Month: January 2025

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

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

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

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

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

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

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

That noted, let’s wriggle!

Observational dodges

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

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

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

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

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

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

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

Blame the stars!

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

Super Efficient Star Formation

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

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

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

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

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

The ideas become less plausible from here.

Blame the IMF!

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

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

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

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

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

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

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

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

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

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

Stochastic Star Formation

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

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

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

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

What else?

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

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

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

Triton Station, 8 February 2022

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

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

Richard Feynman

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

It always seems to come down to special pleading:

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

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

Oh, LCDM. LCDM, honey.

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

Old galaxies in the early universe

Old galaxies in the early universe

Continuing our discussion of galaxy formation and evolution in the age of JWST, we saw previously that there appears to be a population of galaxies that grew rapidly in the early universe, attaining stellar masses like those expected in a traditional monolithic model for a giant elliptical galaxy rather than a conventional hierarchical model that builds up gradually through many mergers. The formation of galaxies at incredibly high redshift, z > 10, implies the existence of a descendant population at intermediate redshift, 3 < z < 4, at which point they should have mature stellar populations. These galaxies should not only be massive, they should also have the spectral characteristics of old stellar populations – old, at least, for how old the universe itself is at this point.

Theoretical predictions from Fig. 1 of McGaugh et al (2024) combined with the data of Fig. 4. The data follow the track of a monolithic model that forms early as a single galaxy rather than that of the largest progenitor of the hierarchical build-up expected in LCDM.

The data follow the track of stellar mass growth for an early-forming monolithic model. Do the ages of stars also look like that?

Here is a recent JWST spectrum published by de Graff et al. (2024). This appeared too recently for us to have cited in our paper, but it is a great example of what we’re talking about. This is an incredibly gorgeous spectrum of a galaxy at z = 4.9 when the universe was 1.2 Gyr old.

Fig. 1 from de Graff et al. (2024): JWST/NIRSpec PRISM spectrum (black line) of the massive quiescent galaxy RUBIES-EGS-QG-1 at a redshift of z = 4.8976.

It is challenging to refrain from nerding out at great length over many of the details on display here. First, it is an incredible technical achievement. I’ve seen worse spectra of local galaxies. JWST was built to obtain images and spectra of galaxies so distant they approach the horizon of the observable universe. Its cameras are sensitive to the infrared part of the spectrum in order to capture familiar optical features that have been redshifted by a huge factor (compare the upper and lower x-axes). The telescope itself was launched into space well beyond the obscuring atmosphere of the earth, pointed precisely at a tiny, faint flicker of light in a vast, empty universe, captured photons that had been traveling for billions of years, and transmitted the data to Earth. That this is possible, and works, is an amazing feat of science, engineering, and societal commitment (it wasn’t exactly cheap).

In the raw 2D spectrum (at top) I can see by eye the basic features in the extracted, 1D spectrum (bottom). This is a useful and convincing reality check to an experienced observer even if at first glance it looks like a bug splot smeared by a windshield wiper. The essential result is apparent to the eye; the subsequent analysis simply fills in the precise numbers.

Looking from right to left, the spectrum runs from red to blue. It ramps up then crashes down around an observed wavelength of 2.3 microns. This is the 4000 Å break in the rest frame, a prominent feature of aging stellar populations. The amount of blue-to-red ramp-up and the subsequent depth of drop is a powerful diagnostic of stellar age.

In addition to the 4000 Å break, a number of prominent spectral lines are apparent. In particular, the Balmer absorption lines Hβ, Hγ, and Hδ are clear and deep. These are produced by A stars, which dominate the light of a stellar population after a few hundred million years. There’s the answer right there: the universe is only 1.2 Gyr old at this point, and the stars dominating the light aren’t much younger.

There are also some emission lines. These can be the sign of on-going star formation or an active galactic nucleus powered by a supermassive black hole. The authors attribute these to the latter, inferring that the star formation happened fast and furious early on, then basically stopped. That’s important to the rest of the spectrum; A stars only dominate for a while, and their lines are not so prominent if a population keeps making new stars. So this galaxy made a lot of stars, made them fast, then basically stopped. That is exactly the classical picture of a monolithic giant elliptical.

Here is the star formation history that de Graff et al. (2024) infer:

Fig. 2 from de Graff et al. (2024): the star formation rate (top) and accumulated stellar mass (bottom) as a function of cosmic time (only the first 1.2 Gyr are shown). Results for stellar populations of two metallicities are shown (purple or blue lines). This affects the timing of the onset of star formation, but once going, an enormous mass of stars forms fast, in ~200 Myr.

There are all sorts of caveats about population modeling, but it is very hard to avoid the basic conclusion that lots of stars were assembled with incredible speed. A stellar mass a bit in excess of that of the Milky Way appears in the time it takes for the sun to orbit once. That number need not be exactly right to see that this is not a the gradual, linear, hierarchical assembly predicted by LCDM. The typical galaxy in LCDM is predicted to take ~7 Gyr to assemble half its stellar mass, not 0.1 Gyr. It’s as if the entire mass collapsed rapidly and experienced an intense burst of star formation during violent relaxation (Lynden-Bell 1967).

