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-ฮCDM 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.
It will take some time to sort out. There are several important aspects to the problem, one of which is agreeing on what LCDM actually predicts. It is fairly robust at predicting the number density of dark matter halos as a function of mass. To convert that into something observable requires understanding how baryons find their way into dark matter halos at early times, how those baryons condense into regions dense enough to form stars, what kinds of stars form there (thus determining observables like luminosity and spectral shape), and what happens in the immediate aftermath of early star formation (does feedback shut off star formation quickly or does it persist or is there some distribution over all possibilities). This is what simulators attempt to do. It is hard work, and they are a long way from agreeing with each other. Many of them appear to be a long way from agreeing with themselves, as their answers continue to evolve – sometimes because of genuine progress in the simulations, but sometimes in response to unanticipated* observations.
Observationally, we can hope to measure at least two distinct things: the masses of individual galaxies, and their number density – how many galaxies of a particular mass exist in a specified volume. I have mostly been worried about the first issue, as it appears that individual galaxies got too big too fast. In the hierarchical galaxy formation picture of LCDM, the massive galaxies of today were assembled from many smaller protogalaxies over an extended period of time, so big galaxies don’t emerge until comparatively late: it takes about seven billion years for a typical bright galaxy to assemble half its stellar mass. (The same hierarchical process is accelerated in MONDso galaxies can already be massive at z โ 10.) That there are examples of individual galaxies that are already massive in the early universe is a big issue.
How common should massive galaxies be? There are always early adopters: objects that grew faster than average for their mass. We’ll always see the brightest things first, so is what we’re seeing with JWST typical? Or is it just the bright tip of an iceberg that is perfectly reasonable in LCDM? This is what the luminosity function helps quantify: just how many galaxies of each mass are there? If we can quantify that, then we can quantify how many we should be able to see with a given survey of specified depth and sky coverage.
Astronomers have been measuring the galaxy luminosity function for a long time. Doing so at high redshift has always been an ambition, so JWST is hardly the first telescope to contribute to the subject. It is the newest and best, opening a regime where we had hoped to see protogalactic fragments directly. Instead, the first thing we see are galaxies bigger than we expected (in LCDM). This has been building for some time, so let’s take a step back to provide some context.
Steinhardt et al. (2016) pointed out what they call “the impossibly early galaxy problem.” They quantified this by comparing the observed luminosity function in various redshift bins to that predicted by LCDM. We’ve discussed their Fig. 1 before, so let’s look now at their Fig. 4:
Figure 4 from Steinhardt et al. (2016).ย Colors correspond to redshift, with z = 4, 5, 6, 7, 8, 9, 10 being represented by blue, green, yellow, orange, red, pink, and black: there are fewer objects at high redshift where they’ve had less time to form. (a) Expected halo mass to monochromatic UV luminosity ratio, along with the required evolution to reconcile observation with theory, and (b) resulting corrected halo-mass functions derived as in Figure 1 with Mhalo/LUV evolving due to a stellar population starting at low metallicity at z = 12 and aging along the star-forming main sequence, as described in Section 4.1.1. Such a model would be reasonable given observational constraints, but cannot produce agreement between measured UV luminosity functions and simulated halo-mass functions.
In a perfect model, the points (data) would match the lines (theory) of the same color (redshift). This is not the case – observed galaxies are persistently brighter than predicted. Making that prediction is subject to all the conversions from dark matter mass to stellar mass to observed luminosity we mentioned above, so they also show what they expect and what it would take to match the data. These are the different lines in the top panel. There is a lot of discussion of this in their paper that boils down to these lines are different, and we cannot plausibly make them the same.
The word “plausibly” is doing a lot of work in that last sentence. Just because one set of authors finds something to be impossible (despite their best efforts) doesn’t mean anyone else accepts that. We usually don’t, even when we should**.
It occurs to me that not every reader may appreciate how redshift corresponds to cosmic time. So here is a graph for vanilla LCDM parameters:
The age-redshift relation for the vanilla LCDM cosmology. Everything at z > 3 is in the early universe, i.e., the first two billion years after the Big Bang. Everything at z > 10 is in the very early universe, the first half billion years when there has not yet been time to form big galaxies hierarchically.
