It has been proposal season for the Hubble Space Telescope, so many astronomers have been busy with that. I am no exception. Talking to others, it is clear that there remain many more excellent Hubble projects than available observing time.
So I haven’t written here for a bit, and I have other tasks to get on with. I did get requests for a report on the last conference I went to, Beyond WIMPs: from Theory to Detection. They have posted video from the talks, so anyone who is interested may watch.
I think this is the worst talk I’ve given in 20 years. Maybe more. Made the classic mistake of trying to give the talk the organizers asked for rather than the one I wanted to give. Conference organizers mean well, but they usually only have a vague idea of what they imagine you’ll say. You should always ignore that and say what you think is important.
When speaking or writing, there are three rules: audience, audience, audience. I was unclear what the audience would be when I wrote the talk, and it turns out there were at least four identifiably distinct audiences in attendance. There were skeptics – particle physicists who were concerned with the state of their field and that of cosmology, there were the faithful – particle physicists who were not in the least concerned about this state of affairs, there were the innocent – grad students with little to no background in astronomy, and there were experts – astroparticle physicists who have a deep but rather narrow knowledge of relevant astronomical data. I don’t think it would have been possible to address the assigned topic (a “Critical Examination of the Existence of Dark Matter“) in a way that satisfied all of these distinct audiences, and certainly not in the time allotted (or even in an entire semester).
It is tempting to give an interruption by interruption breakdown of the sociology, but you may judge that for yourselves. The one thing I got right was what I said at the outset: Attitude Matters. You can see that on display throughout.
In science as in all matters, if you come to a problem sure that you already know the answer, you will leave with that conviction. No data nor argument will shake your faith. Only you can open your own mind.
Note: this is a guest post by David Merritt, following on from his paper on the philosophy of science as applied to aspects of modern cosmology.
Stacy kindly invited me to write a guest post, expanding on some of the arguments in my paper. I’ll start out by saying that I certainly don’t think of my paper as a final word on anything. I see it more like an opening argument — and I say this, because it’s my impression that the issues which it raises have not gotten nearly the attention they deserve from the philosophers of science. It is that community that I was hoping to reach, and that fact dictated much about the content and style of the paper. Of course, I’m delighted if astrophysicists find something interesting there too.
My paper is about epistemology, and in particular, whether the standard cosmological model respects Popper’s criterion of falsifiability— which he argued (quite convincingly) is a necessary condition for a theory to be considered scientific. Now, falsifying a theory requires testing it, and testing it means (i) using the theory to make a prediction, then (ii) checking to see if the prediction is correct. In the case of dark matter, the cleanest way I could think of to do this was via so-called “direct detection”, since the rotation curve of the Milky Way makes a pretty definite prediction about the density of dark matter at the Sun’s location. (Although as I argued, even this is not enough, since the theory says nothing at all about the likelihood that the DM particles will interact with normal matter even if they are present in a detector.)
What about the large-scale evidence for dark matter — things like the power spectrum of density fluctuations, baryon acoustic oscillations, the CMB spectrum etc.? In the spirit of falsification, we can ask what the standard model predicts for these things; and the answer is: it does not make any definite prediction. The reason is that — to predict quantities like these — one needs first to specify the values of a set of additional parameters: things like the mean densities of dark and normal matter; the numbers that determine the spectrum of initial density fluctuations; etc. There are roughly half a dozen such “free parameters”. Cosmologists never even try to use data like these to falsify their theory; their goal is to make the theory work, and they do this by picking the parameter values that optimize the fit between theory and data.
Philosophers of science are quite familiar with this sort of thing, and they have a rule: “You can’t use the data twice.” You can’t use data to adjust the parameters of a theory, and then turn around and claim that those same data support the theory. But this is exactly what cosmologists do when they argue that the existence of a “concordance model” implies that the standard cosmological model is correct. What “concordance” actually shows is that the standard model can bemadeconsistent: i.e. that one does not require differentvalues for the same parameter. Consistency is good, but by itself it is a very weak argument in favor of a theory’s correctness. Furthermore, as Stacy has emphasized, the supposed “concordance” vanishes when you look at the values of the same parameters as they are determined in other, independent ways. The apparent tension in the Hubble constant is just the latest example of this; another, long-standing example is the very different value for the mean baryon density implied by the observed lithium abundance. There are other examples. True “convergence” in the sense understood by the philosophers — confirmation of the value of a single parameter in multiple, independent experiments — is essentially lacking in cosmology.
