A Blog About the Science and Sociology of Cosmology and Dark Matter
Author: tritonstation
Stacy McGaugh is an astrophysicist and cosmologist who studies galaxies, dark matter, and theories of modified gravity. He is an expert on low surface brightness galaxies, a class of objects in which the stars are spread thin compared to bright galaxies like our own Milky Way. He demonstrated that these dim galaxies appear to be dark matter dominated, providing unique tests of theories of galaxy formation and modified gravity.
Professor McGaugh is currently the chair of the Department of Astronomy at Case Western Reserve University in Cleveland, Ohio, and director of the Warner and Swasey Observatory. Previously he was a member of the faculty at the University of Maryland, having also held research fellowships at Rutgers, the Department of Terrestrial Magnetism of the Carnegie Institution of Washington, and the Institute of Astronomy at the University of Cambridge after earning his Ph.D. from the University of Michigan.
Figure 2 from Mistele et al. (2024a).The RAR from weak lensing data (yellow diamonds) is shown together with the binned kinematic RAR from Lelli et al. (2017, gray circles). The solid line is Newtonian gravity without dark matter (gobs = gbar). The shaded region at gbar < 10−13 m/s2 indicates where the isolation criterion may be less reliable according to the estimate by Brouwer et al. (2021). Our results suggest that late type galaxies (LTGs) may be sufficiently isolated down to gbar ≈ 10−14 m/s2. We shade this region where LTGs may still be reliable in a lighter color.
The RAR of weak lensing extends the RAR from kinematics to much lower accelerations. How low we can trust we’ll come back to, but certainly to gbar ≈ 10−13 m/s2 and probably to gbar ≈ 10−14 m/s2. For the mass of the typical galaxy in the KiDS sample, this corresponds to a radius of 300 kpc and 1.1 Mpc, respectively. Hence our claim that the effective gravitational potentials of isolated galaxies are consistent with rotation curves that remain flat indefinitely far out: a million light years at least, and perhaps a million parsecs.
Note that the kinematic and lensing data overlap at log(gbar) = -11.5. These independent methods give the same result. Moreover, this region corresponds to the regions in galaxies where atomic gas rather than stars dominates the baryonic mass budget, which minimizes the systematic uncertainty due to stellar population mass estimates. The lensing results still depend on these, but they agree with the gas-dominated portion of the RAR, and merge smoothly into the star-dominated portion of the kinematic data when the same stellar pop models are used for both. To wit: the agreement is really good.
A flat rotation curve projects into the log(gobs)-log(gbar) plane as a line with slope 1/2. The data adhere closely to this slope, so I knew as soon as I saw the lensing RAR that the implied rotation curves remained flat indefinitely. How far, in radius, depends on galaxy mass, since for a point mass (a good approximation at radii beyond 100 kpc), gbar = GMbar/R2. We can split the lensing data into different mass bins, for which the RAR looks like
Figure 5 from Mistele et al. (2024a).The RAR implied by weak lensing for four baryonic mass bins. The dashed line has the slope a flat rotation curve has when projected into the acceleration plane. That different masses follow the same RAR implies the Baryonic Tully-Fisher relation.
Most dark matter models that I’ve seen or constructed myself predict a mass-dependent shift in the RAR, if they predict a RAR at all (many do not). We see no such shift. But the math is such that the flat rotation speed implied by the slope 1/2 RAR varies with mass in such a way that they only fall on the same RAR, as observed, if there is a Baryonic Tully-Fisher relation with slope 4. So I knew from examination of the above figure that the BTFR was sure to follow, but that’s because I’ve been working on these things for a long time. It isn’t necessarily obvious to everyone else, so it was worth explicitlyshowing.
Our result differs from the original of Brouwer et al. in two subtle but important ways. The first is that we use stellar population models that are the same as we use for the kinematic data. This self-consistency is important to the continuity of the data. We (especially Jim Schombert) took a deep dive into this, and the models used by Brouwer et al. are consistent with ours for late type (spiral) galaxies (LTGs). However, ours are somewhat heavier^ for early type galaxies (ETGs). That’s part of the reason that they find an offset in the RAR between morphological types and we do not.
Another important difference is the strictness of the isolation criterion. We are trying to ascertain the average gravitational potential of isolated galaxies, those with no big neighbors to compound the lensing signal. Brouwer et al. required that there be no galaxies more than a tenth of the luminosity of the primary within 3 Mpc. That seems reasonable, but we explored lots of variations on both aspects of that limit. It seems to be fine for LTGs, but insufficient for ETGs. That in itself is not surprising, as ETGs are known to be more strongly clustered than LTGs, so it is harder to find isolated examples.
To illustrate this, we show the deviation of the data from the kinematic RAR fit as a function of the isolation criterion:
Figure 4 from Mistele et al. (2024a). Top: the difference between the radial accelerations inferred from weak lensing and the RAR fitting function, measured in sigmas, as a function of how isolated the lenses are, quantified by Risol. We separately show the result for ETGs (red) and LTGs (blue) as well as for small (triangles with dashed lines) and large accelerations (diamonds with solid lines). LTGs are mostly unaffected by making the isolation criterion stricter. In contrast, ETGs do depend on Risol, but tend towards with increasing Risol. Middle and bottom: the accelerations behind these sigma values for Risol = 3 Mpc/h70 and Risol = 4 Mpc/h70.
The top panel shows that LTGs do not deviate from the RAR as we vary the radius of isolation. In contrast, ETGs deviate a lot for small Risol. This is what Brouwer et al. found, and it would be a problem for MOND if LTGs and ETGs genuinely formed different sequences: it would be as if they were both obeying their own version of a similar but distinct MOND-like force law rather than a single universal force law.
That said, the ETGs converge towards the same RAR as the LTGs as we make the isolation criterion more strict. The distinction between ETGs and LTGs that appears to be clear for the Risol = 3 Mpc/h70 used by Brouwer et al. (middle panel) goes away when Risol = 4 Mpc/h70 (bottom panel). The random errors grow because fewer galaxies+ meet the stricter criterion, but this seems a price well worth paying to be rid of the systematic variation seen in the top panel. This also dictates how far out we can trust the data, which show no clear deviation from the RAR until below the limit gbar = 10−14 m/s2.
Regardless of the underlying theory, the data paint a consistent picture. This can be summarized by threeempiricallaws of galactic rotation:
Rotation curves become approximately* flat at large radii and remain so indefinitely.
The amplitude of the flat rotation speed scales with the baryonic mass as Mbar ~ Vf4 (the BTFR).
The observed centripetal acceleration follows from that predicted by the baryons (the RAR).
These are the galactic analogs of Kepler’s Laws for planetary motion. There is no theory in these statements; their just a description of what the data do. That’s useful, as they provide an empirical touchstone that has to be satisfactorily explained by any theory for it to be considered viable. No dark matter-based theory currently does that.
^The difference is well within the expected variance for stellar population models. We can reproduce their numbers if we treat ETGs as if they were just red LTGs. I don’t know if that’s what they did, but it ain’t right.
+For the record, the isolated fraction of the entire sample is 16%: most galaxies have neighbors. As a function of mass, the isolation criterion leaves a fraction of 8%, 18%, 30%, and 42% of LTG lenses and 9%, 14%, and 22% of ETG lenses, respectively, in each mass bin. The fraction of isolated LTGs is generally higher than ETGs, as expected. There is also a trend for the isolation fraction to increase as mass decreases. In part this is real; more luminous galaxies are more clustered. It may also be that it is easier for objects that exceed 10% of the primary mass (really luminosity) to evade detection as the primaries get fainter so 10% of that is harder to reach.
*Some people take “flat” way too seriously in this context. While it is often true that rotation curves look pretty darn flat over an extended radial range, I say approximately flat because we never measure, and can never measure, exactly a slope of dV/dR = 0.000. As a practical matter, we have adopted a variation of < 5% from point to point as a working definition. The scatter in Tully-Fisher naturally goes up if one adopts a weaker criterion; what one gets for the scatter is all about data quality.
Last time, we discussed the remarkable result that gravitational lensing extends the original remarkable result of flat rotation curves much farther out, as far as the data credibly probe. This corroborates and extends the result of Brouwer et al. They did a thorough job, but one thing they did not consider was Tully-Fisher. If the circular speed inferred from gravitational lensing remains constant, does this flat velocity fall on the same Tully-Fisher relation that is seen in kinematic data?
We set out to answer this question. Along the way, we did three new things: 1. Dr. Mistele derived an improved method for doing the lensing analysis, extending the radial range over which the data were credible. 2. He explored the criteria by which galaxies were judged to be isolated, finding a morphological type dependence on how far out one had to exclude. 3. We reanalyzed the stellar masses of the KiDS sample to be consistent with those we used when analyzing the kinematic data of SPARC galaxies. The first two are connected, as how far out we can trust the data depends on how well we can define a clean sample of isolated galaxies. The third resolved an apparent offset between early type galaxies (ETGs, aka ellipticals) and late type galaxies (LTGs, aka spirals) seen by Brouwer et al. That appears to be an artifact of stellar population modeling, as I suspected when I first discussed their result. We don’t need to do any fitting of the mass-to-light ratio; the the apparent offset between types disappears when we use use the same population models for both kinematic and lensing data.
I could write a lot about each of these, but most of it is the stuff of technical details that would be dull to many people. If you’re into that sort of thing, go and read the long science paper which is where such details reside. Here I just want to describe the Tully-Fisher result. Spoiler alert: it is the same as that from kinematics.
First off, I’m talking strictly about the Baryonic Tully-Fisher relation: the scaling between baryonic mass and the flat rotation speed. To address this, we bin the lensing data by mass. The mass of each bin is well defined by the average of the many thousands of galaxies within the bin. By far the dominant uncertainty is the systematic in stellar mass caused by stellar population modeling. We went through this with a fine tooth comb, and I’m confident we have an internally self-consistent result. That doesn’t preclude it being wrong in an absolute sense – such is the nature of astronomy – but we can at least make a straight comparison between kinematic and lensing data using the same best-effort stellar mass estimates.
