I was raised to believe that it was rude to tell people I told you so. Yet that’s pretty much the essence of the scientific method: we test hypotheses by making predictions, then checking to see which told us the correct result in advance of the experiment. So: I told you so.
Our paper on massive galaxies at high redshift is out in the Astrophysical Journal today. This is a scientific analysis of the JWST data that has accumulated to date as it pertains to testing galaxy formation as hypothesized by LCDM and MOND. That massive galaxies are observed to form early (z > 10) corroborates the long standing prediction of MOND, going back to Sanders (1998):
Objects of galaxy mass are the first virialized objects to form (by z=10), and larger structure develops rapidly
The contemporaneous LCDM prediction from Mo, Mao, & White (1998) – a touchstone of galaxy formation theory with nearly 2,000 citations – was
present-day disc [galaxies] were assembled recently (at z<=1).
This is not what JWST sees, as morphologically mature spiral galaxies are present to at least z = 6 (Ferreira et al 2024). More generally, LCDM was predicted to take a long time to build up the stellar mass of large galaxies, with the median time to reach half the final stellar mass being about half a Hubble time (seven billion years, give or take). In contrast, JWST has now observed many galaxies that meet this benchmark in the first billion years. That was not expected to happen.
In short, one theory got its prediction right, and the other got it wrong. I say expected, because we can always attempt to modify a theory to accommodate new facts. The a priori predictions of LCDM were wrong, but can it be adjusted to explain the data? Perhaps – but if so, that’s because it is incredibly flexible. That’s normally considered to be a bad thing in a theory, not a strength, especially when a competing theory got it right in the first place.
This has happened over and over and over again. After the initial shock of having MOND’s predictions come true in my own data(how can this be so?), I’ve spent the decades since devising and executing new tests of both theories. When it comes to making a priori predictions, MOND has won over and over again. It has consistently had more predictive success.
If you are a scientist reading this and that statement doesn’t sound right to you, that’s because you haven’t been paying attention. I get it: MOND seems too unlikely to pay attention to. I certainly didn’t before it reared its head in my own data. So ask yourself: what do you actually know about MOND? IT’S WRONG! OK, after that. Seriously: how many papers have you read about MOND? Do you know what its predictions are? Do you know what its successes are, or only just its failings? Can you write down its formula? If the answers to these questions do not come easily to you, it’s because you haven’t taken it seriously. Which, again, I get. But it is also an indication that you may not be playing with a complete set of facts. Ignorance is not a strong position from which to make scientific judgements.
I will expand more on the content of the science paper in future posts. For now, it boils down to I told you so.
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.
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 ≈ 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). 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 Φ of galaxies as a function of their stellar mass 𝑀∗, color coded by redshift with 𝑧=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 M☉ galaxies than expected at z ≈ 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 𝑧=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 ∼7 × 10−6 mag.−1 Mpc−3 at 𝑧≈16. 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 𝑧≈16. 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.
To start the new year, I provide a link to a discussion I had with Simon White on Phil Halper’s YouTube channel:
In this post I’ll say little that we don’t talk about, but will add some background and mildly amusing anecdotes. I’ll also try addressing the one point of factual disagreement. For the most part, Simon & I entirely agree about the relevant facts; what we’re discussing is the interpretation of those facts. It was a perfectly civil conversation, and I hope it can provide an example for how it is possible to have a positive discussion about a controversial topic+ without personal animus.
First, I’ll comment on the title, in particular the “vs.” This is not really Simon vs. me. This is a discussion between two scientists who are trying to understand how the universe works (no small ask!). We’ve been asked to advocate for different viewpoints, so one might call it “Dark Matter vs. MOND.” I expect Simon and I could swap sides and have an equally interesting discussion. One needs to be able to do that in order to not simply be a partisan hack. It’s not like MOND is my theory – I falsified my own hypothesis long ago, and got dragged reluctantly into this business for honestly reporting that Milgrom got right what I got wrong.
That’s a very short summary of a long and distinguished career; Simon has done lots of other things. I highlight these works because they came up at some point in our discussion. Davis, Efstathiou, Frenk, & White are the “gang of four” that was mentioned; around Cambridge I also occasionally heard them referred to as the Cold Dark Mafia. The baryon fraction of clusters was one of the key observations that led from SCDM to LCDM.