Things don’t change much if we adopt slightly different cosmologies: this aspect of LCDM is well established. We used to think it would take a least a couple of billion years to form a big galaxy, so anything at z > 3 is surprising from that perspective. That’s not wrong, as there is an inverse relation between age and redshift, with increasing redshifts crammed into an ever smaller window of time. So while z = 5 and 10 sound very different, there is only about 700 Myr between them. That sounds like a long time to you and me, but the sun will only complete 3 orbits around the Galaxy in that time. This is why it is hard to imagine an object as large as the Milky Way starting from the near-homogeneity of the very early universe then having time to expand, decouple, recollapse, and form into something coherent so “quickly.” There is a much larger distance for material to travel than the current circumference of the solar circle, and not much time in which to do it. If we want to get it done by z = 10, there is less than 500 Myr available – about two orbits of the sun. We just can’t get there fast enough.
We’ve quickly become jaded to the absurdly high redshifts revealed by JWST, but there’s not much difference in cosmic time between these seemingly ever higher redshifts. Very early epochs were already being probed before JSWT; JWST just brings them into excruciating focus. To provide some historical perspective about what “high redshift” means, here is a quote from Schramm (1992). The full text is behind a paywall, so I’ll just quote a relevant paragraph:
Pushing the opposite direction from the “zone of mystery” epoch [the dark ages] between the background radiation and the existence of objects at high redshift is the discovery of objects at higher and higher redshift. The higher the redshift of objects found, the harder it is to have the slow growth of Figure 5 [SCDM] explain their existence. Some high redshift objects can be dismissed as statistical fluctuations if the bulk of objects still formed late. In the last year, the number of quasars with redshifts > 4 has gone to 30, with one having a redshift as large as 4.9… While such constraints are not yet a serious problem for linear growth models, eventually they might be.
David Schramm, 1992
Here we have a cosmologist already concerned 30 years ago that objects exist at z > 4. Crazy, that! Back then, the standard model was SCDM; one of the reasons to switch to LCDM was to address exactly this problem. That only buys us a couple of billion years, so now we’re smack up against the same problem all over again, just shifted to higher redshift. Some people are even invoking statistical fluctuations: same as it ever was.
Consequently, a critical question is how common these massive galaxies are. Sure, massive galaxies exist before we expected them. But are they just statistical fluctuations? This is a question we can address with the luminosity function.
Here is the situation just before JWST was launched. Yung et al. (2019) made a good faith effort to establish a prior: they made predictions for what JWST would see. This is how science is supposed to work. In the figure below, I compare that to what was known (Stefanon et al. 2021) from the Spitzer Space Telescope, in many ways the predecessor to JSWT:
Figure 4 from McGaugh (2024). The number density ฮฆ of galaxies as a function of their stellar mass ๐โ, color coded by redshift with ๐ง=6, 7, 8, 9, 10 in dark blue, light blue, green, orange, and red, respectively. The left panel shows predicted stellar mass functions [lines] with the corresponding data [circles]. The right panel shows the ratio of the observed-to-predicted density of galaxies. There is a clear excess of massive galaxies at high redshifts.
If you just look at the mass functions in the left panel, things look pretty good. This is one of the dangers of the logarithmic plots necessary to illustrate the large dynamic range of astronomical data: large differences may look small in log-log space. So I also plot the ratio of densities at right. There one can see a clear excess in the number density of high mass galaxies. There are nearly an order of magnitude more 1010 Mโ galaxies than expected at z โ 8!
For technical reasons I don’t care to delve into, it is difficult to get the volume estimate right when constructing the luminosity function. So I can imagine there might be some systematic effects to scale the ratio up or down. That wouldn’t do anything to explain the bump at high masses, and it is rather harder to get the shape wrong, especially at the bright end. The faint end of the luminosity function is the hard part!
The Spitzer data already probes the early universe, before JWST reported results. As those have come in, it has started to be possible to construct luminosity functions at very high redshift. Here are some measurements from Harikane et al. (2023), Finkelstein et al. (2023), and Robertson et al. (2023) together with revised predictions from Yung et al. (2024).
Figure 5from McGaugh (2024). The number density of galaxies as a function of their rest-frame ultraviolet absolute magnitude observed by JWST, a proxy for stellar mass at high redshift. The left panel shows predicted luminosity functions [lines], color coded by redshift: blue, green, orange, red for ๐ง=9, 11, 12, 14, respectively. Data in the corresponding redshift bins are shown as squares, circles, and triangles. The right panel shows the ratio of the observed-to-predicted density of galaxies. The observed luminosity function barely evolves, in contrast to the prediction of substantial evolution as the first dark matter halos assemble. There is a large excess of bright galaxies at the highest redshifts observed.