For the velocity, we estimate the average effective rotation curve for each mass bin from the lensing data. We also split the data into morphological types to look for differences. The statistics go down when one divvies up the data like this, so the uncertainties go up, but there are enough KiDS galaxies to define four mass bins. Here are their inferred rotation curves:
Figure 1 from Mistele et al. (2024). Circular velocities implied by weak lensing for four baryonic mass bins (most to least massive from the top row to the bottom) for the whole sample (left column), for LTGs (middle column), and for ETGs (right column). The lowest ETG mass bin is not shown because it contains too few lenses. Instead we show results for lenses with spectroscopic redshifts from GAMA, without splitting by mass or type due to the small sample size (gray and white symbols). For comparison, we also show results for KiDS without splitting by mass or type (small yellow symbols). Open symbols at small radii indicate where lenses are not yet effective point masses. Light-colored symbols (not-outlined) at large radii indicate data points that may still be reliable but where the isolation criterion is less certain. The error bars show the statistical errors. Horizontal lines and the corresponding shaded regions indicate the inferred Vflat values and uncertainties that we use for the BTFR. The extent of the horizontal lines indicates the radial range we consider when calculating Vflat.
Note that the average over all KiDS data shown in the lower right bin is the data shown in the press release image in the previous post, but the x-axis is logarithmic here. The GAMA data in that bin provide an important cross-check, as these galaxies have spectroscopic redshifts. They give the same answer as the larger KiDS sample, which relies on photometric redshifts. We need the larger sample to consider finer bins in mass, which is the rest of the plot.
Another thing to note here is that all the data in all the bins are consistent with remaining flat. There are some hints of a turn down at very large radii, particularly for LTGs in the second and third row, but these are not statistically significant, and only happen where the data start to become untrustworthy. Where exactly that happens is a judgement call.
Let’s take a closer look, with a comparison to radio data:
Figure 2 from Mistele et al. (2024).The circular velocities from weak lensing (circles) compared with those from gas kinematics (diamonds). The individual galaxies illustrated here have among the most extended 21 cm rotation curves in their mass bins; the lensing data continue to much larger radii still. The error bars show the statistical error, while the gray band indicates the systematic uncertainty in the radial accelerations. Symbol colors are as in Figure 1. Open symbols at large radii indicate where lenses are not sufficiently isolated. The solid green lines indicate the circular velocities of NFW halos and baryonic point masses appropriate for each mass bin. Green crosses indicate each NFW halo’s virial radius. The light green band adds a qualitative estimate of a two-halo term contribution to the NFW halo, which may become important at large radii in case our isolation criterion is imperfect there.
Again we see that the lensing data, averaged over many galaxies, extend much further out than the rotation curve of any one individual. The x-axis is again logarithmic, so the lensing data go way further out. They trace to 1 Mpc, which is crazy far beyond the observed ends of the most extended individual galaxies. A more conservative limit is the 300 kpc estimated by Brouwer et al. Surely we can go further than that, but how much further remains a judgement call.
What should we expect? The green lines show the rotation curve we’d expect for galaxy in an NFW halo with parameters specified by the stellar mass-halo mass relation of Kravtsov et al. (2018). Not all such relations agree well with kinematic data; this is the case that agrees most closely. We have intentionally cherry-picked the relation that makes LCDM look best. And it does look good up to a point, for example in the top two mass bins out to the virial radius of the halo (tick marks). Beyond that, not so much, and not at all for the two lower mass bins. The data extend far enough out that we should see the predicted decline. We do not.
The green line only represents the expected halo of the primary galaxy. When one gets so far out, one has to worry about all the other stuff out there. We’ve selected galaxies to be isolated, so there isn’t much that is luminous. But we can only exclude down to some sensitivity limit, there might be lots of tiny dwarf galaxies whose mass adds up and starts to affect the result. And of course there can be completely invisible dark matter. The green band attempts to account for this extra stuff in the so-called 2-halo term. This is hard to do, but we’ve made our best estimate based on the LCDM power spectrum. I’m sure the 2-halo term can be adjusted, but the shape is wrong. It will take some fine-tuning to get an effectively flat rotation curve out of the 1-halo+2 halo terms. They don’t naturally do that.
Something that is easy to do is define a flat value of the rotation speed. That’s just the average over the lensing data. We exclude the points at R < 50 kpc, as the assumption of a spherical mass that we make in the lensing analysis isn’t really valid at those comparatively small scales. We tried averaging over a bunch of different ranges, all of which gave pretty much the same answer. For illustration, we show two cases: a conservative one that only uses the data at R < 300 kpc, and another that goes out to 1 Mpc. Having measured Vflat over these ranges, we can plot Tully-Fisher:
Figure 3 from Mistele et al. (2024). The baryonic Tully–Fisher relation implied by weak lensing for the entire sample (yellow symbols, left column) and for ETGs and LTGs separately (red and blue symbols, right column). The Vflat values are weighted averages of the Vc values shown in Figure 1 for 50 kpc < R < 300 kpc (first row) and 50 kpc < R < 1000 kpc (second row). Vertical error bars represent a 0.1 dex systematic uncertainty on M*/L. For comparison, we also show the best fit to the kinematic data from Lelli et al. (2019; solid gray line) and the corresponding binned kinematic data (white diamonds).
Lo and behold, we find the same Baryonic Tully-Fisher relation from lensing data as we find with kinematics. This does not surprise me, but it didn’t have to be true. It shouldn’t be true in LCDM: if we can measure out to the virial radius, we should see some indication of a decline in velocity. We have and we don’t.
We also see no statistically significant separation between ETGs and LTGs. This is important, as a theory like MOND predicts that there should be no morphology dependence: only the baryonic mass matters. Brouwer et al. did see an indication of such a split, but it was small compared to the uncertainty in stellar population models. We don’t see it when we use our own stellar mass estimates. This is particularly true in the more conservative (300 kpc) case. There is a hint of a segregation when we average out to 1000 kpc, but the statistics say this isn’t significant. Since the lowest mass bin is most affected, I suspect this is a hint that the isolation criterion is failing first for the smallest galaxies. That makes sense, as the sensitivity limit on interlopers makes the lowest mass bin most susceptible to having its signal inappropriately boosted. It also makes sense that ETGs would be affected first, as ETGs are known to be more clustered than LTGs. It is really hard to define an isolated sample of ETGs, as discussed at length by Mistele et al.
That hasn’t prevented people from overlooking these basic facts in order to get to the apparent if statistically meaningless difference between ETGs and LTGs. Nevermind the successes! The slight offset between ETGs and LTGs falsify MOND! Seriously: other scientists have already made this argument to me while completely eliding the successes of MOND. It’s a case of refusing to see the forest for a tree that’s a little away from the others.
I think I said something about how this would happen when I first wrote about Brouwer et al‘s lensing result. Ah yes, here it is:
MOND predicted this behavior well in advance of the observation, so one would have to bend over backwards, rub one’s belly, and simultaneously punch oneself in the face to portray this as anything short of a fantastic success of MOND.
I say that because I’m sure people will line up to punch themselves in the face in exactly this fashion.
And so it has come to pass. Sometimes human behavior is as predictable as galaxy dynamics.
*There are many claims to explain limited portions of these results, but none are satisfactory. There is no LCDM model that matches the entire dynamic range of the radial acceleration relation. See, for example, Fig. 5 of Brouwer et al. (reproduced below), which shows the MICE and BAHAMAS simulations. Neither extend into the regime that is well-constrained by kinematic data; there is no reason to think they would successfully do so and good reason to think otherwise. MICE comes nowhere close to this regime and has no baryonic physics that would allow it do even address this question. BAHAMAS comes close but appears to turn away from the kinematic data before it gets there. We’ve built our own LCDM models; they don’t work either. We can make them come close, but only over a limited dynamic range, not over the full span of the data. It isn’t good enough to only explain a limited range of the data. One has to explain the full range, and the only theory that does that so far is MOND.
Fig. 5 from Brouwer et al. showing the radial acceleration relation inferred from the MICE (red band) and BAHAMAS (orange band) simulations. Not also that in our assessment of stellar masses, the lower acceleration points translate a bit to the right.
That rotation curves become flat at large radii is one of the most famous results in extragalactic astronomy. This had been established by Vera Rubin and her collaborators by the late 1970s. There were a few earlier anecdotal cases to this effect, but these seemed like mild curiosities until Rubin showed that the same thing was true over and over again for a hundred spiral galaxies. Flat rotation curves took on the air of a de facto natural law and precipitated the modern dark matter paradigm.
Optical and radio data
Rotation curves shouldn’t be flat. If what we saw was what we got, the rotation curve would reach a peak within the light distribution and decline further out. Perhaps an illustration is in order:
The rotation curve (data points, left) of NGC 6946 (right). The red line shows the expected rotation curve for the detected normal matter, which includes both the stars (yellow, from 2MASS) and atomic gas (blue, from THINGS). This provides a good description of the inner rotation curve but falls short further out. The excess observed rotation leads to the need for dark matter or MOND. Also noted is the extent of the rotation curve measured optically to the effective edge of the stars (Daigle et al. 2006; Epinat et al. 2008) and that measured with radio interferometric observations of the gas (Boomsma et al. 2008).
An obvious question is how far out rotation curves remain flat. In the rotation curves traced with optical observations by Rubin et al., the discrepancy was clear but modest – typically a factor of two in mass. It was possible to imagine that the mass-to-light ratios of stars increased with radius in a systematic way, bending the red line above to match the data out to the edge of the stars. This seemed unlikely, but neither did it seem like a huge ask.
Once one gets to the edge of the stellar distribution, most of the mass has been encompassed, and the rotation curve really should start to decline. Increasing the mass-to-light ratio of the stars ceases to be an option once we run out of stars*. Fortunately, the atomic gas typically extends to larger radii, so provides a tracer further out. Albert Bosma pursued this until there were again enough examples to establish that yes, flat rotation curves were the rule. They extended much further out, well beyond where the mass of the observed stars and gas could explain the data.
How much further out? It depends on the galaxy. A convenient metric is the scale length of the disk, which is a measure of the extent of the light distribution. Some galaxies are bigger than others. The peak of the contribution of the stars to the rotation curve occurs around 2.2 scale lengths. The rotation curve of NGC 6946 extends to about 7 scale lengths, far enough to make the discrepancy clear. For a long time, the record holder was NGC 2403, with a rotation curve that remains flat for 20 scale lengths.
Twenty scale lengths is a long way out. It is observations like this that demanded dark matter halos that are much larger than the galaxies they contain. They also posed a puzzle, since we were still nowhere near finding the edge of the mass distribution. Rotation curves seemed to persist in being flat indefinitely.