Now, even though those half-dozen parameters give cosmologists a great deal of freedom to adjust their model and to fit the data, the freedom is not complete. This is because — when adjusting parameters — they fix certain things: what Imre Lakatos called the “hard core” of a research program: the assumptions that a theorist is absolutely unwilling to abandon, come hell or high water. In our case, the “hard core” includes Einstein’s theory of gravity, but it also includes a number of less-obvious things; for instance, the assumption that the dark matter responds to gravity in the same way as any collisionless fluid of normal matter would respond. (The latter assumption is not made in many alternative theories.) Because of the inflexibility of the “hard core”, there are going to be certain parameter values that are also more-or-less fixed by the data. When a cosmologist says “The third peak in the CMB requires dark matter”, what she is really saying is: “Assuming the fixed hard core, I find that any reasonable fit to the data requires the parameter defining the dark-matter density to be significantly greater than zero.” That is a much weaker statement than “Dark matter must exist”. Statements like “We know that dark matter exists” put me in mind of the 18th century chemists who said things like “Based on my combustion experiments, I conclude that phlogiston exists and that it has a negative mass”. We know now that the behavior the chemists were ascribing to the release of phlogiston was actually due to oxidation. But the “hard core” of their theory (“Combustibles contain an inflammable principle which they release upon burning”) forbade them from considering different models. It took Lavoisier’s arguments to finally convince them of the existence of oxygen.
The fact that the current cosmological model has a fixed “hard core” also implies that — in principle — it can be falsified. But, at the risk of being called a cynic, I have little doubt that if a new, falsifying observation should appear, even a very compelling one, the community will respond as it has so often in the past: via a conventionalist stratagem. Pavel Kroupa has awonderful graphic, reproduced below, that shows just how often predictions of the standard cosmological model have been falsified — a couple of dozen times, according to latest count; and these are only the major instances. Historians and philosophers of science have documented that theories that evolve in this way often end up on the scrap heap. To the extent that my paper is of interest to the astronomical community, I hope that it gets people to thinking about whether the current cosmological model is headed in that direction.
A recent paper in Nature by Genzel et al. reports declining rotation curves for high redshift galaxies. I have been getting a lot of questions about this result, which would be very important if true. So I thought I’d share a few thoughts here.
Nature is a highly reputable journal – in most fields of science. In Astronomy, it has a well earned reputation as the place to publish sexy but incorrect results. They have been remarkably consistent about this, going back to my earliest grad school memories, like a quasar pair being interpreted as a wide gravitational lens indicating the existence of cosmic strings. This was sexy at that time, because cosmic strings were thought to be a likely by-product of cosmic Inflation, threading the universe with remnants of the Inflationary phase. Cool, huh? Many Big Names signed on to this Exciting Discovery, which was Widely Discussed at the time. The only problem was that it was complete nonsense.
Genzel et al. look likely to build on this reputation. In Astronomy, we are always chasing the undiscovered, which often means the most distant. This is a wonderful thing: the universe is practically infinite; there is always something new to discover. An occasional downside is the temptation to over-interpret and oversell data on the edge.
Lets start with some historical perspective. Here is the position-velocity diagram of NGC 7331 as measured by Rubin et al. (1965):
The rotation curve goes up, then it goes down. One would not claim the discovery of flat rotation curves from these data.
Here is the modern rotation curve of the same galaxy:
As the data improved, the flattening became clear. In order to see this, you need to observe to large radius. The original data didn’t do that. It isn’t necessarily wrong; it just doesn’t go far enough out.
Now lets look at the position-velocity diagrams published by Genzel et al.:
They go up, they go down. This is the normal morphology of the rotation curves of bright, high surface brightness galaxies. First they rise steeply, then they roll over, then they decline slowly and gradually flatten out.
It looks to me like the Genzel el al. data do the first two things. They go up. They roll over. Maybe they start to come down a tiny bit. Maybe. They simply do not extend far enough to see the flattening, if it is there. Their claim that the rotation curves are falling is not persuasive: this is asking more of the data than is warranted. Historically, there are many examples of claims of “declining” rotation curves. DDO 154 is one famous example. These claims were not very persuasive at the time, and did not survive closer examination.
