wrong tree with dark matter, I asked myself what could falsify it. It was hard to come up with good answers, and I worried it wasn’t falsifiable. So I started asking other people what would falsify cold dark matter. Most did not answer. They often had a shocked look like they’d never thought about it, and would rather not^***. It’s a bind: no one wants it to be false, but most everyone accepts that for it to qualify as physical science it should be falsifiable. So it was a question that always provoked a record-scratch moment in which most scientists simply freeze up.

Simon was one of the first to give a straight answer to this question without hesitation, circa 1999. At that point it was clear that dark matter halos formed central density cusps in simulations; so those “cusps had to exist” in the centers of galaxies. At that point, we believed that to mean all galaxies. The question was complicated by the large dynamical contribution of stars in high surface brightness galaxies, but low surface brightness galaxies were dark matter dominated down to small radii. So we thought these were the ideal place to test the cusp hypothesis.

We no longer believe that. After many attempts at evasion, cold dark matter failed this test; feedback was invoked, and the goalposts started to move. There is now a consensus among simulators that feedback in intermediate mass galaxies can alter the inner mass distribution of dark matter halos. Exactly how this happens depends on who you ask, but it is at least possible to explain the absence of the predicted cusps. This goes in the right direction to explain some data, but by itself does not suffice to address the thornier question of why the distribution of baryons is predictive of the kinematics even when the mass is dominated by dark matter. This is why the discussion focused on the lowest mass galaxies where there hasn’t been enough star formation to drive the feedback necessary to alter cusps. Some of these galaxies can be described as having cusps, but probably not all. Thinking only in those terms elides the fact that MOND has a better record of predictive success. I want to know why this happens; it must surely be telling us something important about how the universe works.

The one point of factual disagreement we encountered had to do with the mass profile of galaxies at large radii as traced by gravitational lensing. It is always necessary to agree on the facts before debating their interpretation, so we didn’t press this far. Afterwards, Simon sent a citation to what he was talking about: this paper by Wang et al. (2016). In particular, look at their Fig. 4:

Fig. 4 of Wang et al. (2016). The excess surface density inferred from gravitational lensing for galaxies in different mass bins (data points) compared to mock observations of the same quantity made from within a simulation (lines). Looks like excellent agreement.

This plot quantifies the mass distribution around isolated galaxies to very large scales. There is good agreement between the lensing observations and the mock observations made within a simulation. Indeed, one can see an initial downward bend corresponding to the outer part of an NFW halo (the “one-halo term”), then an inflection to different behavior due to the presence of surrounding dark matter halos (the “two-halo term”). This is what Simon was talking about when he said gravitational lensing was in good agreement with LCDM.

I was thinking of a different, closely related result. I had in mind the work of Brouwer et al. (2021), which I discussed previously. Very recently, Dr. Tobias Mistele has made a revised analysis of these data. That’s worthy its own post, so I’ll leave out the details, which can be found in this preprint. The bottom line is in Fig. 2, which shows the radial acceleration relation derived from gravitational lensing around isolated galaxies:

*The radial acceleration relation from weak gravitational lensing (colored points) extending existing kinematic data (grey points) to lower acceleration corresponding to very large radii (~ 1 Mpc)*. The dashed line is the prediction of MOND. Looks like excellent agreement.

This plot quantifies the radial acceleration due to the gravitational potential of isolated galaxies to very low accelerations. There is good agreement between the lensing observations and the extrapolation of the radial acceleration relation predicted by MOND. There are no features until extremely low acceleration where there may be a hint of the external field effect. This is what I was talking about when I said gravitational lensing was in good agreement with MOND, and that the data indicated a single halo with an r^-2 density profile that extends far out where we ought to see the r^-3 behavior of NFW.

The two plots above use the same method applied to the same kind of data. They should be consistent, yet they seem to tell a different story. This is the point of factual disagreement Simon and I had, so we let it be. No point in arguing about the interpretation when you can’t agree on the facts.