Postdoc Tobias Mistele worked out an elegant technique to improve the analysis of lensing data. His analysis corroborates the findings of Brouwer et al. It also provides the opportunity to push further out.
Weak gravitational lensing is a subtle effect – so subtle that one must coadd thousands of galaxies to get a signal. Beyond that, the limiting effect on the result is how isolated the galaxies are. Lensing is sensitive to all mass; if you go far enough out you start to run into other galaxies whose mass contributes to the signal. So one key is to identify isolated galaxies, and restrict the sample to them. KiDS is large enough to do this. Indeed, Mistele was able to show that while neighbors+ were a definite concern for elliptical galaxies, they were much less of a problem for spirals. Consequently, we can trace the implied rotation curve way far out.
How far out? In a new paper, Mistele shows that rotation curves continue way far out. Way way way far out. I mean, damn.
The average rotation curve of isolated galaxies (blue points) inferred from KiDS gravitational lensing data. This remains flat well beyond a million light-years with no end in sight. The width of the figure is the distance between the Milky Way and Andromeda. For comparison, the rotation curve of a single galaxy, UGC 6614, is shown in red. An image of the galaxy is shown to scale centered at the origin. UGC 6614 was selected for this illustration because it has a comparable rotation speed to the KiDS average and because it is one of the largest galaxies known: the red points are already a very extended rotation curve. Image credit: Mistele, Lelli, & McGaugh 2024.
Optical rotation curves typically extend to the edge of the stellar disk. That’s about 8 kpc in the example of NGC 6946 given above. Radio observations of the atomic gas of that galaxy extend to 17 kpc. That fits within the first two tick marks on the graph with the lensing rotation curve.
UGC 6614 is a massive galaxy with a very extended low surface brightness disk. Its rotation curve is traced by radio data to over 60 kpc. It is one of the most extended individual rotation curves known. The statistical lensing data push this out by a factor of ten, and more, with no end in sight. The flat rotation curves found by Rubin and Bosma and everyone else appear to persist indefinitely.
So what does it mean? First, flat rotation curves really are a law of nature, in the same sense of Kepler’s laws of planetary motion. Galaxies don’t obey those planetary rules, they have their own set of rules. This is what nature does.
In terms of dark matter halos, the extent of isolated galaxy rotation curves is surprisingly large. Just as we come to the edge of the stellar disk, then the gas disk, we should eventually hit the edge of the dark matter halo. In principle we can imagine this to be arbitrarily large, but in practice there are other galaxies in the universe so this cannot go one forever.
In the context of LCDM, we now have a pretty good idea of how extended halos should be from abundance matching. A galaxy of the mass of UGC 6614 should live in a halo with a virial radius of about 300 kpc or less. There is some uncertainty in this, of course, but we really should have hit the edge with the lensing data. There should be some sign of it, but we see none.
One complication is the so-called 2-halo term. In addition to the primary dark matter halo that hosts a galaxy, when you get very far out, you run into other halos. Isolated galaxies are selected to avoid this to the extent possible, but eventually there will be some extra mass that causes extra lensing signal that would cause an overestimate of the rotation speed. I’ll forgo a detailed discussion of this for now (see Mistele et al. if you’re eager), but the bottom line is that it would require some unnatural fine-tuning for the 1+2 halo terms to add up to such flat rotation curves. There ought to be a perceptible feature in the transition from the primary halo to the surrounding environment. We don’t see that.
In the context of MOND, a flat rotation curve that persists indefinitely is completely natural. That’s what an isolated galaxy should do. Even in MOND there should be an environmental effect: the mass of everything else in the universe should impose an external field effect that eventually limits the extent of the rotation curve. How this transition happens depends on the density of other galaxies; by selecting isolated galaxies this effect is put off as much as possible. Hopefully it will be detected as the data improve from projects like Euclid.
The primary prediction of MOND is an indefinitely extended rotation curve; the external field effect is a subtle detail. Yet again, that is what we see: MOND gets it right without really trying, and in a way that makes little sense in terms of dark matter. Sometimes I wish MOND had never been invented so we could claim to have discovered something profoundly new, or at least discuss the empirical result without concern that the data would get confused with the theory. MOND predictions keep being corroborated, yet the community persists in ignoring its implications, even in terms of dark matter. It’s gotta be telling us something.
We have a press release about this result, so perhaps you will see it kicking around your news feed.
*We could, of course, invoke dark stars, but that’s just an invisible horse of a different color.
+There is a well known correlation between morphology and density such that elliptical galaxies tend to live in the densest environments. This means that they are more likely to have neighbors that interfere with the lensing measurement, so finding that identifying isolated ellipticals with a clean lensing signal is more challenging that finding isolated spirals comes as no surprise. Isolated ellipticals do exist so it is possible, but one has to be very restrictive with the sample.
This is an update to a post from a few years ago, which itself was an update to a webpage I wrote in 2008, with many updates in between. At that time, the goalposts for detecting WIMPs had already moved repeatedly. I felt some need then to write down a brief synopsis of the history of a beloved hypothesis (including by myself) that had obviously failed as the goalposts were in motion again. That was sixteen years ago.
It is important to remember where we started from, which is now ancient history lost in the myths of time to most who are now working in the field. Indeed, when I search for mention of the WIMP miracle, the theoretical argument that launched a thousand underground detection experiments, little comes up: this essential element of the field has been memory-holed after its failure. I suppose that’s to be expected, as the same thing happened with the decay of the B0 meson: once heralded as the “golden test” for supersymmetry, it simply stopped getting mentioned after it didn’t work out.
The original expectation for WIMPs was a particle of mass around 100 GeV/c2 with an interaction cross-section of about 10-39 cm2. While I remember this, it is getting rare to find this statement, so let me quote a particle physicist:
“The most appealing possibility – a weak scale dark matter particle interacting with matter via Z-boson exchange – leads to the cross section of order 10-39 cm2“
To translate a little bit, the Z-boson is a carrier of the weak nuclear force (as photons are for electromagnetism), so this envisions an otherwise normal interaction that involves a new particle, the WIMP. The weak force is, well, weak, so the interaction probability is small, as quantified by the tiny cross section of 10-39 cm2. That makes such interactions rare, but particle physicists are talented at detecting such phenomena. It helps to have a lot of target material in your detector in a place that is well-shielded from background interference, hence all the giant underground WIMP experiments. Consequently, to continue the quote above,
“the cross section of order 10-39 cm2 … was excluded back in the 80s by the first round of dark matter experiments.”
And so the goalposts were set in motion. There were many steps along this path, so I’ll highlight only one, circa 2008. To complete the quote from Resonaances,
“There exists another natural possibility for WIMP dark matter: a particle interacting via Higgs boson exchange. This would lead to the cross section in the 10-42 – 10-46 cm2 ballpark (depending on the Higgs mass and on the coupling of dark matter to the Higgs).”
So the interaction via the Z-boson had been excluded, but one can have other interactions, this one via the Higgs (which had not quite yet been detected: discovery was in 2012; the Resonaances quote is from 2011. Since then, the Higgs might be said to be “too normal” to make room for any of this.) The possibility of Higgs exchange leads to the blue-green predicted region of Trotta et al. (2008) in the exclusion diagram shown below. If one looks for such plots in the literature, one finds a natural tendency for their upper limits to migrate downwards along with the limits they portray. I thought it might be instructive to update the plot to show the full range of progress:
The interaction cross section as a function of WIMP mass. The original expectation of 10-39 cm2 is at top. Gray areas are regions that were experimentally excluded by 2008 (before the blue-green prediction) and by 2022, which is the most recent update as of this writing. The most sensitive limit is 10-47 cm2, eight orders of magnitude below the original prediction.
I call out the 2008 threshold because we had a conference here at CWRU in 2009 (while I was at the University of Maryland) at which the Trotta et al. prediction was presented. I had already become skeptical of the moving goalposts, so I wondered how much of the probability density was in the tail to low cross-section. A low-likelihood tail seems a lot more probable once the head is lopped off! I made this point at the time, and asked how important the tail was. The answer was about 2% or the probability. The speaker went on to express the usual overconfidence that WIMPs would be detected in the more likely region (marked by an X in the blue region with the handy arrow pointing to it).
The experimentalists have done a fabulous job in increasing the sensitivity of their experiments so that they can see to ever lower interaction cross section. Had WIMPs existed as predicted initially, or subsequently, they would have been detected by now. These experiments have succeeded in failing quite brilliantly. I had long before shown that the astronomical data did not add up for any flavor of dark matter. Maybe WIMPs don’t live in this universe?
While we’d be happy to detect dark matter anywhere in parameter space, the WIMP does have sweet spots: first 10-39 cm2 then 10-44 cm2. Now that those are gone, what’s next? From the particle physics perspective, I’ve heard it said that the next logical expectation for the cross-section is around 10-48 cm2. This apparently follows from “two-loop corrections.” I have only a vague idea of what that means, but in my practical experience it translates to “a difficult-to-compute effect so exotic that it likely has no bearing on reality, except maybe in the sixth place of decimals.”
More generally, this continual moving of the cross section goalpost is what I meant back in 2008 by the scientific version of the express elevator to hell. It just keeps going down, and can do so forever. I keep warning my colleagues about these things, and they keep not heeding the warnings. Being a scientific Cassandra is getting old.
The problem with pushing detection limits to still lower cross-sections like 10-48 cm2 is that the universe is indeed full of weakly interacting particles with at least a little bit of mass: neutrinos. These are not as massive as WIMPs, and should not be confused with them: neutrinos are Standard Model particles that are known to exist and to have a very small mass (< 1 eV) while WIMPs are expected to be hundreds of GeV and require entirely new physics beyond the Standard Model. I shouldn’t need to say this, but WIMPs and neutrinos are very different beasts. However, they do both have mass and interact weakly, so I’ve noticed that some of the more rabid advocates of dark matter mix these two in order to claim that we know weakly interacting dark matter exists. That much is technically true, but in technical parlance it is also some bold bullshit. Hmmm, actually, I think it is worse than ordinary bullshit. It is willful scientific disinformation that intentionally sews confusion by conflating the unconfirmed existence of WIMPs with the known existence of neutrinos in order to lend an air of certainty to a failed hypothesis.