The subject of galaxy formation runs throughout our discussion. It is always a fraught issue how things form in astronomy. It is one thing to understand how stars evolve, once made; making them in the first place is another matter. Hard as that is to do in simulations, galaxy formation involves the extra element of dark matter in an expanding universe. Understanding how galaxies come to be is essential to predicting anything about what they are now, at least in the context of LCDM*. Both Simon and I have worked on this subject our entire careers, in very much the same framework if from different perspectives – by which I mean he is a theorist who does some observational work while I’m an observer who does some theory, not LCDM vs. MOND.
When Simon moved to Max Planck, the center of galaxy formation work moved as well – it seemed like he took half of Cambridge astronomy with him. This included my then-office mate, Houjun Mo. At one point I refer to the paper Mo & I wrote on the clustering of low surface brightness galaxies and how I expected them to reside in late-forming dark matter halos**. I often cite Mo, Mao, & White as a touchstone of galaxy formation theory in LCDM; they subsequently wrote an entire textbook about it. (I was already warning them then that I didn’t think their explanations of the Tully-Fisher relation were viable, at least not when combined with the effect we have subsequently named the diversity of rotation curve shapes.)
When I first began to worry that we were barking up the wrong tree with dark matter, I asked myself what could falsify it. It was hard to come up with good answers, and I worried it wasn’t falsifiable. So I started asking other people what would falsify cold dark matter. Most did not answer. They often had a shocked look like they’d never thought about it, and would rather not***. It’s a bind: no one wants it to be false, but most everyone accepts that for it to qualify as physical science it should be falsifiable. So it was a question that always provoked a record-scratch moment in which most scientists simply freeze up.
Simon was one of the first to give a straight answer to this question without hesitation, circa 1999. At that point it was clear that dark matter halos formed central density cusps in simulations; so those “cusps had to exist” in the centers of galaxies. At that point, we believed that to mean all galaxies. The question was complicated by the large dynamical contribution of stars in high surface brightness galaxies, but low surface brightness galaxies were dark matter dominated down to small radii. So we thought these were the ideal place to test the cusp hypothesis.
We no longer believe that. After many attempts at evasion, cold dark matter failed this test; feedback was invoked, and the goalposts started to move. There is now a consensus among simulators that feedback in intermediate mass galaxies can alter the inner mass distribution of dark matter halos. Exactly how this happens depends on who you ask, but it is at least possible to explain the absence of the predicted cusps. This goes in the right direction to explain some data, but by itself does not suffice to address the thornier question of why the distribution of baryons is predictive of the kinematics even when the mass is dominated by dark matter. This is why the discussion focused on the lowest mass galaxies where there hasn’t been enough star formation to drive the feedback necessary to alter cusps. Some of these galaxies can be described as having cusps, but probably not all. Thinking only in those terms elides the fact that MOND has a betterrecord of predictivesuccess. I want to know why this happens; it must surely be telling us something important about how the universe works.
The one point of factual disagreement we encountered had to do with the mass profile of galaxies at large radii as traced by gravitational lensing. It is always necessary to agree on the facts before debating their interpretation, so we didn’t press this far. Afterwards, Simon sent a citation to what he was talking about: this paper by Wang et al. (2016). In particular, look at their Fig. 4:
Fig. 4 of Wang et al. (2016). The excess surface density inferred from gravitational lensing for galaxies in different mass bins (data points) compared to mock observations of the same quantity made from within a simulation (lines). Looks like excellent agreement.
This plot quantifies the mass distribution around isolated galaxies to very large scales. There is good agreement between the lensing observations and the mock observations made within a simulation. Indeed, one can see an initial downward bend corresponding to the outer part of an NFW halo (the “one-halo term”), then an inflection to different behavior due to the presence of surrounding dark matter halos (the “two-halo term”). This is what Simon was talking about when he said gravitational lensing was in good agreement with LCDM.