Again, we see that there is an excess of bright galaxies at the highest redshifts.
As we look to progressively higher redshift, the light we observe shifts from familiar optical bands to the ultraviolet. This was a huge part of the motivation to build JWST: it is optimized for the infrared, so we can observed the redshifted optical light as our eyes would see it. Astronomers always push to the edge of what a telescope can do, so we start to run into this problem again at the highest redshifts. The mapping of ultraviolet light to stellar mass is one of the harder tasks in stellar population work, much less mapping that to a dark matter halo mass. So one promising conventional idea is “the up-scattering in UV luminosity of small, abundant halos due to stochastic, high efficiency star formation during the initial phases of galaxy formation (unregulated star formation)” discussed$ by Finkelstein et al. (2023). I like this because, yeah, we expect lots of little halos, star formation is messy and star formation during the first phases of galaxy formation should be especially messy, so it is easy to imagine little halos stochastically lighting up in the UV. But can this be enough?
It remains to be seen if the observations can be explained by this or any of the usual tweaks to star formation. It seems like a big gap to overcome. I mean, just look at the left panel of the final figure above. The observed UV luminosity function is barely evolving while the prediction of LCDM is dropping like a rock. Indeed, the mass functions get jagged, which may be an indication that there are so few dark matter halos in the simulation volume at the redshift in question that they do not suffice to define a smooth mass function. Indeed, Harikane et al. estimate a luminosity density of โผ7 รย 10โ6 mag.โ1 Mpcโ3 at ๐งโ16. This point is omitted from the figure above because the corresponding prediction is NAN (not a number): there just isn’t anything big enough in the simulation to do be so bright that early.
There is good reason to be skeptical of the data at ๐งโ16. There is also good reason to be skeptical of the simulations. These have yet to converge, and even the predictions of the same group continue to evolve. Yung et al. (2019) did the right thing to establish a prior before JWST’s launch, but they haven’t stuck by it. The density of rare, massive galaxies has gone up by a factor of 2 to 2.5 in Yung et al. (2024). They attribute this to the use of higher resolution simulations, which may very well be correct: in order to track the formation of the earliest structures, you have to resolve them. But it doesn’t exactly inspire confidence that we actually know what LCDM predicts, and it feels like the same sort of moving of the goalposts that I’ve witnessed over and over and over and over and over again.
Please don’t falsify LCDM! I ran out of computer time. I had a disk crash. I didn’t have a grant for supercomputer time. My simulation data didn’t come back from the processing center. A senior colleague insisted on a rewrite. Someone stole my laptop. There was an earthquake, a terrible flood, locusts! It wasn’t my fault! I swear to God!
And the community loves LCDM, so we fall for it every time.
Oh, LCDM. LCDM, honey.
*There is always a danger in turning knobs to fit the data, and there are plenty of knobs to turn. So what LCDM predicts is a very serious matter – a theory is only as good as its prior, and we should be skeptical if theorists keep adjusting what that is in response to observations they failed to predict. This is true even in the absence of the existential threat of MOND which implies that the entire field of cosmological simulations is betrayed by its most fundamental assumptions, reducing it to “garbage in, garbage out.”
**When I first found that MOND had predictedour observations of low surface brightness galaxies where dark matter had not, despite my best efforts to make it work out, Ortwin Gerhard asked me if he “had to believe it.” My instant reaction was “this is astronomy, we don’t have to believe anything.” More seriously, this question applies on many levels: do we believe the data? do we believe the interpretation? is this the only possible conclusion? At the time, I had already tried very hard to fix it, and had failed. Still, I was willing to imagine there might be some way out, and maybe someone could figure out something I had not. Since that time, lots of other people have tried and also failed. This has not kept some of them from claiming that they have succeeded, but they never seem to address the underlying problem, and most of these models are mere variations on things I tried and dismissed as obviously unworkable.
Now, as then, what we are obliged to believe is the data, to the limits of their accuracy. The data have improved substantially, and at this point it is clear that the radial acceleration relation exists+ and has remarkably small intrinsic scatter. What we can always argue about is the interpretation: sure, it looks exactly like MOND, and MOND was the only theory that predicted it in advance, and we haven’t been able to come up with a reasonable explanation in terms of dark matter, but perhaps one can be found in some dark matter model that does not yet exist.