WIMP experimental limits (via Hamdan 2021) with the expected neutrino background in orange. Once this sensitivity is reached, any WIMP signal becomes obscured by the neutrino background.
Meanwhile, experimental progress proceeds apace. The coming generation of WIMP detectors should be sensitive to the solar and atmospheric neutrino background. That is astrophysically interesting, as it can probe nuclear reactions in the sun and, in principle, those in every supernova that have ever exploded. This has bugger all to do with dark matter. However, since that’s what people are looking for, what they built these detectors to find, and they’re completely convinced dark matter exists, and a Nobel prize awaits whoever detects it first, I expect that the first neutrino detections will be misinterpreted as WIMP detections. There will be much arguing between groups, claims and counterclaims, and after a few years it will be recognized that these coming detections are neutrinos not WIMPs. First there will probably be many over-hyped claims that mislead the public into thinking dark matter has been detected.
Aurora over my house in Cleveland Heights, Ohio, USA, the evening of Friday, May 10.
The sun is nearing the peak of its eleven year sunspot cycle. That means lots of sunspots and associated activity. Solar prominences, visible to the naked eye during the eclipse, are bands of plasma entrained in the magnetic field connecting pairs of sunspots. Once in a while, these break out in solar flares. Lately, the sun has produced a series of X-class flares (the largest type) with associated coronal mass ejections (CMEs) that send huge blobs of plasma hurtling out into space.
Space is big, so CMEs usually don’t impact Earth. But sometimes they do, and they have a number of effects. The plasma impinges on Earth’s magnetic field, which funnels charged particles towards the poles. When these high-speed particles hit atoms and molecules high up in the atmosphere, they transfer energy that excites quantum states. The relaxation of these states leads to the emission of the light we perceive as aurora.
I heard there was a possibility of aurora being visible at our latitude Friday night. I didn’t expect much – the northern lights are notoriously fickle, and usually only appear much further to the north – hence the name. It has to be fully dark to see them at all, so I walked out at about 10 PM and looked up. Not much. Maybe some thin clouds. Only that’s a strangely shaped cloud. And, as my eyes adjusted, one shone red, the other green. The northern lights had come to me.
Aurora wax and wane with the plasma breeze; this is the view a few minutes later.
NOAA has a good explainer. The greens and reds are from excited atomic oxygen, at different altitudes owing to the different lifetimes of the associated quantum states. Atoms can be de-excited as well as excited by collisions, so we only get emission lines when the density* of surrounding atoms is low enough that light gets emitted before collisional de-excitation. That means the green comes from oxygen over 100 km up; the red comes from even higher, more like 300 km. There is barely any atmosphere at all at these altitudes.
Similar views were reported all over the planet. Aurora are usually restricted to very northerly latitudes, hence the moniker northern lights. A big CME floods the Earth’s magnetic field (and can distort it), leading to the appearance of aurora at lower latitudes. I had only seen them once before, in Ann Arbor in 1989, and then only as a ghostly grey wisp on the northern horizon. It takes a big event to produce colorful aurora overhead in Ohio.
The blues and purples are from molecular nitrogen, the predominant component of our atmosphere.
It wasn’t just Ohio! Bright aurora were reported at all longitudes – I’ve seen lots of great pictures from Europe – to remarkably southerly latitudes, extending even to Florida and the Caribbean. This southerly reach is remarkable, but not uniform. One could see aurora overhead at the Apache Point Observatory in New Mexico, but they only appeared on the northern horizon at Kitt Peak in Arizona. Even that is an incredibly rare event!
Flares and CMEs have effects besides auroras – so much so that there is an entire field of space weather. The weather in space is particularly relevant to satellite operations, as big flares can blind or even damage sensors on satellites. It also affects their orbits. The radiation is also a hazard to would-be space travelers: you don’t want to get caught in a CME during a multi-month trip to Mars.
*The atomic lines we see in aurora are from neutral oxygen, [O I] in the parlance of spectroscopy. This is strange to me, as I’ve worked on nebular spectra, where prominent emission lines are due to singly and doubly ionized oxygen – [O II] and [O III] in the parlance of spectroscopy. These lines thrive only in the extremely low density, practical vacuum of space (densities of tens or maybe hundreds of atoms per cubic centimeter), and were unknown in the laboratory when first observed astronomically. For a time, it was thought that, like helium in the sun, they represented a new element, nebulium – the stuff of which nebula were made.
I have been spending a lot of time lately writing up a formal paper on high redshift galaxies, so haven’t had much time to write here. The paper is a lot more involved than I told you so, but yeah, I did. Repeatedly. I do have a start on a post on self-interacting dark matter that I hope eventually to get back to. Today, I want to give a quick note about the MHONGOOSE survey. But first, a non-commercial interruption.
Triton Station joins Rogue Scholar
In internet news, Triton Station has joined Rogue Scholar. The blog itself hasn’t moved; Rogue Scholar is a community of science blogs. It provides some important capabilities, including full-text search, long-term archiving, DOIs, and metadata. The DOIs (Digital Object Identifiers) were of particular interest to me, as they have become the standard for identifying unique articles in regular academic journals now that these have mostly (entirely?) gone on-line. I had not envisioned ever citing this blog in a refereed journal, but a DOI makes it possible to do so. Any scientists who find a post useful are welcome to make use of this feature. I’m inclined to follow the example of JCAP and make the format volume, page be yearmonth, date (YYMM, DD), which comes out to Triton Station (2022), 2201, 03 in the standard astronomy journal format. I do not anticipate continuing to publish in the twenty second century, so no need for YYYYMM, Y2K experience notwithstanding.
For everyone interested in science, Rogue Scholar is a great place to find new blogs.
MHONGOOSE
In science news, the MHONGOOSE collaboration has released its big survey summary paper. Many survey science papers are in the pipeline. Congratulations to all involved, especially PI Erwin de Blok.
I was involved in the early phases of the MHONGOOSE project, helping to select the sample of target galaxies (it is really important to cover the full dynamic range of galaxy properties, dwarf to giant) and define the aspirational target sensitivity. HI observations often taper off below a column density of 1020 hydrogen atoms per cm2 (about 1 solar mass per square parsec). With work, one can get down to a few times 1019 cm-2. We want to go much deeper to see how much farther out the atomic gas extends. It was already known to go further out than the stars, but how far? Is there a hard edge, or just a continuous fall off?
We also hope to detect new dwarf galaxies that are low surface brightness in HI. There could, in theory, be zillions of such things lurking in all the dark matter subhalos that are predicted to exist around big galaxies. Irrespective of theory, are there HI gas-rich galaxies that are entirely devoid of stars? Do such things exist? People have been looking for them a long time, and there are now many examples of galaxies that are well over 95% gas, but there always seem to be at least a few stars associated with them. Is this always true? If we have cases that are 98, 99% gas, why not 100%? Do galaxies with gas always manage to turn at least a little of it into stars? They do have a Hubble time to work on it, so it is also a question why there is so much gas still around in these cases.
And… a lot of other things, but I don’t want to be here all day. So just a few quick highlights from the main survey paper. First, the obligatory sensitivity diagram. This shows how deep the survey reaches (lower column density) as a function of resolution (beam size). You want to see deeply and you want to resolve what you see, so ideally both of these numbers would be small. MHONGOOSE undercuts existing surveys, and is unlikely to be bettered until the full SKA comes on-line, which is still a long way off.
Sensitivity versus resolution in HI surveys.
And here are a couple of individual galaxy observations:
Optical images and the HI moment zero, one, and two maps. The moment zero map of the intensity of 21 cm radiation tells us where the atomic gas is, and how much of it there is. The moment one map is the velocity field from which we can construct a rotation curve. The second moment measures the velocity dispersion of the gas.
These are beautiful data. The spiral arms appear in the HI as well as in starlight, and continue in HI to larger radii. The outer edge of the HI disk is pretty hard; there doesn’t seem to be a lot of extra gas at low column densities extending indefinitely into the great beyond. I’m particular struck by the velocity dispersion of NGC 1566 tracking the spiral structure: this means the spiral arms have mass, and any stirring caused by star formation is localized to the spirals where much of the star formation goes on. That’s natural, but the surroundings seem relatively unperturbed: feedback is happening locally, but not globally. The velocity field of NGC 5068 has a big twist in the zero velocity contour (the thick line dividing the red receding side from the blue approaching side); this is a signature of non-circular motion, probably caused in this case by the visible bar. These are two-dimensional examples of Renzo’s rule (Sancisi’s Law), in which features in the visible mass distribution correspond to features in the kinematics.
I’ll end with a quick peak at the environments around some MHONGOOSE target galaxies:
Fields where additional galaxies (in blue) are present around the central target.
This is nifty on many levels. First, some (presumptively satellite) dwarf galaxies are detected. That in itself is a treat to me: once upon a time, Renzo Sancisi asked me to smooth the bejeepers out of the LSB galaxy data cubes to look for satellites. After much work, we found nada. Nothing. Zilch. It turns out that LSB galaxies are among the most isolated galaxy types in the universe. So that we detect some things here is gratifying, even in targets that are not LSBs.
Second, there are not a lot of new detections. The halos of big galaxies are not swimming in heretofore unseen swarms of low column density gas clouds. There can always be more at sensitivities yet unreached, but the data sure don’t encourage that perspective. MHONGOOSE is sensitive to very low mass gas clouds. The exact limit is distance-dependent, but a million solar masses of atomic gas should be readily visible. That’s a tiny amount by extragalactic standards, about one globular cluster’s worth of material. There’s just not a lot there.
Disappointing as the absence of zillions of new detections may be discovery-wise, it does teach us some important lessons. Empirically, galaxies look like island universes in gas as well as stars. There may be a few outlying galaxies, but they are not embedded in an obvious cosmic network of ephemeral cold gas. Nor are there thousands of unseen satellites/subhalos suddenly becoming visible – at least not in atomic gas. Theorists can of course imagine other things, but we observers can only measure one thing at a time, as instrumentation and telescope availability allows. This is a big step forward.
We will return to our usual programming shortly. But first, a few words on the eclipse experiencelast Monday. It. Was. Awesome.
That’s a few words, so Mission Accomplished.
That’s really all I had planned to say. However, I find I am still giddy from this momentous event, so will share my experience of the day, such as words can humbly convey.