I have developed the habit of looking at the data before I read the text of a paper. I did that in this case, and saw what I expected to see from years of experience working on low redshift galaxies. I wasn’t surprised until I read the text as saw the claim that these galaxies somehow differed from those at low redshift.
It takes some practice to look at the data without being influenced by lines drawn to misguide the eye. That’s what the model lines drawn in red do. I don’t have access to the data, so I can’t re-plot them without those lines. So instead I have added, by eye, a crude estimate of what I would expect for galaxies like this. In most cases, the data do not distinguish between falling and flat rotation curves. In the case labeled 33h, the data look slightly more consistent with a flat rotation curve. In 10h, they look slightly more consistent with a falling rotation curve. That appearance is mostly driven by the outermost point with large error bars on the approaching side. Taken literally, this velocity is unphysical: it declines faster than Keplerian. They interpret this in terms of thick disks, but it could be a clue that Something is Wrong.
The basic problem is that the high redshift data do not extend to large radii. They simply do not go far enough out to distinguish between flat and declining rotation curves. Most do not extend beyond 10 kpc. If we plot the data for NGC 7331 with R < 10 kpc, we get this:
Here I’ve plotted both sides in order to replicate the appearance of Genzel’s plots. I’ve also included an exponential disk model in red. Never mind that this is a lousy representation of the true mass model. It gives a good fit, no?
The rotation curve is clearly declining. Unless you observe further out:
The data of Genzel et al. do not allow us to distinguish between “normal” flat rotation curves and genuinely declining ones.
This is just taking the data as presented. I have refrained from making methodological criticisms, and will continue to do so. I will only note that it is possible to make a considerably more sophisticated, 3D analysis. Di Teodoro et al. (2016) have done this for very similar data. They find much lower velocity dispersions (not the thick disks claimed by Genzel et al.) and flat rotation curves:
There is no guarantee that the same results will follow for the Genzel et al. data, but it would be nice to see the same 3D analysis techniques applied.
Since I am unpersuaded that the Genzel et al. data extend far enough out to test for flat rotation, I looked for a comparison that I could make so far as the data do go. Fig. 3 of Genzel et al. shows the dark matter fraction as a function of circular velocity. This contains the same information as Fig. 12 of McGaugh (2016), which I re-plot here in terms of the dark matter fraction:
The data of Genzel et al. follow the trends established by local galaxies. They are confined to the bright, high surface brightness end of these relations, but that is to be expected: the brightest galaxies are always the most readily observed, especially at high redshift.
Genzel et al. only plot the left panel. As I have shown manytimesbefore, the strongest correlation of dynamical-to-baryonic mass is with surface brightness, not mass or its proxies luminosity and circular velocity. This is an essential aspect of the mass discrepancy problem; it is unfortunate that many scientists working on the topic appear to remain unaware of this basic fact.
From these diagrams, I infer that there is no discernible evolution in the properties of bright galaxies out to high redshift (z = 2.4 for their most distant case). The data presented by Genzel et al. sit exactly where one would expect from the relations established by local galaxies. That in itself might seem surprising, and perhaps warrants a Letter to Nature. But most of the words in Genzel et al. are about a surprising sort of evolution in which galaxy rotation curves decline at high redshift, so they have less dark matter then than now. I do not see that their data sustain such an interpretation.
So far everything I have said is empirical. If I put on a theory hat, the claims of Genzel et al. persist in making no sense.
First, ΛCDM. Fundamental to the ΛCDM cosmogony is the notion that dark matter halos form first, with baryons falling in subsequently. It has to happen in that order to satisfy the constraints on the growth of structure from the cosmic microwave background. The temperature fluctuations in the CMB are small because the baryons haven’t yet been able to clump up. In order for them to form galaxies as quickly as observed, the dark matter must already be forming the seeds of dark matter halos for the baryons to subsequently fall into. Without this order of battle, our explanation of structure formation is out the window.