I do not know why these results differ, and I’m not going to attempt to solve it here. I suspect it has something to do with sample selection. Both studies rely on isolated galaxies, but how do we define that? How well do we achieve the goal of identifying isolated galaxies? No galaxy is an island; at some level, there is always a neighbor. But is it massive enough to perturb the lensing signal, or can we successfully define samples of galaxies that are effectively isolated, so that we’re only looking at the gravitational potential of that galaxy and not that of it plus some neighbors? Looks like there is some work left to do to sort this out.

Stepping back from that, we agreed on pretty much everything else. MOND as a fundamental theory remains incomplete. LCDM requires us to believe that 95% of the mass-energy content of the universe is something unknown and perhaps unknowable. Dark matter has become familiar as a term but remains a mystery so long as it goes undetected in the laboratory. Perhaps it exists and cannot be detected – this is a logical possibility – but that would be the least satisfactory result possible: we might as well resume counting angels on the head of a pin.

The community has been working on these issues for a long time. I have been working on this for a long time. It is a big problem. There is lots left to do.

⁺I get a lot of kill the messenger from people who are not capable of discussing controversial topics without personal animus. A lot – inevitably from people who know assume they know more about the subject than I do but actually know much less. It is really amazing how many scientists equate me as a person with MOND as a theory without bothering to do any fact-checking. This is logical fallacy 101.

^*The predictions of MOND are insensitive to the details of galaxy formation. Though of course an interesting question, we don’t need that in order to make predictions. All we need is the mass distribution that the kinematics respond to – we don’t need to know how it got that way. This is like the solar system, where it suffices to know Newton’s laws to compute orbits; we don’t need to know how the sun and planets formed. In contrast, one needs to know how a galaxy was assembled in LCDM to have any hope of predicting what its distribution of dark matter is and then using that to predict kinematics.

^**The ideas Mo & I discussed thirty years ago have reappeared in the literature under the designation “assembly bias.”

^***It was often accompanied by “why would you even ask that?” followed by a pained, constipated expression when they realized that every physical theory has to answer that question.

Full speed in reverse!

People have been asking me about comments in a recent video by Sabine Hossenfelder. I have not watched it, but the quote I’m asked about is “the higher the uncertainty of the data, the better MOND seems to work” with the implication that this might mean that MOND is a systematic artifact of data interpretation. I believe, because they consulted me about it, that the origin of this claim emerged from recent work by Sabine’s student Maria Khelashvili on fitting the SPARC data.

Let me address the point about data interpretation first. Fitting the SPARC data had exactly nothing to do with attracting my attention to MOND. Detailed MOND fits to these data are not particularly important in the overall scheme of these things as I’ll discuss in excruciating detail below. Indeed, these data didn’t even exist until relatively recently.

It may, at this juncture in time, surprise some readers to learn that I was once a strong advocate for cold dark matter. I was, like many of its current advocates, rather derisive of alternatives, the most prominent at the time being baryonic dark matter. What attracted my attention to MOND was that it made a priori predictions that were corroborated, quite unexpectedly, in my data for low surface brightness galaxies. These results were surprising in terms of dark matter then and to this day remain difficult to understand. After a lot of struggle to save dark matter, I realized that the best we could hope to do with dark matter was to contrive a model that reproduced after the fact what MOND had predicted a priori. That can never be satisfactory.

So – I changed my mind. I admitted that I had been wrong to be so completely sure that the solution to the missing mass problem had to be some new form of non-baryonic dark matter. It was not easy to accept this possibility. It required lengthy and tremendous effort to admit that Milgrom had got right something that the rest of us had got wrong. But he had – his predictions came true, so what was I supposed to say? That he was wrong?

Perhaps I am wrong to take MOND seriously? I would love to be able to honestly say it is wrong so I can stop having this argument over and over. I’ve stipulated the conditions whereby I would change my mind to again believe that dark matter is indeed the better option. These conditions have not been met. Few dark matter advocates have answered the challenge to stipulate what could change their minds.

People seem to have become obsessed with making fits to data. That’s great, but it is not fundamental. Making a priori predictions is fundamental, and has nothing to do with fitting data. By construction, the prediction comes before the data. Perhaps this is one way to distinguish between incremental and revolutionary science. Fitting data is incremental science that seeks the best version of an accepted paradigm. Successful predictions are the hallmark of revolutionary science that make one take notice and say, hey, maybe something entirely different is going on.