Prelude
We had good weather here in Cleveland, with the temperature reaching the upper 60s Fahrenheit. It was cloudy in the morning and many people were concerned about the prospects to see the eclipse. I was not. Having spent a lifetime as an observer with many nights at mountaintop observatories wishing for clouds to go away, and obsessively refreshing satellite maps to try to judge when they might do so, I knew there was no point in fretting about it at this juncture. Either it would clear, or clear not.
To indulge in a little superstition, I was more concerned that the date of the eclipse coincided with the home opener for the Cleveland Guardians. Opening day is always a happy, celebratory time, with people jamming the ballpark to enjoy the return of baseball and mark the coming halcyon days of summer. The weather here on opening day inevitably seems to repay that optimism with cold, clouds, and various forms of precipitation. Opening day weather is always miserable. I cannot think of a single home opener in the past quarter century for which I wanted to be in the stadium, and quite a few for which I was grateful not to have been. In local experience, a few inches or more of snow is as likely than a nice day.
A typical April in Cleveland. This was April 21, 2021.
This is a recurring theme.
April 7, 2017, seven years and a day before the eclipse.
I could go on – I have lots of epic snow pictures from Aprils past. We got a full foot of snow one Easter. But April also brings daffodils, so not all hope is extinguished.
Given this sterling record of opaque skies and outright blizzards, many people traveled to Texas to see the eclipse. The climate statistics for clear skies there are better there than here, and indeed, better than most other places along the path of totality, making it the destination of choice for serious eclipse chasers. But weather is notoriously fickle: climate is what you expect; weather is what you get. The day of the eclipse it was cloudy in Texas. You make your bets and you roll the dice.
The Build Up
Here in Cleveland, the early clouds had cleared to a brilliant blue by noon. At this time there was a special lunch followed by a panel discussion that I served on, together with Prof. Paul Iverson, an expert on ancient culture and the Antikythera Mechanism, a remarkably advanced analog computer for accurately predicting planetary motions including eclipses, Prof. Aviva Rothman, an historian of the Scientific Revolution and Kepler in particular, and Prof. Chris Zorman, an engineer involved in conducting radio experiments on the reaction of the ionosphere to the passage of the moon’s shadow. I opened by describing what was happening physically, and closed with a description of what to expect to see. There were good questions form the audience; perhaps my favorite being if we could extend the eclipse experience by chasing it in a plane. Yes, but the shadow sweeps past at over a thousand miles per hour, so to keep up you’d have to go supersonic, so totality could only be extended for however long your fuel could last. Attendance was great but limited* to the largest ballroom in the Tinkham Veale University Center; I’m told it filled within minutes of registration being opened. Duh – I had been trying to impress the enormity of this event on the powers that be on campus for years without success. Most people seem incapable of thinking that far ahead. Still, they did eventually get on it, and did a good job organizing everything, albeit at a predictably desperate clip for the last few weeks. The campus event turned out well, if for a rather smaller audience than demand might have had it.
People gather on Freiberger Field to witness the eclipse. The little picket fence for the VIPs can be seen, with the Tinkham Veale University Center behind.
By design, the panel ended right as the partial eclipse started. Freiberger Field next door to Tinkham Veale had been designated for eclipse viewing, complete with portapotties and, bemusingly, a little fenced-off area$ for us VIPs who had been at the lunch. I preferred to watch it with my colleagues and students who had set up a small telescope with a projection screen nearby.
Students with one of the department’s portable telescopes. The partial eclipse has progressed far enough to begin to give things a sepia tone. Note the high-tech cardboard aperture reducer that Dr. Bill Janesh rigged for persistent observation of the sun, which can overheat optical elements.
Many of our students are wearing the t-shirt I designed to commemorate the occasion.
Commemorative eclipse t-shirt. The location and time is given in words and again as latitude, longitude, and Julian date. Trivia points for those who can identify the inspiration of the font in the middle lines. (Not the Case Astronomy part – I did that free hand.)
First, though, I walked back to my office to drop off the sports coat I had donned for the panel, as it had become downright warm in the sun. It would take a bit over an hour to reach totality, so I had plenty of time to walk across campus and back. It also gave me something to do besides mill about in anticipation: I looked up occasionally on the walk over, checking the progress of the moon through eclipse glasses; it was casually devouring the sun one bite at a time as I casually crossed campus.
I grabbed a bundle of eclipse glasses from my office. There were plenty at Freiberger, but we had started stocking up on them before that had been arranged, and what else were we going to use them for? As soon as I stepped outside, I encountered a couple of students who needed them. Immediately after that, a visitor from Pittsburgh who was originally form Armenia asked where he could get paper supplies to make a pinhole camera. I handed him a pair of eclipse glasses and pointed him towards the nearby FedEx, with directions on to the campus bookstore should that prove helpful. By this time, I could tell that the light was starting to dim.
On the way back, the weather worsened. Some murk started to roll in, and for a bit it looked like it might become completely opaque. But the clouds remained limited to cirrus clouds that amounted to only a thin veil, and which provided a rainbow halo completely encircling the sun. A few commercial jetliners left long, fat contrails+ whose shadows could be seen cast on the cirrus at lower elevation.
Rainbow halo around the sun in cirrus clouds. A few contrails cast shadows on the clouds. The sun is more than half obscured by the moon at this point, but my phone’s camera can only see that it is still really bright.
At this point, it started to cool off. One could viscerally feel the effect of the shade cast by the moon. The temperature dropped 7oF, then rebounded some afterwards. I did not regret having abandoned my jacket – it was still a pleasant spring day – but probably would have put it back on for a bit if I still had it with me. I could hear some mild grumbles in the crowd that they wanted one. You could definitely feel the difference as a mild breeze picked up.
The partial eclipse as totality nears, as seen projected by the small telescope seen above.
Partial Eclipses Past
Partial eclipses are just that: partial. In the 2014 my younger daughter and I went to the roof of a parking structure to watch one that reached about 30% coverage. And indeed, it looked like a clean bite had been taken out of the sun. But if you didn’t know when to look (and have appropriate eye protection), you wouldn’t notice. The sun was still plenty bright, and there was no perceptible change in the environment. Indeed, we noticed that people didn’t notice. We had come prepared with welder’s glass, and offered a glimpse to passers by. No one took us up on it. Indeed, every single one gave us a wide berth as obviously crazy people.
On 21 August 2017, there was a major eclipse for which the path of totality passed several hundred miles to our south. We saw about 80% coverage in Cleveland on that occasion. I figured that people who were serious about it would have left town to see it. However, there had been a lot of hype about this eclipse, so I expected that, come the day of, a lot of folks would be calling up us astronomers asking what’s up.
In anticipation, we (the CWRU Department of Astronomy) had stocked up on eclipse glasses. The day of, we sallied forth to entertain those who found a sudden interest in astronomical events. This included many people from both on and off campus, but especially new freshmen – it happened during Discovery Week, which is freshmen orientation here. On that occasion, I had difficult persuading the people running orientation that they needed to account for the eclipse in their scheduling. They were having none of it: they had a very busy schedule, it was important the the freshmen attend all orientation events, and if we wanted to host an astronomical event, we should schedule it sometime else. Eventually I had to appeal to the provost, pointing out that students would have heard of the eclipse, so were likely to walk out of whatever orientation event was running at the time, so it would be better to embrace the event than pretend it wasn’t happening. So we did.
Dr. Paul Harding (left) and Prof. Chris Mihos (right) help the gathered crowd witness the partial eclipse of 2017. Not pictured: Charley Knox, who had opened the 9″ refracting telescope bequeathed to us by Warner & Swasey to visitors. Perched atop a campus building, a line to use it promptly formeddown five flights of stairs and out onto the quad.
The weather in August 2017 was clear and hot. While my colleagues operated the telescopes, I ran around handing out eclipse glasses and playing carnival barker. This included announcing the time of maximum coverage, which this time was enough to cause a perceptible dimming. It was weird – it wasn’t like a cloud blocking the sun; indeed, the sky was completely clear. Everything just seemed… tuned down. Nature stilled. The light gave everything a sepia tone; sort of a golden hour from above rather than from the horizon.
At this point, anything with a small hole acted as a pinhole camera to project an image of the partial eclipse. A colander works quite well for this. Heck, even the leaves of the trees got into it.
Images of the 2017 partial eclipse cast by the leaves of the trees acting as pinhole cameras.
We were lucky with the weather. We were hot and dehydrated, but we got through it all. After we had packed up but before I could even walk back to the department, storm clouds gathered and the heavens opened with torrential rain: a classic summer thunderstorm. I was happy to wait it out in Tinkham Veale, quite exhausted. I realized then that we couldn’t pull off a similar event for a full eclipse, which would have exponentially more interest. The partial eclipse was all we could manage, and the department is half the size now that it was then#.
Totality Approaches
The light level at the maximum of the 2017 partial eclipse returns us to the 2024 eclipse. We had reached a point that was uncharted territory for me. With some help from a filter, the phone camera could now kinda sorta make out that something was happening.
As totality neared, even a phone camera could discern that the sun was no longer round.
The light obtained the same weird, bright-yet-dim sepia tone I recalled from 2017. It continued to darken, and began to look like sunset on the horizon, only all 360o around. Then the umbral shadow swept in, the cirrus clouds above marking its path. We were in a giant dark shadow, with daylight perceptible at a distance all around us. But for us, it got dark.
I watched the last limb of the sun disappear behind the moon through the eclipse shades, the thin horns of light contracting rapidly. It broke into segments, atmospheric seeing warring with lunar topography. When I could see no more, I took them off just in time to see the diamond ring effect just as the sun disappeared entirely. The total eclipse had arrived.
Totality
I’m pretty jaded. I’ve worked at major observatories in Arizona and New Mexico, in the Chilean Andes, on La Palma in the Canary islands. I’ve traveled the world debating deep matters of cosmology and philosophy with renowned scientists from all over, each brilliant in their own way, some the most admirable people you could hope to meet; others, not so much. I’ve seen partial lunar eclipses, total lunar eclipses, the 2004 and 2012 transits^ of Venus, and partial solar eclipses. At this point, I’m very hard to impress. But I had never a total solar eclipse.
I was gobsmacked.
Totality in Cleveland lasted for 3 minutes and 49 seconds. Venus is visible below the sun/moon. Jupiter was also visible on the opposite side from the sun; some people spotted Saturn near the horizon. But the true star of the show was the solar corona.