Next, MOND. If rotation curves are indeed falling as claimed, this would falsify MOND, or at least make it a phenomenon that only applies in the local universe. But, as discussed, the high-z galaxies look like local ones. That doesn’t falsify MOND; it rather encourages the basic picture of structure formation we have in that context: galaxies form early and settle down into the form the modified force law stipulates. Indeed, the apparent lack of evolution implies that Milgrom’s acceleration constant a0 is indeed constant, and does not vary (as sometimes speculated) in concert with the expansion rate as hinted at by the numerical coincidence a0 ~ cH0. I cannot place a meaningful limit on the evolution of a0 from the data as presented, but it appears to be small. Rather than falsifying MOND, the high-z data look to be consistent with it – so far as they go.
So, in summary: the data at high redshift appear completely consistent with those at low redshift. The claim of falling rotation curves would be problematic to both ΛCDM and MOND. However, this claim is not persuasive – the data simply do not extend far enough out.
Early 21st century technology has enabled us to do at high redshift what could barely be done at low redshift in the mid-20th century. That’s impressive. But these high-z data look a lot like low-z data circa 1970. A lot has changed since then. Right now, for the exploration of the high redshift universe, I will borrow one of Vera Rubin’s favorite phrases: These are Early Days.
There is a new article in Science on the expansion rate of the universe, very much along the lines of my recent post. It is a good read that I recommend. It includes some of the human elements that influence the science.
When I started this blog, I recalled my experience in the ’80s moving from a theory-infused institution to a more observationally and empirically oriented one. At that time, the theory-infused cosmologists assured us that Sandage had to be correct: H0 = 50. As a young student, I bought into this. Big time. I had no reason not to; I was very certain of the transmitted lore. The reasons to believe it then seemed every bit as convincing a the reasons to believe ΛCDM today. When I encountered people actually making the measurement, like Greg Bothun, they said “looks to be about 80.”
This caused me a lot of cognitive dissonance. This couldn’t be true. The universe would be too young (at most ∼12 Gyr) to contain the oldest stars (thought to be ∼18 Gyr at that time). Worse, there was no way to reconcile this with Inflation, which demanded Ωm = 1. The large deceleration of the expansion caused by high Ωm greatly exacerbated the age problem (only ∼8 Gyr accounting for deceleration). Reconciling the age problem with Ωm = 1 was hard enough without raising the Hubble constant.
Presented with this dissonant information, I did what most of us humans do: I ignored it. Some of my first work involved computing the luminosity function of quasars. With the huge distance scale of H0 = 50, I remember noticing how more distant quasars got progressively brighter. By a lot. Yes, they’re the most luminous things in the early universe. But they weren’t just outshining a galaxy’s worth of stars; they were outshining a galaxy of galaxies.
That was a clue that the metric I was assuming was very wrong. And indeed, since that time, every number of cosmological significance that I was assured in confident tones by Great Men that I Had to Believe has changed by far more than its formal uncertainty. In struggling with this, I’ve learned not to be so presumptuous in my beliefs. The universe is there for us to explore and discover. We inevitably err when we try to dictate how it Must Be.
The amplitude of the discrepancy in the Hubble constant is smaller now, but the same attitudes are playing out. Individual attitudes vary, of course, but there are many in the cosmological community who take the attitude that the Planck data give H0 = 67.8 so that is the right number. All other data are irrelevant; or at best flawed until brought into concordance with the right number.
It is Known, Khaleesi.
Often these are the same people who assured us we had to believe Ωm = 1 and H0 = 50 back in the day. This continues the tradition of arrogance about how things must be. This attitude remains rampant in cosmology, and is subsumed by new generations of students just as it was by me. They’re very certain of the transmitted lore. I’ve even been trolled by some who seem particularly eager to repeat the mistakes of the past.
From hard experience, I would advocate a little humility. Yes, Virginia, there is a real tension in the Hubble constant. And yes, it remains quite possible that essential elements of our cosmology may prove to be wrong. I personally have no doubt about the empirical pillars of the Big Bang – cosmic expansion, Big Bang Nucleosynthesis, and the primordial nature of the Cosmic Microwave Background. But Dark Matter and Dark Energy may well turn out to be mere proxies for some deeper cosmic truth. IF that is so, we will never recognize it if we proceed with the attitude that LCDM is Known, Khaleesi.
In 1984, I heard Hans Bethe give a talk in which he suggested the dark matter might be neutrinos. This sounded outlandish – from what I had just been taught about the Standard Model, neutrinos were massless. Worse, I had been given the clear impression that it would screw everything up if they did have mass. This was the pervasive attitude, even though the solar neutrino problem was known at the time. This did not compute! so many of us were inclined to ignore it. But, I thought, in the unlikely event it turned out that neutrinos did have mass, surely that would be the answer to the dark matter problem.