I was thinking of a different, closely related result. I had in mind the work of Brouwer et al. (2021), which I discussed previously. Very recently, Dr. Tobias Mistele has made a revised analysis of these data. That’s worthy its own post, so I’ll leave out the details, which can be found in this preprint. The bottom line is in Fig. 2, which shows the radial acceleration relation derived from gravitational lensing around isolated galaxies:
The radial acceleration relation from weak gravitational lensing (colored points) extending existing kinematic data (grey points) to lower acceleration corresponding to very large radii (~ 1 Mpc). The dashed line is the prediction of MOND. Looks like excellent agreement.
This plot quantifies the radial acceleration due to the gravitational potential of isolated galaxies to very low accelerations. There is good agreement between the lensing observations and the extrapolation of the radial acceleration relation predicted by MOND. There are no features until extremely low acceleration where there may be a hint of the external field effect. This is what I was talking about when I said gravitational lensing was in good agreement with MOND, and that the data indicated a single halo with an r-2 density profile that extends far out where we ought to see the r-3 behavior of NFW.
The two plots above use the same method applied to the same kind of data. They should be consistent, yet they seem to tell a different story. This is the point of factual disagreement Simon and I had, so we let it be. No point in arguing about the interpretation when you can’t agree on the facts.
I do not know why these results differ, and I’m not going to attempt to solve it here. I suspect it has something to do with sample selection. Both studies rely on isolated galaxies, but how do we define that? How well do we achieve the goal of identifying isolated galaxies? No galaxy is an island; at some level, there is always a neighbor. But is it massive enough to perturb the lensing signal, or can we successfully define samples of galaxies that are effectively isolated, so that we’re only looking at the gravitational potential of that galaxy and not that of it plus some neighbors? Looks like there is some work left to do to sort this out.
Stepping back from that, we agreed on pretty much everything else. MOND as a fundamental theory remains incomplete. LCDM requires us to believe that 95% of the mass-energy content of the universe is something unknown and perhaps unknowable. Dark matter has become familiar as a term but remains a mystery so long as it goes undetected in the laboratory. Perhaps it exists and cannot be detected – this is a logical possibility – but that would be the least satisfactory result possible: we might as well resume counting angels on the head of a pin.
The community has been working on these issues for a long time. I have been working on this for a long time. It is a big problem. There is lots left to do.
*The predictions of MOND are insensitive to the details of galaxy formation. Though of course an interesting question, we don’t need that in order to make predictions. All we need is the mass distribution that the kinematics respond to – we don’t need to know how it got that way. This is like the solar system, where it suffices to know Newton’s laws to compute orbits; we don’t need to know how the sun and planets formed. In contrast, one needs to know how a galaxy was assembled in LCDM to have any hope of predicting what its distribution of dark matter is and then using that to predict kinematics.
**The ideas Mo & I discussed thirty years ago have reappeared in the literature under the designation “assembly bias.”
***It was often accompanied by “why would you even ask that?” followed by a pained, constipated expression when they realized that every physical theory has to answer that question.
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.
Cosmology is challenged at present by two apparently unrelated problems: the apparent formation of large galaxies at unexpectedly high redshift observed by JWST, and the tension between the value of the Hubble constant obtained by traditional methods and that found in multi-parameter fits to the acoustic power spectrum of the cosmic microwave background (CMB).
Early results in precision cosmology from WMAP obtained estimates of the Hubble constant h = 0.73 ± 0.03 [I adopt the convention h = H0/(100 km s-1 Mpc-1) so as not to have to have to write the units every time.] This was in good agreement with contemporaneous local estimates from the Hubble Space Telescope Key Project to Measure the Hubble Constant: h = 0.72 ± 0.08. This is what Hubble was built to do. It did it, and the vast majority of us were satisfied* at the time that it had succeeded in doing so.
Since that time, a tension has emerged as accuracy has improved. Precise local measures** give h = 0.73 ± 0.01 while fits to the Planck CMB data give h = 0.6736 ± 0.0054. This is around the 5 sigma threshold for believing there is a real difference. Our own results exclude h < 0.705 at 95% confidence. A value as low as 67 is right out.
Given the history of the distance scale, it is tempting to suppose that local measures are at fault. This seems to be the prevailing presumption, and it is just a matter of figuring out what went wrong this time. Of course, things can go wrong with the CMB too, so this way of thinking raises the ever-present danger of confirmation bias, ever a scourge in cosmology. Looking at the history of H0 determinations, it is not local estimates of H0 but rather those from CMB fits that have diverged from the concordance region.