This clickbait title is inspired by the clickbait title of a recent story about high redshift galaxies observed by JWST. To speak in the same vernacular:
This story is one variation on the work of Labbe et al. that has been making the rounds since it appeared in Nature in late February. The concern is that these high redshift galaxies are big and bright. They got too big too soon.
Six high redshift galaxies from the JWST CEERS survey, as reported by Labbe et al. (2023). Not much to look at, but bear in mind that these objects are pushing the edge of the observable universe. By that standard, they are both bright and disarmingly obvious.
Stellar masses and redshifts of galaxies from Labbe et al. The pink squares are the initial estimates that appeared in their first preprint in July 2022. The black squares with error bars are from the version published in February 2023. The shaded regions represent where galaxies are too massive too early for LCDM. The lighter region is where very few galaxies were expectedto exist; the darker region is a hard no.
The results here are mixed. On the one hand, we were right to be concerned about the initial analysis. This was based in part on a ground-based calibration of the telescope before it was launched. That’s not the same as performance on the sky, which is usually a bit worse than in the lab. JWST breaks that mold, as it is actually performing better than expected. That means the bright-looking galaxies aren’t quite as intrinsically bright as was initially thought.
The correct calibration reduces both the masses and the redshifts of these galaxies. The change isn’t subtle: galaxies are less massive (the mass scale is logarithmic!) and at lower redshift than initially thought. Amusingly, only one galaxy is above redshift 9 when the early talking point was big galaxies at z = 10. (There are othercrediblecandidates for that.) Nevertheless, the objects are clearly there, and bright (i.e., massive). They are also early. We like to obsess about redshift, but there is an inverse relation between redshift and time, so there is not much difference in clock time between z = 7 and 10. Redshift 10 is just under 500 million years after the big bang; redshift 7 just under 750 million years. Those are both in the first billion years out of a current age of over thirteen billion years. The universe was still in its infancy for both.
Regardless of your perspective on cosmic time scales, the observed galaxies remain well into LCDM’s danger zone, even with the revised calibration. They are no longer fully in the no-go zone, so I’m sure we’ll see lots of papers explaining how the danger zone isn’t so dangerous after all, and that we should have expected it all along. That’s why it matters more what we predict before an observation than after the answer is known.
*I emphasize science here because one of the reactions I get when I point out that this was predicted is some variation on “That doesn’t count! [because I don’t understand the way it was done.]” And yet, the predictions made and published in advance of the observations keep coming true. It’s almost as if there might be something to this so-called scientific method.
On the one hand, I understand the visceral negative reaction. It is the same reaction I had when MOND first reared its ugly head in my own data for low surface brightness galaxies. This is apparently a psychological phasethrough which we must pass. On the other hand, the community seems stuck in this rut: it is high time to get past it. I’ve been trying to educate a reluctant audience for over a quarter century now. I know how it pains them because I shared that pain. I got over it. If you’re a scientist still struggling to do so, that’s on you.
There are some things we have to figure out for ourselves. If you don’t believe me, fine, but then get on with doing it yourself instead of burying your head in the sand. The first thing you have to do is give MOND a chance. When I allowed that possibility, I suddenly found myself working less hard than when I was desperately trying to save dark matter. If you come to the problem sure MOND is wrong+, you’ll always get the answer you want.
+I’ve been meaning to write a post (again) about the very real problems MOND suffers in clusters of galaxies. This is an important concern. It is also just one of hundreds of things to consider in the balance. We seem willing to give LCDM infinite mulligans while any problem MOND encounters is immediately seen as fatal. If we hold them to the same standard, both are falsified. If all we care about is explanatory power, LCDM always has that covered. If we care more about successful a priori predictions, MOND is less falsified than LCDM.
There is an important debate to be had on these issues, but we’re not having it. Instead, I frequently encounter people whose first response to any mention of MOND is to cite the bullet cluster in order to shut down discussion. They are unwilling to accept that there is a debate to be had, and are inevitably surprised to learn that LCDM has trouble explaining the bullet cluster too, let alone other clusters. It’s almost as if they are just looking for an excuse to not have to engage in serious thought that might challenge their belief system.
Triton Station 