Words really can’t do justice to a full eclipse. Totality is just stunning. The disk of the moon completely covers the body of the sun, and lurks there for a few minutes. This natural occultation experiment reveals the solar corona. Always there but never otherwise seen, the corona shimmers like a phantasm of white silk around the dark circle of the moon; it is so mesmerizing you’d think it overdone if it were a special effect. I was enthused to make out the small, pink glow of a solar prominence near the bottom of the disk from our perspective: a band of plasma entrained in the magnetic field of sunspots like cosmic iron filings that glow in the pinkish Balmer line of hydrogen. Venus and Jupiter were easily visible; some folks saw Saturn as well. Saturn was over towards the horizon; I didn’t look that far aside for 3 minutes and 49 seconds. Pictures really don’t do it justice. They seem ill-suited to illustrate the extend of the corona without overexposing the prominences.
You literally had to see it to appreciate it.
Fade Out
People cheered as totality started, and again as it came to an end. Daylight returned, albeit the weird dim sepia light of the partial eclipse. What had seemed stunning in its own right a few short minutes before now seemed almost mundane. We talked and milled about and shared a general sense of well-being stemming from bearing common witness to a remarkable event that is both phenomenally rare and stunningly beautiful, a shared feeling that reminds me of Melville’s words:
Oh! my dear fellow beings, why should we longer cherish any social acerbities, or know the slightest ill-humor or envy!
Melville, in Moby Dick
As the light trended back to normal, we decided to pay a visit to the rooftop telescope, where Bill and Charley had watched the eclipse. We were joined by roving groups of astronomy students and alumni, and found Charley in the dome of the 9″ with a projector in place, the brass of the eyepiece warm to the touch.
Charley Knox in his element. The moon is receding, but still blocking a portion of the sun.
There was a communal feeling of satisfaction and general well-being that I can describe no better than totality itself. Classes had been cancelled for the day, and rightly so – nothing could be more educational, nothing could match this experience, and there was no going back inside afterwards.
As the moon passed away, one could see sunspots in the projection from the 9″. That was true during the 2017 partial eclipse as well; I share an image from that time as it shows the sunspots most clearly:
The sun with sunspots, regions of magnetic disturbance that appear dark against the surface of the sun by virtue of being slightly less hot than the surrounding surface. The moon recedes at lower right.
For perspective, recall the spectacular coincidences that make eclipse observations possible. The sun is vastly larger than the moon, but also farther away. Yet they appear very nearly the same angular size in the sky, with the greater distance to the sun relative to the moon almost exactly right to balance the greater size of the sun relative to the moon. It didn’t have to be that way. Indeed, it seems phenomenally unlikely that it should be so. That it is so makes total eclipses extraordinarily rare, as the point of the conical shadow of the moon only just reaches the surface of the earth, so only a small spot is in eclipse at a given time. Indeed, the slight eccentricity of the moon’s orbit means that sometimes the point of the umbra doesn’t even reach the surface, and we get an annular eclipse in which the sun is mostly but not quite fully covered. We were lucky to get nearly four minutes of totality, but the small size of the shadow cast by the moon on the Earth by itself guarantees that eclipses are rare. Add in that the moon’s orbit is tipped about 5 degrees to the plane of the ecliptic (the orbit of the Earth around the sun) and that none of the relevant periods (day, lunar month, year) are integer multiples of one another means that the perfect alignment (syzygy) required for an eclipse rarely repeats over the same spot. But it does happen, and we humans noticed it – by the time of the ancient Babylonians, the lengthy periods on which eclipses were likely to repeat were known – they lacked sufficiently accurate data to predict exactly when and where an eclipse would occur, but they knew when it was eclipse season – a sort of astronomical weather forecast: scattered clouds with a chance of eclipses. These events made a big impression on us; it would have taken careful observations conveyed over many generations to work this out.
Eclipses on planet Earth are quite remarkable. We could have had a bigger moon or a smaller moon or lots of moons or no moon at all. But we got a moon that is exactly the right size at exactly the right distance to almost exactly cover the disk of the sun, and reveal to the human eye the corona that is otherwise lost in the glare of the solar photosphere. This coincidence in space is remarkable enough, but it is also a coincidence in time. The moon helps raise the tides on the Earth, and the tides pull back against the moon. The net effect is a slow transfer of angular momentum from the spin of the Earth to the orbit of the moon. As a consequence, the moon is slowly getting farther away (a few cm/year) and the length of the day is gradually getting longer, having been about 22 hours a mere 600 million years ago, around the time of the Cambrian explosion when multicellular life proliferated. Consequently, the moon would have been a bit closer and appeared somewhat larger on the sky for early land animals; dinosaurs would have seen somewhat more frequent eclipses of longer duration, but would have had a worse view of the corona and prominences, as the larger moon would have blocked more of the emission from near the surface of the sun.
The coincidences that make our current eclipse experience are rather special in both time and space. Make of that what you will.
*There had been so many preparatory emails that the precise location of the discussion panel was lost in the hectic babble. I remembered it was in Tinkham Veale, which is big, but not so big that I was worried about finding the right room. That would surely be easier than finding it in the enormous email thread. When I arrived, I figured the most likely location was the ballroom on the second floor, and indeed, I found the stairs blocked by a sign 2ND FLOOR CLOSED FOR PRIVATE EVENT. Bypassing this, I was greeted by enhanced campus security and a person who asked my name. Scrolling a handheld device, she got that concerned look officious people get when you’re not on the list. She politely checked the spelling of my name, checked again, then apologized that I wasn’t on the list. As this was going on, I realized this must be a list for people who registered to hear the panel, so I said “I’m the astronomer ON the panel.” Her eyes got big. “Oh!” she said. “Come right in…”
So, the moral of that story is that you can always talk your way into an exclusive event by claiming to be an astronomer – provided, of course, that it is a very specialized subset of exclusive events about astronomy.
$I found it bemusing because it was just a tiny picket fence set up in the midst of a much larger field. There was nothing special or meritorious about the location, so it was just exclusionary, which is a thing I’m generally against.
+Contrails like this are usually a bad sign for observational astronomy, being a harbinger of bad seeing as well as high humidity. In this case, it was just part of the show – and a very small part at that. Mostly I pitied the fools who had paid to confine themselves inside a metal tube at 10 km altitude while the most amazing of celestial events was going on.
#In 2017, the academic staff of the Department of Astronomy consisted of five faculty and one research scientist. By 2019 attrition had reduced us to three faculty. That no hires have been made since then is a long story of administrative incompetence and malfeasance.
^I almost missed the 2004 transit, which was conveniently observable in Europe but which we nearly over by the time the sun rose in the U.S. Not only did one have to get up at the literal crack of daen, but that meant the sun was on the eastern horizon. The only way I could find to witness it was to hold a pair of binoculars at a window in our attic and project the image onto the wall.
The 2012 transit was more friendly to observers in North America, occurring mid-day. I set up a small telescope in front of my house; the neighbors took turns holding the projection screen for all to see. Many stayed for hours to follow the gradual progress of Venus against the face of the sun.
Venus appears as the small, dark circle at the top left of the disk of the sun during its 2012 transit.
Perhaps the most compelling astronomical phenomenon accessible to a naked-eye observer is a total eclipse of the sun. These rare events have always fascinated us, and often terrified us. It is abnormal and disturbing for the sun to be blotted from the sky!
A solar eclipse will occur on Monday, 8 April 2024. A partial eclipse will be visible from nearly every part of North America. The path of totality will sweep from Mexico through Texas, the Midwest, New England, and across the maritime provinces of Canada. If you are anywhere where this event is visible, go out, don a pair of eclipse glasses, and look up. This is especially true in the path of totality. Partial eclipse are cool. Total eclipses are so much more that they have inspired science, art, and literature, with descriptions frequently evincing the deep emotion of profound religious experience*.
The American Astronomical Society has posted lots of useful information, including a map of the path of totality and advice about proper eclipse glasses. These are super-cheap, but that doesn’t preclude bad actors from selling ineffective versions. Simple rule of thumb: don’t look straight at the sun. A proper pair of eclipse glasses enable you to comfortably do so. If it hurts, stop+: close your eyes and look away. Listen to the messages from your pain receptors.
If you can get to the path of totality, it is worth doing so. Expect crowds and plan accordingly. This is a draw of epic proportions, and for many will be the only practical opportunity of their lifetime. Totality is brief, only a few minutes, so be sure to be in the right place at the right time$.
The AAS provides a good list of the phenomena to expect. Most of the action is around and during totality. The partial eclipse is a long (hour+) build up to the brief main show (a few minutes of totality). In addition to seeing the corona, the diamond ring and Baily’s Beads effects, this should be a good time to see solar prominences as the sun is nearing the maximum in its eleven year sunspot cycle. What we will see is unknown, as this is the solar analog of weather phenomena. The forecast calls for a high chance of prominences, but that doesn’t guarantee they’ll show.
One last thing I’ll note is that all the planets are relatively close to the sun on the sky at present, and some might be visible during the eclipse. Venus and Jupiter will be most prominent and easy to spot. Uranus and Neptune, not so much. The others maybe. Also present is Comet 12P/Pons-Brooks (aka the devil comet) in the vicinity of Jupiter. It is quite a temporal coincidence for this comet with a 71 year period to be in the inner solar system during this eclipse. It is unlikely to put on much of a show: comets are notoriously fickle, and the odds are that it will be invisible to the naked eye. But it is there, so keep a weather eye out, just in case.
All the planets and even a comet will be in the sky during the eclipse.
Now go forth this Monday and witness one of nature’s greatest marvels.
*There are many myths and monsters associated with eclipses. Until the light pollution of recent times, the motions of the sky were very much in our faces. People cared deeply about these things. They were well aware of more than the daily rising and setting of the sun. The phases of the moon, the patterns in the stars, and the wandering of the planets was obvious to everyone who looked up. People learned long ago to keep close track of these events, even those as rare as eclipses. Some of the earliest tablets unearthed from ancient Babylon are elaborate tables of eclipse seasons recognizing lengthy periods like the roughly 18 year Saros cycle. One doesn’t just up and write down this sort of knowledge on a whim one day, as it requires centuries of careful observation and record keeping to recognize the recurrence of events with such long periods, especially for solar eclipses that do not visit exactly the same spot every exeligmos cycle. I suspect there was a strong oral tradition of astronomical record keeping for long ages before we learned to write. Astronomy is the oldest science: this was important knowledge to acquire, preserve, and pass on.