The cosmic mass density parameter and Hubble constant. These covary in CMB fits along the line Ωmh3 = 0.09633 ± 0.00029 (red). Also shown are best-fit values from CMB experiments over time, as labeled (WMAP3 is the earliest shown; Planck2018 the most recent). These all fall along the line of constant Ωmh3, but have diverged over time from concordance with local data. There are many examples of local constraints; for illustration I show examples from Cole et al. (2005), Mohayaee & Tully (2005), Tully et al. (2016), and Riess et al. (2001). The divergence has occurred as finer angular scales have been observed in the CMB power spectrum and correspondingly higher multiples ℓ have been incorporated into fits.
The divergence between local and CMB-determined H0 has occurred as finer angular scales have been observed in the CMB power spectrum and correspondingly higher multiples ℓ have been incorporated into fits. That suggests that the issue resides in the high-ℓ part of the CMB data*** rather than in some systematic in the local determinations. Indeed, if one restricts the analysis of the Planck (“TT”) data to ℓ < 801, one obtains h = 0.70 ± 0.02 (see their Fig. 22), consistent with earlier CMB estimates as well as with local ones.
Photons must traverse the entire universe to reach us from the surface of last scattering. Along the way, they are subject to 21 cm absorption by neutral hydrogen, Thomson scattering by free electrons after reionization, blue and redshifting from traversing gravitational potentials in an expanding universe (the late ISW effect, aka the Rees-Sciama effect), and deflection by gravitational lensing. Lensing is a subtle effect that blurs the surface of last scattering and adds a source of fluctuations not intrinsic to it. The amount of lensing can be calculated from the growth rate of structure; anomalously fast galaxy formation would induce extra power at high ℓ.
Early Galaxy Formation
JWST observations evince the early emergence of massive galaxies at z ≈ 10. This came as a great surprise theoretically, but the empirical result extends previous observations that galaxies grew too bigtoo fast. Taking the data at face value, more structure appears to exist in the early universe than anticipated in the standard calculation. This would cause excess lensing and an anomalous source of power on fine scales. This would be a real, physical anomaly (new physics), not some mistake in the processing of CMB data (which may of course happen, just as with any other sort of data). Here are the Planck data:
Unbinned Planck data with the best-fit power spectrum (red line) and a model (blue line) with h=0.73 and Ωm adjusted to maintain constant Ωmh3. The ratio of the models is shown at bottom, that with = 0.67 divided by the model with h = 0.73. The difference is real; h = 0.67 gives the better fit****. The ratio illustrates the subtle need for slightly greater power with increasing ℓ than provided by the model with h = 0.73. Perhaps this high-ℓ power has a contribution from anomalous gravitational lensing that skews the fit and drives the Hubble tension.
If excess lensing by early massive galaxies occurs but goes unrecognized, fits to the CMB data would be subtly skewed. There would be more power at high ℓ than there should be. Fitting this extra power would drive up Ωm and other relevant parameters*****. In response, it would be necessary to reduce h to maintain a constant Ωmh3. This would explain the temporal evolution of the best fit values, so I posit that this effect may be driving the Hubble tension.
The early formation of massive galaxies would represent a real, physical anomaly. This is unexpected in ΛCDM but not unanticipated. Sanders (1998) explicitly predicted the formation of massive galaxies by z = 10. Excess gravitational lensing by these early galaxies is a natural consequence of his prediction. Other things follow as well: early reionization, an enhanced ISW/Rees-Sciama effect, and high redshift21 cm absorption. In short, everything that is puzzling about the early universe from the ΛCDM perspective was anticipated and often explicitly predicted in advance.
The new physics driving the prediction of Sanders (1998) is MOND. This is the same driver of anomalies in galaxy dynamics, and perhaps now also of the Hubble tension. These predictive successes must be telling us something, and highlight the need for a deeper theory. Whether this finally breaks ΛCDM or we find yet another unsatisfactory out is up to others to decide.