One of the predictions of MOND is that the RAR should exist. It was not expected in dark matter. As a quick review of the history, here is the RAR as it was known in 2004 and now (as of 2016):

*The radial acceleration relation constructed from data available in 2004 and that from 2016.*

The big improvement provided by SPARC was a uniform estimate of the stellar mass surface density of galaxies based on Spitzer near-infrared data. These are what are used to construct the x-axis: g_bar is what Newton predicts for the observed mass distribution. SPARC was a vast improvement over the optical data we had previously, to the point that the intrinsic scatter is negligibly small: the observed scatter can be attributed to the various uncertainties and the expected scatter in stellar mass-to-light ratios. The latter never goes away, but did turn out to be at the low end of the range we expected. It could easily have looked worse, as it did in 2004, even if the underlying physical relation was perfect.

Negligibly small intrinsic scatter is the best one can hope to find. The issue now is the fit quality to individual galaxies (not just the group plot above). We already know MOND fits rotation curve data. The claim that appears in Dr. Hossenfelder’s video boils down to dark matter providing better fits. This would be important if it told us something about nature. It does not. All it teaches us about is the hazards of fitting data for which the errors are not well behaved.

While SPARC provides a robust estimate of g_bar, g_obs is based on a heterogeneous set of rotation curves drawn from a literature spanning decades. The error bars on these rotation curves have not been estimated in a uniform way, so we cannot blindly fit the data with our favorite software tool and expect that to teach us something about physical reality. I find myself having to say this to physicists over and over and over and over and over again: you cannot trust astronomical error bars to behave as Gaussian random variables the way one would like and expect in a controlled laboratory setting.

Astronomy is not conducted in a controlled laboratory. It is an observational science. We cannot put the entire universe in a box and control all the variables. We can hope to improve the data and approach this ideal, but right now we’re nowhere near it. These fitting analyses assume that we are.

Screw it. I really am sick of explaining this over and over, so I’m just going to cut & paste verbatim what I told Hossenfelder & Khelashvili by email when they asked. This is not the first time I’ve written an email like this, and I’m sure it won’t be the last.

Excruciating details: what I said to Hossenfelder & Khelashvili about the perils of rotation curve fitting on 22 September 2023 in response for their request for comments on the draft of the relevant paper:

First, the work of Desmond is a good place to look for an opinion independent of mine.

Second, in my experience, the fit quality you find is what I’ve found before: DM halos with a constant density core consistently give the best fits in terms of chi^2, then MOND, then NFW. The success of cored DM halos happens because it is an extremely flexible fitting function: the core radius and core density can be traded off to fit any dog’s leg, and is highly degenerate with the stellar M*/L. NFW works less well because it has a less flexible shape. But both work because they have more parameters [than MOND].

Third, statistics will not save us here. I once hoped that the BIC would sort this out, but having gone down that road, I believe the BIC does not penalize models sufficiently for adding free parameters. You allude to this at the end of section 3.2. When you go from MOND (with fixed a₀ it has only one parameter, M*/L, to fit to account for everything) to a dark matter halo (which has at a minimum 3 parameters: M*/L plus two to describe the halo) then you gain an enormous amount of freedom – the volume of possible parameter space grows enormously. But the BIC just says if you had 20 degrees of freedom before, now you have 22. That does not remotely represent the amount of flexibility that represents: some free parameters are more equal than others. MOND fits and DM halo fits are not the same beast; we can’t compare them this way any more than we can compare apples and snails.

Worse, to do this right requires that the uncertainties be real random errors. They are not. SPARC provides homogeneous mass models based on near-IR observations of the stellar mass distribution. Those should be OK to the extent that near-IR light == stellar mass. That is a decent mapping, but not perfect. Consequently, we expect the occasional galaxy to misbehave. UGC 128 is a case where the MOND fit was great with optical data then became terrible with near-IR data. The absolute difference in the data are not great, but in terms of the formal chi^2 it is. So is that a failure of the model, or of the data to represent what we want it to represent?