Flash forward a few decades, and sure enough, neutrinos do have mass. Oscillations between flavors of neutrinos have been observed in both solar and atmospheric neutrinos. This implies non-zero mass eigenstates. We don’t yet know the absolute value of the neutrino mass, but the oscillations do constrain the separation between mass states (Δmν,212 = 7.53×10−5 eV2 for solar neutrinos, and Δmν,312 = 2.44×10−3 eV2 for atmospheric neutrinos).
Though the absolute values of the neutrino mass eigenstates are not yet known, there are upper limits. These don’t allow enough mass to explain the cosmological missing mass problem. The relic density of neutrinos is
Ωνh2 = ∑mν/(93.5 eV)
In order to make up the dark matter density (Ω ≈ 1/4), we need ∑mν ≈ 12 eV. The experimental upper limit on the electron neutrino mass is mν < 2 eV. There are three neutrino mass eigenstates, and the difference in mass between them is tiny, so ∑mν < 6 eV. Neutrinos could conceivably add up to more mass than baryons, but they cannot add up to be the dark matter.
In recent years, I have started to hear the assertion that we have already detected dark matter, with neutrinos given as the example. They are particles with mass that only interact with us through the weak nuclear force and gravity. In this respect, they are like WIMPs.
Here the equivalence ends. Neutrinos are Standard Model particles that have been known for decades. WIMPs are hypothetical particles that reside in a hypothetical supersymmetric sector beyond the Standard Model. Conflating the two to imply that WIMPs are just as natural as neutrinos is a false equivalency.
That said, massive neutrinos might be one of the few ways in which hierarchical cosmogony, as we currently understand it, is falsifiable. Whatever the dark matter is, we need it to be dynamically cold. This property is necessary for it to clump into dark matter halos that seed galaxy formation. Too much hot (relativistic) dark matter (neutrinos) suppresses structure formation. A nascent dark matter halo is nary a speed bump to a neutrino moving near the speed of light: if those fast neutrinos carry too much mass, they erase structure before it can form.
One of the great successes of ΛCDM is its explanation of structure formation: the growth of large scale structure from the small fluctuations in the density field at early times. This is usually quantified by the power spectrum – in the CMB at z > 1000 and from the spatial distribution of galaxies at z = 0. This all works well provided the dominant dark mass is dynamically cold, and there isn’t too much hot dark matter fighting it.
How much is too much? The power spectrum puts strong limits on the amount of hot dark matter that is tolerable. The upper limit is ∑mν < 0.12 eV. This is an order of magnitude stronger than direct experimental constraints.
Usually, it is assumed that the experimental limit will eventually come down to the structure formation limit. That does seem likely, but it is also conceivable that the neutrino mass has some intermediate value, say mν ≈ 1 eV. Such a result, were it to be obtained experimentally, would falsify the current CDM cosmogony.
Such a result seems unlikely, of course. Shooting for a narrow window such as the gap between the current cosmological and experimental limits is like drawing to an inside straight. It can happen, but it is unwise to bet the farm on it.
If experiments measure a neutrino mass in excess of the cosmological limit, it would be powerful motivation to consider MOND-like theories as a driver of structure formation. If instead the neutrino does prove to be tiny, ΛCDM will have survived another test. That wouldn’t falsify MOND (or really have any bearing on it), but it would remove one potential “out” for the galaxy cluster problem.
Tiny though they be, neutrinos got mass! And it matters!
David Merritt recently published the article “Cosmology and convention” in Studies in History and Philosophy of Science. This article is remarkable in many respects. For starters, it is rare that a practicing scientist reads a paper on the philosophy of science, much less publishes one in a philosophy journal.
I was initially loathe to start reading this article, frankly for fear of boredom: me reading about cosmology and the philosophy of science is like coals to Newcastle. I could not have been more wrong. It is a genuine page turner that should be read by everyone interested in cosmology.
I have struggled for a long time with whether dark matter constitutes a falsifiable scientific hypothesis. It straddles the border: specific dark matter candidates (e.g., WIMPs) are confirmable – a laboratory detection is both possible and plausible – but the concept of dark matter can never be excluded. If we fail to find WIMPs in the range of mass-cross section parameters space where we expected them, we can change the prediction. This moving of the goal post has already happened repeatedly.