*Indeed, the ± 0.08 rather undersells the accuracy of the result. I quote that because the Key Project team gave it as their bottom line. However, if you read the paper, you see statements like h = 0.71 ± 0.02 (random) ± 0.06 (systematic). The first is the statistical error of the experiment, while the latter is an estimate of how badly it might go wrong (e.g., susceptibility to a recalibration of the Cepheid scale). With the benefit of hindsight, we can say now that the Cepheid calibration has not changed that much: they did indeed get it right to something more like ± 0.02 than ± 0.08.
***I recall being at a conference when the Planck data were fresh where people were visibly puzzled at the divergence of their fit from the local concordance region. It was obvious to everyone that this had come about when the high ℓ data were incorporated. We had no idea why, and people were reluctant to contradict the Authority of the CMB fit, but it didn’t sit right. Since that time, the Planck result has been normalized to the point where I hear its specific determination of cosmic parameters used interchangeably with ΛCDM. And indeed, the best fit is best for good reason; determinations that are in conflict with Planck are either wrong or indicate new physics.
****The sharp eye will also notice a slight offset in the absolute scale. This is fungible with the optical depth due to reionization, which acts as a light fog covering the whole sky: higher optical depth τ depresses the observed amplitude of the CMB. The need to fit the absolute scale as well as the tip in the shape of the power spectrum would explain another temporal evolution in the best-fit CMB parameters, that of declining optical depth from WMAP and early (2013) Planck (τ = 0.09) to 2018 Planck (τ = 0.0544).
*****The amplitude of the power spectrum σ8 would also be affected. Perhaps unsurprisingly, there is also a tension between local and CMB determinations of this parameter. All parameters must be fit simultaneously, so how it comes out in the wash depends on the details of the history of the nonlinear growth of structure. Such a calculation is beyond the scope of this note. Indeed, I hope someone else takes up the challenge, as I tire of solving all the problems only to have them ignored. Better if everyone else comes to grip with this for themselves.
I noted last time that in the rush to analyze the first of the JWST data, that “some of these candidate high redshift galaxies will fall by the wayside.” As Maurice Aabe notes in the comments there, this has already happened.
I was concerned because of previous work with Jay Franck in which we found that photometric redshifts were simply not adequately precise to identify the clusters and protoclusters we were looking for. Consequently, we made it a selection criterion when constructing the CCPC to require spectroscopic redshifts. The issue then was that it wasn’t good enough to have a rough idea of the redshift, as the photometric method often provides (what exactly it provides depends in a complicated way on the redshift range, the stellar population modeling, and the wavelength range covered by the observational data that is available). To identify a candidate protocluster, you want to know that all the potential member galaxies are really at the same redshift.
This requirement is somewhat relaxed for the field population, in which a common approach is to ask broader questions of the data like “how many galaxies are at z ~ 6? z ~ 7?” etc. Photometric redshifts, when done properly, ought to suffice for this. However, I had noticed in Jay’s work that there were times when apparently reasonable photometric redshift estimates went badly wrong. So it made the ganglia twitch when I noticed that in early JWST work – specifically Table 2 of the first version of a paper by Adams et al. – there were seven objects with candidate photometric redshifts, and three already had a preexisting spectroscopic redshift. The photometric redshifts were mostly around z ~ 9.7, but the three spectroscopic redshifts were all smaller: two z ~ 7.6, one 8.5.
Three objects are not enough to infer a systematic bias, so I made a mental note and moved on. But given our previous experience, it did not inspire confidence that all the available cases disagreed, and that all the spectroscopic redshifts were lower than the photometric estimates. These things combined to give this observer a serious case of “the heebie-jeebies.”
Adams et al have now posted a revised analysis in which many (not all) redshifts change, and change by a lot. Here is their new Table 4:
There are some cases here that appear to confirm and improve the initial estimate of a high redshift. For example, SMACS-z11e had a very uncertain initial redshift estimate. In the revised analysis, it is still at z~11, but with much higher confidence.
That said, it is hard to put a positive spin on these numbers. 23 of 31 redshifts change, and many change drastically. Those that change all become smaller. The highest surviving redshift estimate is z ~ 15 for SMACS-z16b. Among the objects with very high candidate redshifts, some are practically local (e.g., SMACS-z12a, F150DB-075, F150DA-058).