This happens all the time in astronomy. Here, we want to know the circular velocity of a test particle in the gravitational potential predicted by the baryonic mass distribution. We never measure either of those quantities. What we measure is the (i) stellar light distribution and the (ii) Doppler velocities of gas. We assume we can map stellar light to stellar mass and Doppler velocity to orbital speed, but no mass model is perfect, nor is any patch of observed gas guaranteed to be on a purely circular orbit. These are known unknowns: uncertainties that we know are real but we cannot easily quantify. These assumptions that we have to make to do the analysis dominate over the random errors in many cases. We also assume that galaxies are in dynamical equilibrium, but 20% of spirals show gross side-to-side asymmetries, and at least 50% mild ones. So what is the circular motion in those cases? (F579-1 is a good example)

While SPARC is homogeneous in its photometry, it is extremely heterogeneous in its rotation curve measurements. We’re working on fixing that, but it’ll take a while. Consequently, as you note, some galaxies have little constraining power while others appear to have lots. That’s because many of the rotation curve velocity uncertainties are either grossly over or underestimated. To see this, plot the cumulative distribution of chi^2 for any of your models (or see the CDF published by Li et al 2018 for the RAR and Li et al 2020 for dark matter halos of many flavors. So many, I can’t recall how many CDF we published.) Anyway, for a good model, chi^2 is always close to one, so the CDF should go up sharply and reach one quickly – there shouldn’t be many cases with very low chi^2 or very high chi^2. Unfortunately, rotation curve data do not do this for any type of model. There are always way too many cases with chi^2 << 1 and also too many with chi^2 >> 1. One might conclude that all models are unacceptable – or that the error bars are Messed Up. I think the second option is the case. If so, then this sort of analysis will always have the power to mislead.

I insert Fig. 1 from Li et al. (2020) so you don’t have to go look it up. The CDF of a statistically good model would rise sharply, being an almost vertical line at chi^2 = 1. No model of any flavor does that. That’s in large part because the uncertainties on some rotation curves are too large, while those on others are too small. The greater flexibility of dark matter models make them incrementally better than MOND for the cases with error bars that are too small – hence the corollary statement that “the higher the uncertainty of the data, the better MOND seems to work.” *This happens because dark matter models are allowed to chase bogus outliers with tiny error bars in a way that MOND cannot. That doesn’t make dark matter better, it just makes it is easier to fool.*

A key thing to watch out for is the outsized effects of a few points with tiny error bars. Among galaxies with high chi^2, what often happens is that there is one point with a tiny error bar that does not agree with any of the rest of the data for any smoothly continuous rotation curve. Fitting programs penalize a model for missing this point by many sigma, so will do anything they can to make it better. So what happens is that if you let a₀ vary with a flat prior, it will got to some very silly values in order to buy a tiny improvement in chi^2. Formally, that’s a better fit, so you say OK, a₀ has to vary. But if you plot the fitted RCs with fixed and variable a₀, you will be hard pressed to see the difference. Chi^2 is different, sure, but both will have chi^2 >> 1, so a lousy fit either way, and we haven’t really gained anything meaningful from allowing for the greater fitting freedom. Really it is just that one point that is Wrong even though it has a tiny error bar – which you can see relative to the other points, never mind the model. Dark matter halos have more flexibility from the beginning, so this is less obvious for them even though the same thing happens.