The ancients managed to deduce cycles of eclipse seasons, so they could forecast the chance for eclipses, but only with the same precision as a weather forecast: there is a chance of rain, but we can’t be sure exactly when and where. Now we have measured planetary motions accurately enough and understand the geometry of what is going on so we can forecast exactly when and where eclipses will occur. This is a staggering achievement of human intellect and communal effort.
+There are a lot of misconceptions about the dangers of eclipse viewing. Looking straight at the sun is uncomfortable and dangerous at any time. The only thing special about a total eclipse is that it becomes truly dark for a few minutes, and your pupils start to expand to adapt to the darkness. Consequently, the most dangerous moment is at the end of totality, when your eyes have grown wide and the sun suddenly reappears. Be sure to don your eclipse glasses or look away right before the sun reappears; you don’t want to look straight into the sun at that moment.
Time and Date is a great resource for getting the timing of the eclipse for your specific location, accurate to within a few seconds.
$As with any astronomical observation, no guarantee is made that the skies will be clear of clouds. I have spent many a night at observatories wishing for the sky to clear and obsessively refreshing the satellite maps to discern when it might do so. It doesn’t help – it’s almost as if nature doesn’t care that we want to witness one of its greatest displays. So my advice is to go where you can and don’t sweat the weather forecast. Either the sky cooperates or it doesn’t.
I’ve agreed to serve on a discussion panel about the eclipse on campus, so I’ll be here in Cleveland. We are right in the path of totality, but the weather statistics here are… not good. To make matters worse for the superstitious, April 8 is also the home opener for the Cleveland Guardians. Opening day is always a joyous time with a packed stadium, but the weather is inevitably miserable. Nevertheless, all we need is a brief opening in the clouds at just the right time. At an observatory we would call a that a sucker hole – a gap in the clouds big enough to get the inexperienced observer to run around prepping the instrument and the telescope, an intense amount of work, to open up and observe just in time for the clouds to cover up the sky again. Come Monday, I’ll happily accept a well-timed sucker hole.
I just got back from a visit to the Carnegie Institution of Washington where I gave a talk and saw some old friends. I was a postdoc at the Department of Terrestrial Magnetism (DTM) in the ’90s. DTM is so-named because in their early days they literally traveled the world mapping the magnetic field. When I was there, DTM+ had a small extragalactic astronomy group including Vera Rubin*, Francois Schweizer, and John Graham. Working there as a Carnegie Fellow gave me great latitude to pursue whatever science I wanted, with the benefit of discussions with these great astronomers. After my initial work on low surface brightness galaxies had brought MOND to my attention, much of the follow-up work checking all (and I do mean all) the other constraints was done there, ultimately resulting in the triptych of papers showing that the bulk of the evidence available at that time favored MOND over the dark matter interpretation.
When I joined the faculty at the University of Maryland in 1998, I saw the need to develop a graduate course on cosmology, which did not exist there at that time. I began to consider how cosmic structure might form in MOND, but was taken aback when Simon White asked me to referee a paper on the subject by Bob Sanders. He had found much what I was finding, that there was no way to avoid an early burst of speedy galaxy formation. I had been scooped!
It has taken a quarter century to test our predictions, so any concern about who said what first seems silly now. Indeed, the bigger problem is informing people that these predictions were made at all. I had a huge eye roll last month when Physics Magazine came out with
February 12, 2024 NEWS FEATURE JWST Sees More Galaxies than Expected February 9, 2024
The new JWST observatory is revealing far more bright galaxies in the early Universe than anyone predicted, and astrophysicists have more than one explanation for the puzzle.
Far more bright galaxies in the early Universe than anyone predicted! Who could have predicted it? I guess I am anyone.
Joking aside, this is a great illustration of the inefficiency of scientific communication. I wrote a series of papers on the subject. I wasn’t alone; so did others. I gave talks about it. I’ve emphasized it in scientific reviews. My papers are frequently cited, ranking in the top 2% among the top 2% across all sciences. They’re cited by prominent cosmologists. Heck, I’ve even blogged about it. And yet, it comes as such a surprise that it couldn’t have possibly happened, to the extent that no one bothers to check what is in the literature. (There was a similar sociology around the prediction of the CMB second peak. It didn’t happen if we don’t look.)
So what did the Physics Magazine article talk about? More than one explanation, most of which are the conventionalist approaches we’ve talked about before – make star formation more efficient, or adjust the IMF (the mass spectrum with which stars form) to squeeze more UV photons out of fewer baryons. But there is also a paper by Sabti et al. that basically asserts “this can’t be happening!” which is exactly the point.
Sabti et al. ask whether the can boost the amplitude of structure formation in a way that satisfies both the new JWST observations and previous Hubble data. The answer is no:
We consider beyond-ΛCDM power-spectrum enhancements and show that any departure large enough to reproduce the abundance of ultramassive JWST candidates is in conflict with the HST data.
At first, this struck me as some form of reality denial, like an assertion that the luminosity density could not possible exceed LCDM predictions, even though that is exactly what it is observed to do:
The integrated UV luminosity density as a function of redshift from Adams et al. (2023). The data exceed the expectation for z > 10, even with the goal posts in motion.
On a closer read, I realized my initial impression was wrong; they are making a much better argument. The star formation rate is what is really constrained by the UV luminosity, but if that is attributed to stellar mass, you can’t get there from here – even with some jiggering of structure formation. That appears to be correct, within the framework of their considerations. Yet an alteration of structure formation is exactly what led to the now-corroborated prediction of Sanders (1998), so something still seemed odd. Just how were they altering it?
It took a close read, but the issue is in their equation 3. They allow for more structure formation by increasing the amplitude. However, they maintain the usual linear growth rate. In effect, they boost the amplitude of the linear dashed line in the left panel below, while maintaining its shape:
The growth rate of structure in CDM (linear, at left) and MOND (nonlinear, at right).
This is strongly constrain at both higher and lower redshifts, so only a little boost in amplitude is possible, assuming linear growth. So what they’ve correctly shown is that the usual linear growth rate of LCDM cannot do what needs to be done. That just emphasizes my point: to get the rapid growth we observe in the narrow time range available above redshift ten, the rate of growth needs to be nonlinear.
Nonlinearity is unavoidable in MOND – hence the prediction of big galaxies at high redshift. Nonlinearity is a bear to calculate, which is part of the reason nobody wants to go there. Tough nougies. They teach us in grad school that the early universe is simple. It is a mantra to many who work in the field. I’m sorry, did God promise this? I understand the reasons why the early universe should be simple in standard FLRW cosmology, but what if the universe we live in isn’t that? No one has standing to promise that the early universe is as simple as expected. That’s just a fairy tale cosmologists tell their young so they can sleep at night.
+DTM has since been merged with the Geophysical Laboratory to become the Earth and Planets Laboratory. These departments shared the Broad Branch Road campus but maintained a friendly rivalry in the soccer Mud Cup, so named because the first Mud Cup was played on a field that was a such a quagmire that we all became completely covered in mud. It was great fun.
*Vera was always adamant that she was not a physicist, and yet a search returns the thumbnail
even though the Wikipedia article itself does not (at present) make this spurious “and physicist” assertion.
The results from the high redshift universe keep pouring in from JWST. It is a full time job, and then some, just to keep track. One intriguing aspect is the luminosity density of the universe at z > 10. I had not thought this to be problematic for LCDM, as it only depends on the overall number density of stars, not whether they’re in big or small galaxies. I checked this a couple of years ago, and it was fine. At that point we were limited to z < 10, so what about higher redshift?
It helps to have in mind the contrasting predictions of distinct hypotheses, so a quick reminder. LCDM predicts a gradual build up of the dark matter halo mass function that should presumably be tracked by the galaxies within these halos. MOND predicts that galaxies of a wide range of masses form abruptly, including the biggest ones. The big distinction I’ve focused on is the formation epoch of the most massive galaxies. These take a long time to build up in LCDM, which typically takes half a Hubble time (~7 billion years; z < 1) for a giant elliptical to build up half its final stellar mass. Baryonic mass assembly is considerably more rapid in MOND, so this benchmark can be attained much earlier, even within the first billion years after the Big Bang (z > 5).
In both theories, astrophysics plays a role. How does gas condense into galaxies, and then form into stars? Gravity just tells us when we can assemble the mass, not how it becomes luminous. So the critical question is whether the high redshift galaxies JWST sees are indeed massive. They’re much brighter than had been predicted by LCDM, and in-line with the simplest models evolutionary models one can build in MOND, so the latter is the more natural interpretation. However, it is much harder to predict how many galaxies form in MOND; it is straightforward to show that they should form fast but much harder to figure out how many do so – i.e., how many baryons get incorporated into collapsed objects, and how many get left behind, stranded in the intergalactic medium? Consequently, the luminosity density – the total number of stars, regardless of what size galaxies they’re in – did not seem like a straight-up test the way the masses of individual galaxies is.
It is not difficult to produce lots of stars at high redshift in LCDM. But those stars should be in many protogalactic fragments, not individually massive galaxies. As a reminder, here is the merger tree for a galaxy that becomes a bright elliptical at low redshift:
Merger tree from De Lucia & Blaizot 2007 showing the hierarchical build-up of massive galaxies from many protogalactic fragments.
At large lookback times, i.e., high redshift, galaxies are small protogalactic fragments that have not yet assembled into a large island universe. This happens much faster in MOND, so we expect that for many (not necessarily all) galaxies, this process is basically complete after a mere billion years or so, often less. In both theories, your mileage will vary: each galaxy will have its own unique formation history. Nevertheless, that’s the basic difference: big galaxies form quickly in MOND while they should still be little chunks at high z in LCDM.
The hierarchical formation of structure is a fundamental prediction of LCDM, so this is in principle a place it can break. That is why many people are following the usual script of blaming astrophysics, i.e., how stars form, not how mass assembles. The latter is fundamental while the former is fungible.
Gradual mass assembly is so fundamental that its failure would break LCDM. Indeed, it is so deeply embedded in the mental framework of people working on it that it doesn’t seem to occur to most of them to consider the possibility that it could work any other way. It simply has to work that way; we were taught so in grad school!