So… I had expected that this could go wrong, but I didn’t think it would go this wrong. I was concerned about the photometric redshift method – how well we can model stellar populations, especially at young ages dominated by short lived stars that in the early universe are presumably lower metallicity than well-studied nearby examples, the degeneracies between galaxies at very different redshifts but presenting similar colors over a finite range of observed passbands, dust (the eternal scourge of observational astronomy, expected to be an especially severe affliction in the ultraviolet that gets redshifted into the near-IR for high-z objects, both because dust is very efficient at scattering UV photons and because this efficiency varies a lot with metallicity and the exact gran size distribution of the dust), when is a dropout really a dropout indicating the location of the Lyman break and when is it just a lousy upper limit of a shabby detection, etc. – I could go on, but I think I already have. It will take time to sort these things out, even in the best of worlds.
We do not live in the best of worlds.
It appears that a big part of the current uncertainty is a calibration error. There is a pipeline for handling JWST data that has an in-built calibration for how many counts in a JWST image correspond to what astronomical magnitude. The JWST instrument team warned us that the initial estimate of this calibration would “improve as we go deeper into Cycle 1” – see slide 13 of Jane Rigby’s AAS presentation.
I was not previously aware of this caveat, though I’m certainly not surprised by it. This is how these things work – one makes an initial estimate based on the available data, and one improves it as more data become available. Apparently, JWST is outperforming its specs, so it is seeing as much as 0.3 magnitudes deeper than anticipated. This means that people were inferring objects to be that much too bright, hence the appearance of lots of galaxies that seem to be brighter than expected, and an apparent systematic bias to high z for photometric redshift estimators.
I was not at the AAS meeting, let alone Dr. Rigby’s presentation there. Even if I had been, I’m not sure I would have appreciated the potential impact of that last bullet point on nearly the last slide. So I’m not the least bit surprised that this error has propagated into the literature. This is unfortunate, but at least this time it didn’t lead to something as bad as the Challenger space shuttle disaster in which the relevant warning from the engineers was reputed to have been buried in an obscure bullet point list.
So now we need to take a deep breath and do things right. I understand the urgency to get the first exciting results out, and they are still exciting. There are still some interesting high z candidate galaxies, and lots of empirical evidence predating JWST indicating that galaxies may have become too big too soon. However, we can only begin to argue about the interpretation of this once we agree to what the facts are. At this juncture, it is more important to get the numbers right than to post early, potentially ill-advised takes on arXiv.
That said, I’d like to go back to writing my own ill-advised take to post on arXiv now.
There has been a veritable feeding frenzy going on with the first JWST data. This is to be expected. Also to be expected is that some of these early results will ultimately prove to have been premature. So – caveat emptor! That said, I want to highlight one important aspect of these early results, there being too many to do all them all justice.
The basic theme is that people are finding very faint yet surprisingly bright galaxies that are consistent with being at redshift 9 and above. The universe has expanded by a factor of ten since then, when it was barely half a billion years old. That’s a long time to you and me, and even to a geologist, but it is a relatively short time for a universe that is now over 13 billion years old, and it isn’t a lot of time for objects as large as galaxies to form.
In the standard LCDM cosmogony, we expect large galaxies to build up from the merger of many smaller galaxies. These smaller galaxies form first, and many of the stars that end up in big galaxies may have formed in these smaller galaxies prior to merging. So when we look to high redshift, we expect to catch this formation-by-merging process in action. We should see lots of small, actively star forming protogalactic fragments (Searle-Zinn fragments in Old School speak) before they’ve had time to assemble into the large galaxies we see relatively nearby to us at low redshift.
So what are we seeing? Here is one example from Labbe et al.:
JWST images of a candidate galaxy at z~10 in different filters, ordered by increasing wavelength from optical light (left) to the mid-infrared (right). Image credit:Labbe et al.
Not much to look at, is it? But really it is pretty awesome for light that has been traveling 13 billion years to get to us and had its wavelength stretched by a factor of ten. Measuring the brightness in these various passbands enables us to estimate both its redshift and stellar mass:
The JWST data plotted as a spectrum (points) with template stellar population models (lines) that indicate a mass of nearly 85 billion suns at z=9.92. Image credit:Labbe et al.