So that’s another big point – what is the prior for a dark matter halo? [Your] Table 1 allows V₂₀₀ and C₂₀₀ to be pretty much anything. So yes, you will find a fit from that range. For Burkert halos, there is no prior, since these do not emerge from any theory – they’re just a flexible French curve. For NFW halos, there is a prior from cosmology – see McGaugh et al (2007) among a zillion other possible references, including Li et al (2020). In any[L]CDM cosmology, the parameters V200 and C200 correlate – they are not independent. So a reasonable prior would be a Gaussian in log(C200) at a given V200 as specified by some simulation (Macio et al; see Li et al 2020). Another prior is how V200 (or M200) relates to the observed baryonic mass (or stellar mass). This one is pretty dodgy. Originally, we expected a fixed ratio between baryonic and dark mass. So when I did this kind of analysis in the ’90s, I found NFW flunked hard compared to MOND. (I didn’t know about the BIC then.) Galaxy DM halos simply do not look like NFW halos that form in LCDM and host galaxies with a few percent of their mass in the luminous disk even though this was the standard model for many years (Mo, Mao, & White 1998). If we drop the assumption that luminous galaxies are always a fixed fraction of their dark matter halos, then better fits can be obtained. I suspect your uniform prior fits have halo masses all over the place; they probably don’t correlate well with the baryonic mass, nor are their C and V200 parameters likely to correlate as they are predicted to do. You could apply the expected mass-concentration and stellar mass-halo mass relations as priors, then NFW will come off worse in your analysis because you’ve restricted them to where they ought to live.

So, as you say – it all comes down to the prior.

Even applying a stellar mass-halo mass relation from abundance matching isn’t really independent information, though that’s the best you can hope to do. But I was saying 20+ years ago that fixed mass ratios wouldn’t work, but nobody then wanted to abandon that obvious assumption. Since then, they’ve been forced to do so. But there is no good physical reason for it (feedback is the deus ex machina of all problems in the field), what happened is that the data forced us to drop the obvious assumption. Data including kinematic data (McGaugh et al 2010). So adopting a modern stellar mass-halo mass relation will give you a stronger prior than a uniform prior, but that choice has already been informed by the kinematic data that you’re trying to fit. How do we properly penalize the model for cheating about its “prior” by peaking at past data?

So, as you say – it all comes down to the prior. I think it would be important here to better constrain the priors on the DM halo fits. Li et al (2020) discuss this. Even then we’re not done, because galaxy formation modifies the form of the halo function we’re fitting. They shouldn’t end up as NFW even if they start out that way – see Li et al 2022a & b. Those papers consider the inevitable effects of adiabatic compression, but not of feedback. If feedback really has the effects on DM halos that is frequently advertised, then neither NFW or Burkert are appropriate fitting functions – they’re not what LCDM+feedback predicts. Good luck extracting a legitimate prediction from simulations, though. So we’re stuck doing what you’re trying to do: adopt some functional form to represent the DM halo, and see what fits. What you’ve done here agrees with my experience: cored DM halos work best. But they don’t represent an LCDM prediction, or any other broader theory, so – so what?

Another detail to be wary of – the radial range over which the RC data constrain the DM halo fit is often rather limited compared to the size of the halo. To complicate matters further, the inner regions are often star-dominated, so there is not much of a handle on DM from where the data are best, at least beyond many galaxies preferring not to have a cusp since the stars already get the job done at small R. So, one ends up with V_DM(R) constrained from 3% to 10% of the virial radius, or something like that. V200 and C200 are defined at the notional virial radius, so there are many combinations of these parameters that might adequately fit the observed range while being quite different elsewhere. Even worse, NFW halos are pretty self-similar – there are combinations of (C200,V200) that are highly degenerate, so you can’t really tell the difference between them even with excellent data – the confidence contours look like bananas in C200-V200 space, with low C/high V often being as good as high C/low V. Even even even worse is that the observed V_DM(R) is often approximately a straight line. Any function looks like a straight line if you stretch it out enough. Consequently, the fits to LSB galaxies often tend to absurdly low C and high V200: NFW never looks like a straight line, but it does if you blow it up enough. So one ends up inferring that the halo masses of tiny galaxies are nearly as big as those of huge galaxies, or more so! My favorite example was NGC 3109, a tiny dwarf on the edge of the Local Group. A straight NFW fit suggests that the halo of this one little galaxy weighs more than the entire Local Group, M31 + MW + everything else combined. This is the sort of absurd result that comes from fitting the NFW halo form to a limited radial range of data.

I don’t know that this helps you much, but you see a few of the concerns.

Triton Station

A Blog About the Science and Sociology of Cosmology and Dark Matter

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