Here is a sketch of how structures grow over time under the influence of cold dark matter (left, from Schramm 1992) and MOND (right, from Sanders & McGaugh 2002; see also this further discussion). The slow linear growth of CDM (long-dashed line, left panel) is replaced by a rapid, nonlinear growth in MOND (solid lines at right; numbers correspond to different scales). Nonlinear growth moderates after cosmic expansion begins to accelerate (dashed vertical line in right panel).
A principle result in perturbation theory applied to density fluctuations in an expanding universe governed by General Relativity is that the growth rate of these proto-objects is proportional to the expansion rate of the universe – hence the linear long-dashed line in the left diagram. The baryons cannot match the observations by themselves because the universe has “only” expanded by a factor of a thousand since recombination while structure has grown by a factor of a hundred thousand. This was one of the primary motivations for inventing cold dark matter in the first place: it can grow at the theory-specified rate without obliterating the observed isotropy% of the microwave background. The skeletal structure of the cosmic web grows in cold dark matter first; the baryons fall in afterwards (short-dashed line in left panel).
That’s how it works. Without dark matter, structure cannot form, so we needn’t consider MOND nor speak of it ever again forever and ever, amen.
Except, of course, that isn’t necessarily how structure formation works in MOND. Like every other inference of dark matter, the slow growth of perturbations assumes that gravity is normal. If we consider a different force law, then we have to revisit this basic result. Exactly how structure formation works in MOND is not a settled subject, but the panel at right illustrates how I think it might work. One seemingly unavoidable aspect is that MOND is nonlinear, so the growth rate becomes nonlinear at some point, which is rather early on if Milgrom’s constant a0 does not evolve. Rather than needing dark matter to achieve a growth factory of 105, the boost to the force law enables baryons do it on their own. That, in a nutshell, is why MOND predicts the early formation of big galaxies.
The same nonlinearity that makes structure grow fast in MOND also makes it very hard to predict the mass function. My nominal expectation is that the present-day galaxy baryonic mass function is established early and galaxies mostly evolve as closed boxes after that. Not exclusively; mergers still occasionally happen, as might continued gas accretion. In addition to the big galaxies that form their stars rapidly and eventually become giant elliptical galaxies, there will also be a population for which gas accretion is gradual^ enough to settle into a preferred plane and evolve into a spiral galaxy. But that is all gas physics and hand waving; for the mass function I simply don’t know how to extract a prediction from a nonlinear version of the Press-Schechter formalism. Somebody smarter than me should try that.
We do know how to do it for LCDM, at least for the dark matter halos, so there is a testable prediction there. The observable test depends on the messy astrophysics of forming stars and the shape of the mass function. The total luminosity density integrates over the shape, so is a rather forgiving test, as it doesn’t distinguish between stars in lots of tiny galaxies or the same number in a few big ones. Consequently, I hadn’t put much stock in it. But it is also a more robustly measured quantity, so perhaps it is more interesting than I gave it credit for, at least once we get to such high redshift that there should be hardly any stars.
Here is a plot of the ultraviolet (UV) luminosity density from Adams et al. (2023):
Fig. 8 from Adams et al. (2023) showing the integrated UV luminosity density as a function of redshift. UV light is produced by short-lived, massive stars, so makes a good proxy for the star formation rate (right axis).
The lower line is one+ a priori prediction of LCDM. I checked this back when JWST was launched, and saw no issues up to z=10, which remains true. However, the data now available at higher redshift are systematically higher than the prediction. The reason for this is simple, and the same as we’ve discussed before: dark matter halos are just beginning to get big; they don’t have enough baryons in them to make that many stars – at least not for the usual assumptions, or even just from extrapolating what we know quasi-empirically. (I say “quasi” because the extrapolation requires a theory-dependent rate of mass growth.)
The dashed line is what I consider to be a reasonable adjustment of the a priori prediction. Putting on an LCDM hat, it is actually closer to what I would have predicted myself because it has a constant star formation efficiency which is one of the knobs I prefer to fix empirically and then not touch. With that, everything is good up to z=10.5, maybe even to z=12 if we only believe* the data with uncertainties. But the bulk of the high redshift data sit well above the plausible expectation of LCDM, so grasping at the dangling ends of the biggest error bars seems unlikely to save us from a fall.
Ignoring the model lines, the data flatten out at z > 10, which is another way of saying that the UV luminosity function isn’t evolving when it should be. This redshift range does not correspond to much cosmic time, only a few hundred million years, so it makes the empiricist in me uncomfortable to invoke astrophysical causes. We have to imagine that the physical conditions change rapidly in the first sliver of cosmic time at just the right fine-tuned rate to make it look like there is no evolution at all, then settle down into a star formation efficiency that remains constant in perpetuity thereafter.
Harikane et al. (2023) also come to the conclusion that there is too much star formation going on at high redshift (their Fig. 18 is like that of Adams above, but extending all the way to z=0). Like many, they appear to be unaware that the early onset of structure formation had been predicted, so discuss three conventional astrophysical solutions as if these were the only possibilities. Translating from their section 6, the astrophysical options are:
Star formation was more efficient early on
Active Galactic Nuclei (AGN)
A top heavy IMF
This is a pretty broad view of the things that are being considered currently, though I’m sure people will add to this list as time goes forward and entropy increases.
Taking these in reverse order, the idea of a top heavy IMF is that preferentially more massive stars form early on. These produce more light per unit mass, so one gets brighter galaxies than predicted with a normal IMF. This is an idea that recurs every so often; see, e.g., section 3.1.1 of McGaugh (2004) where I discuss it in the related context of trying to get LCDM models to reionize the universe early enough. Supermassive Population III stars were all the rage back then. Changing the mass spectrum& with which stars form is one of those uber-free parameters that good modelers refrain from twiddling because it gives too much freedom. It is not a single knob so much as a Pandora’s box full of knobs that invoke a thousand Salpeter’s demons to do nearly anything at the price of understanding nothing.
As it happens, the option of a grossly variable IMF is already disfavored by the existence of quenched galaxies at z~3 that formed a normal stellar population at much higher redshift (z~11). These galaxies are composed of stars that have the spectral signatures appropriate for a population that formed with a normal IMF and evolved as stars do. This is exactly what we expect for galaxies that form early and evolve passively. Adjusting the IMF to explain the obvious makes a mockery of Occam’s razor.
AGN is a catchall term for objects like quasars that are powered by supermassive black holes at the centers of galaxies. This is a light source that is non-stellar, so we’ll overestimate the stellar mass if we mistake some light from AGN# as being from stars. In addition, we know that AGN were more prolific in the early universe. That in itself is also a problem: just as forming galaxies early is hard, so too is it hard to form enough supermassive black holes that early. So this just becomes the same problem in a different guise. Besides, the resolution of JWST is good enough to see where the light is coming from, and it ain’t all from unresolved AGN. Harikane et al. estimate that the AGN contribution is only ~10%.
That leaves the star formation efficiency, which is certainly another knob to twiddle. On the one hand, this is a reasonable thing to do, since we don’t really know what the star formation efficiency in the early universe was. On the other, we expected the opposite: star formation should, if anything, be less efficient at high redshift when the metallicity was low so there were few ways for gas to cool, which is widely considered to be a prerequisite for initiating star formation. Indeed, inefficient cooling was an argument in favor of a top-heavy IMF (perhaps stars need to be more massive to overcome higher temperatures in the gas from which they form), so these two possibilities contradict one another: we can have one but not both.
To me, the star formation efficiency is the most obvious knob to twiddle, but it has to be rather fine-tuned. There isn’t much cosmic time over which the variation must occur, and yet it has to change rapidly and in such a way as to precisely balance the non-evolving UV luminosity function against a rapidly evolving dark matter halo mass function. Once again, we’re in the position of having to invoke astrophysics that we don’t understand to make up for a manifest deficit the behavior of dark matter. Funny how those messy baryons always cover up for that clean, pure, simple dark matter.
I could go on about these possibilities at great length (and did in the 2004 paper cited above). I decline to do so any farther: we keep digging this hole just to fill it again. These ideas only seem reasonable as knobs to turn if one doesn’t see any other way out, which is what happens if one has absolute faith in structure formation theory and is blissfully unaware of the predictions of MOND. So I can already see the community tromping down the familiar path of persuading ourselves that the unreasonable is reasonable, that what was not predicted is what we should have expected all along, that everything is fine with cosmology when it is anything but. We’ve done it so many times before.
Initially I had the cat stuffed back in the bag image here, but that was really for a theoretical paper that I didn’t quite make it to in this post. You’ll see it again soon. The observations discussed here are by observers doing their best in the context they know, so it doesn’t seem appropriate to that.
^The assembly of baryonic mass can and in most cases should be rapid. It is the settling of gas into a rotationally supported structure that takes time – this is influenced by gas physics, not just gravity. Regardless of gravity theory, gas needs to settle gently into a rotating disk in order for spiral galaxies to exist.
+There are other predictions that differ in detail, but this is a reasonable representative of the basic expectation.
*This is not necessarily unreasonable, as there is some proclivity to underestimate the uncertainties. That’s a general statement about the field; I have made no attempt to assess how reasonable these particular error bars are.
&Top-heavy refers to there being more than the usual complement of bright but short-lived (tens of millions of years) stars. These stars are individually high mass (bigger than the sun), while long-lived stars are low mass. Though individually low in mass, these faint stars are very numerous. When one integrates over the population, one finds that most of the total stellar mass resides in the faint, low mass stars while much of the light is produced by the high mass stars. So a top heavy IMF explains high redshift galaxies by making them out of the brightest stars that require little mass to build. However, these stars will explode and go away on a short time scale, leaving little behind. If we don’t outright truncate the mass function (so many knobs here!), there could be some longer-lived stars leftover, but they must be few enough for the whole galaxy to fade to invisibility or we haven’t gained anything. So it is surprising, from this perspective, to see massive galaxies that appear to have evolved normally without any of these knobs getting twiddled.
#Excess AGN were one possibility Jay Franck considered in his thesis as the explanation for what we then considered to be hyperluminous galaxies, but the known luminosity function of AGN up to z = 4 couldn’t explain the entire excess. With the clarity of hindsight, we were just seeing the same sorts of bright, early galaxies that JWST has brought into sharper focus.