Eighty five billion solar masses is a lot of stars. It’s a bit bigger than the Milky Way, which has had the full 13+ billion years to make its complement of roughly 60 billion solar masses of stars. Object 19424 is a big galaxy, and it grew up fast.
In LCDM, it is not particularly hard to build a model that forms a lot of stars early on. What is challenging is assembling this many into a single object. We should see lots of much smaller fragments (and may yet still) but we shouldn’t see many really big objects like this already in place. How many there are is a critical question.
Labbe et al. make an estimate of the stellar mass density in massive high redshift galaxies, and find it to be rather a lot. This is a fraught exercise in the best of circumstances when one has excellent data for thousands of galaxies. Here we have only a handful. We must also assume that the small region surveyed is typical, which it may not be. Moreover, the photometric redshift method illustrated above is fraught. It looks convincing. It is convincing. It also gives me the heebie-jeebies. Many times I have seen photometric redshifts turn out to be wrong when good spectroscopic data are obtained. But usually the method works, and it’s what we got so far, so let’s see where this ride takes us.
A short paper that nicely illustrates the prime issue is provided by Prof. Boylan-Kolchin. His key figure:
The integrated mass density of stars as a function of the stellar mass of individual galaxies, or equivalently, the baryons available to form stars in their dark matter halos. The data of Labbe et al. reside in the forbidden region (shaded) where there are more stars than there is normal matter from which to make them. Image credit: Boylan-Kolchin.
The basic issue is that there are too many stars in these big galaxies. There are many astrophysical uncertainties about how stars form: how fast, how efficiently, with what mass distribution, etc., etc. – much of the literature is obsessed with these issues. In contrast, once the parameters of cosmology are known, as we think them to be, it is relatively straightforward to calculate the number density of dark matter halos as a function of mass at a given redshift. This is the dark skeleton on which large scale structure depends; getting this right is absolutely fundamental to the cold dark matter picture.
Every dark matter halo should host a universal fraction of normal matter. The baryon fraction (fb) is known to be very close to 16% in LCDM. Prof. Boylan-Kolchin points out that this sets an important upper limit on how many stars could possibly form. The shaded region in the figure above is excluded: there simply isn’t enough normal matter to make that many stars. The data of Labbe et al. fall in this region, which should be impossible.
The data only fall a little way into the excluded region, so maybe it doesn’t look that bad, but the real situation is more dire. Star formation is very inefficient, but the shaded region assumes that all the available material has been converted into stars. A more realistic expectation is closer to the gray line (ε = 0.1), not the hard limit where all the available material has been magically turned into stars with a cosmic snap of the fingers.
Indeed, I would argue that the real efficiency ε is likely lower than 0.1 as it is locally. This runs into problems with precursors of the JWST result, so we’ve already been under pressure to tweak this free parameter upwards. Turning it up to eleven is just the inevitable consequence of needing to get more stars to form in the first big halos to appear sooner than the theory naturally predicts.
So, does this spell doom for LCDM? I doubt it. There are too many uncertainties at present. It is an intriguing result, but it will take a lot of follow-up work to sort out. I expect some of these candidate high redshift galaxies will fall by the wayside, and turn out to be objects at lower redshift. How many, and how that impacts the basic result, remains to be determined.
After years of testing LCDM, it would be ironic if it could be falsified by this one simple (expensive, technologically amazing) observation. Still, it is something important to watch, as it is at least conceivable that we could measure a stellar mass density that is impossibly high. Wither then?
I went on a bit of a twitter bender yesterday about the early claims about high mass galaxies at high redshift, which went on long enough I thought I should share it here.
For those watching the astro community freak out about bright, high redshift galaxies being detected by JWST, some historical context in an amusing anecdote…
The 1998 October conference was titled “After the dark ages, when galaxies were young (the universe at 2 < z < 5).” That right there tells you what we were expecting. Redshift 5 was high – when the universe was a mere billion years old. Before that, not much going on (dark ages).
This was when the now famous SN Ia results corroborating the acceleration of the expansion rate predicted by concordance LCDM were shiny and new. Many of us already strongly suspected we needed to put the Lambda back in cosmology; the SN results sealed the deal.