I do not find it encouraging that the goal posts keep moving. This raises the question, how far can we go? Arbitrarily low cross-sections can be extracted from theory if we work at it hard enough. How hard should we work? That is, what criteria do we set whereby we decide the WIMP hypothesis is mistaken?
There has to be some criterion by which we would consider the WIMP hypothesis to be falsified. Without such a criterion, it does not satisfy the strictest definition of a scientific hypothesis. If at some point we fail to find WIMPs and are dissatisfied with the theoretical fine-tuning required to keep them hidden, we are free to invent some other dark matter candidate. No WIMPs? Must be axions. Not axions? Would you believe light dark matter? [Worst. Name. Ever.] And so on, ad infinitum. The concept of dark matter is not falsifiable, even if specific dark matter candidates are subject to being made to seem very unlikely (e.g., brown dwarfs).
Faced with this situation, we can consult the philosophy science. Merritt discusses how many of the essential tenets of modern cosmology follow from what Popper would term “conventionalist stratagems” – ways to dodge serious consideration that a treasured theory is threatened. I find this a compelling terminology, as it formalizes an attitude I have witnessed among scientists, especially cosmologists, many times. It was put more colloquially by J.K. Galbraith:
“Faced with the choice between changing one’s mind and proving that there is no need to do so, almost everybody gets busy on the proof.”
Boiled down (Keuth 2005), the conventionalist strategems Popper identifies are
ad hoc hypotheses
modification of ostensive definitions
doubting the reliability of the experimenter
doubting the acumen of the theorist
These are stratagems to be avoided according to Popper. At the least they are pitfalls to be aware of, but as Merritt discusses, modern cosmology has marched down exactly this path, doing each of these in turn.
The ad hoc hypotheses of ΛCDM are of course Λ and CDM. Faced with the observation of a metric that cannot be reconciled with the prior expectation of a decelerating expansion rate, we re-invoke Einstein’s greatest blunder, Λ. We even generalize the notion and give it a fancy new name, dark energy, which has the convenient property that it can fit any observed set of monotonic distance-redshift pairs. Faced with an excess of gravitational attraction over what can be explained by normal matter, we invoke non-baryonic dark matter: some novel form of mass that has no place in the standard model of particle physics, has yet to show any hint of itself in the laboratory, and cannot be decisively excluded by experiment.
We didn’t accept these ad hoc add-ons easily or overnight. Persuasive astronomical evidence drove us there, but all these data really show is that something dire is wrong: General Relativity plus known standard model particles cannot explain the universe. Λ and CDM are more a first guess than a final answer. They’ve been around long enough that they have become familiar, almost beyond doubt. Nevertheless, they remain unproven ad hoc hypotheses.
The sentiment that is often asserted is that cosmology works so well that dark matter and dark energy must exist. But a more conservative statement would be that our present understanding of cosmology is correct if and only if these dark entities exist. The onus is on us to detect dark matter particles in the laboratory.
That’s just the first conventionalist stratagem. I could given many examples of violations of the other three, just from my own experience. That would make for a very long post indeed.
Instead, you should go read Merritt’s paper. There are too many things there to discuss, at least in a single post. You’re best going to the source. Be prepared for some cognitive dissonance.
Of historical interest are a series of papers written in the mid-60s in collaboration with Margaret Burbidge. These show some early rotation curves. Many peter out around the turn-over of the rotation curve. With the benefit of hindsight, one can see what the data will do – extend more or less flat from the last measured points.
Here is an example from Burbidge et al. (1964). In this case, NGC 3521, they got a bit further than the turnover. You may judge for yourself how convincing the detection of flat rotation is.
As it happens, NGC 3521 is a near kinematic twin to the Milky Way. Here is the modern rotation curve from THINGS compared with an estimate of the Milky Way rotation curve.
Hopefully it is obvious why it helps to have extended data (usually from 21 cm data, as in the example from THINGS).
This reminds me of something Vera frequently said. Early Days. In many ways, we are far down the path of dark matter. But we still have no idea what it is, or even whether what we call dark matter now is merely a proxy for some more general concept.
Vera always appreciated this. In many ways, these are still Early Days.