One of the many lines of evidence leading to the rehabilitation of Lambda – previously anathema – was that we needed a bit more time to get observed structures to form. One wants the universe to be older than its contents, an off and on problem with globular clusters for forever.
A natural question that arises is just how early do galaxies form? The horizon of z=7 came up in discussion at lunch, with those of us who were observers wondering how we might access that (JWST being the answer long in the making).
Famed simulator Carlos Frenk was there, and assured us not to worry. He had already done LCDM simulations, and knew the timing.
“There is nothing above redshift 7.”
He also added “don’t quote me on that,” which I’ve respected until now, but I think the statute of limitations has expired.
Everyone present immediately pulled out their wallet and chipped in $5 to endow the “7-up” prize for the first persuasive detection of an object at or above redshift seven.
A committee was formed to evaluate claims that might appear in the literature, composed of Carlos, Vera Rubin, and Bruce Partridge. They made it clear that they would require a high standard of evidence: at least two well-identified lines; no dropouts or photo-z’s.
That standard wasn’t met for over a decade, with z=6.96 being the record holder for a while. The 7-up prize was entirely tongue in cheek, and everyone forgot about it. Marv Leventhal had offered to hold the money; I guess he ended up pocketing it.
I believe the winner of the 7-up prize should have been Nial Tanvir for GRB090423 at z~8.2, but I haven’t checked if there might be other credible claims, and I can’t speak for the committee.
At any rate, I don’t think anyone would now seriously dispute that there are galaxies at z>7. The question is how big do they get, how early? And the eternal mobile goalpost, what does LCDM really predict?
Carlos was not wrong. There is no hard cutoff, so I won’t quibble about arbitrary boundaries like z=7. It takes time to assemble big galaxies, & LCDM does make a reasonably clear prediction about the timeline for that to occur. Basically, they shouldn’t be all that big that soon.
Here is a figure adapted from the thesis Jay Franck wrote here 5 years ago using Spitzer data (round points). It shows the characteristic brightness (Schechter M*) of galaxies as a function of redshift. The data diverge from the LCDM prediction (squares) as redshift increases.
The divergence happens because real galaxies are brighter (more stellar mass has assembled into a single object) than predicted by the hierarchical timeline expected in LCDM.
Remarkably, the data roughly follow the green line, which is an L* galaxy magically put in place at the inconceivably high redshift of z=10. Galaxies seem to have gotten big impossibly early. This is why you see us astronomers flipping our lids at the JWST results. Can’t happen.
Except that it can, and was predicted to do so by Bob Sanders a quarter century ago: “Objects of galaxy mass are the first virialized objects to form (by z=10) and larger structure develops rapidly.”
The reason is MOND. After decoupling, the baryons find themselves bereft of radiation support and suddenly deep in the low acceleration regime. Structure grows fast and becomes nonlinear almost immediately. It’s as if there is tons more dark matter than we infer nowadays.
I referreed that paper, and was a bit disappointed that Bob had beat me to it: I was doing something similar at the time, with similar results. Instead of being hard to form structure quickly as in LCDM, it’s practically impossible to avoid in MOND.
He beat me to it, so I abandoned writing that paper. No need to say the same thing twice! Didn’t think we’d have to wait so long to test it.
I’ve reviewed this many times. Most recently in January, in anticipation of JWST, on my blog.
But you get the point. Every time you see someone describe the big galaxies JWST is seeing as unexpected, what they mean is unexpected in LCDM. It doesn’t surprise me at all. It is entirely expected in MOND, and was predicted a priori.
The really interesting thing to me, though, remains what LCDM really predicts. I already see people rationalizing excuses. I’ve seen this happen before. Many times. That’s why the field is in a rut.
Progress towards the dark land.
So are we gonna talk our way out of it this time? I’m no longer interested in how; I’m sure someone will suggest something that will gain traction no matter how unsatisfactory.
Special pleading.
The only interesting question is if LCDM makes a prediction here that can’t be fudged. If it does, then it can be falsified. If it doesn’t, it isn’t science.
Experimentalist with no clue what he has signed up for about to find out how hard it is to hunt down an invisible target.
But can we? Is LCDM subject to falsification? Or will we yet again gaslight ourselves into believing that we knew it all along?