Collapse of shells within shells to form a massive galaxy rapidly in MOND (Sanders 2008). Note that the inner shells (inset) where most of the stars will be collapse even more rapidly than the overall monolith (dotted line).

Where MOND provides a natural explanation for this observation, the fiducial population model of de Graff et al. violates the LCDM baryon limit: there are more stars than there are baryons to make them from. It should be impossible to veer into the orange region above as the inferred star formation history does. The obvious solution is to adopt a higher metallicity (the blue model) even if that is a worse fit to the spectrum. Indeed, I find it hard to believe that so many stars could be made in such a small region of space without drastically increasing their metallicity, so there are surely things still to be worked out. But before we engage in too much excuse-making for the standard model, note that the orange region represents a double-impossibility. First, the star formation efficiency is 100%. Second, this is for an exceptionally rare, massive dark matter halo. The chances of spotting such an object in the area so far surveyed by JWST is small. So we not only need to convert all the baryons into stars, we also need to luck into seeing it happen in a halo so massive that it probably shouldn’t be there. And in the strictist reading, there still aren’t enough baryons. Does that look right to you?

Do these colors look right to you? Getting the color right is what stellar population modeling is all about.

OK, so I got carried away nerding out about this one object. There are other examples. Indeed, there are enough now to call them a population of old and massive quiescent galaxies at 3 < z < 4. These have the properties expected for the descendants of massive galaxies that form at z > 10.

Nanayakkara et al. (2024) model spectra for a dozen such galaxies. The spectra provide an estimate of the stellar mass at the redshift of observation. They also imply a star formation history from which we can estimate the age/redshift at which the galaxy had formed half of those stars, and when it quenched (stopped forming stars, or in practice here, when the 90% mark had been reached). There are, of course, large uncertainties in the modeling, but it is again hard to avoid the conclusion that lots of stars were formed early.

Figure 7 from McGaugh et al. (2024): The stellar masses of quiescent galaxies from Nanayakkara et al. (2024). The inferred growth of stellar mass is shown for several cases, marking the time when half the stars were present (small green circles) to the quenching time when 90% of the stars were present (midsize orange circles) to the epoch of observation (large red circles). Illustrative star formation histories are shown as dotted lines with the time of formation ti and the quenching timescale τ noted in Gyr. We omit the remaining lines for clarity, as many cross. There is a wide distribution of formation times from very early (ti = 0.2 Gyr) to relatively late (>1 Gyr), but all of the galaxies in this sample are inferred to build their stellar mass rapidly and quench early (τ < 0.5 Gyr).

The dotted lines above are models I constructed in the spirit of monolithic models. The particular details aren’t important, but the inferred timescales are. To put galaxies in this part of the stellar mass-redshift plane, they have to start forming early (typically in the first billion years), form stars at a prolific rate, then quench rapidly (typically with e-folding timescales < 1 Gyr). I wouldn’t say any of these numbers are particularly well-measured, but they are indicative.

What is missing from this plot is the LCDM prediction. That’s not because I omitted it, it’s because the prediction for typical L* galaxies doesn’t fall within the plot limits. LCDM does not predict that typical galaxies should become this massive this early. I emphasize typical because there is always scatter, and some galaxies will grow ahead of the typical rate.

Not only are the observed galaxies massive, they have mature stellar populations that are pretty much done forming stars. This will sound normal to anyone who has studied the stellar populations of giant elliptical galaxies. But what does LCDM predict?

I searched through the Illustris TNG50 and TNG300 simulations for objects at redshift 3 that had stellar masses in the same range as the galaxies observed by Nanayakkara et al. (2024). The choice of z = 3 is constrained by the simulation output, which comes in increments of the expansion factor. To compare to real galaxies at 3 < z < 4 one can either look at the snapshot at z = 4 or the one at z = 3. I chose z = 3 to be conservative; this gives the simulation the maximum amount of time to produce quenched, massive galaxies.

These simulations do indeed produce some objects of the appropriate stellar mass. These are rare, as they are early adopters: galaxies that got big quicker than is typical. However, they are not quenched as observed: the simulated objects are still on the star forming main sequence (the correlation between star formation rate and stellar mass). The distribution of simulated objects does not appear to encompass that of real galaxies.

Figure 8 from McGaugh et al. (2024): The stellar masses and star formation rates of galaxies from Nanayakkara et al. (2024; red symbols). Downward-pointing triangles are upper limits; some of these fall well below the edge of the plot and so are illustrated as the line of points along the bottom. Also shown are objects selected from the TNG50 (Pillepich et al. 2019; filled squares) and TNG300 (Pillepich et al. 2018; open squares) simulations at z = 3 to cover the same range of stellar mass. Unlike the observed galaxies, simulated objects with stellar masses comparable to real galaxies are mostly forming stars at a rapid pace. In the higher-resolution TNG50, none have quenched as observed.

If we want to hedge, we can note that TNG300 has a few objects that are kinda in the right ballpark. That’s a bit misleading, as the data are mostly upper limits. Moreover, these are the rare objects among a set of objects selected to be rare: it isn’t a resounding success if we have to scrape the bottom of the simulated barrel after cherry-picking which barrel. Worse, these few semi-quenched simulated objects are not present in TNG50. TNG50 is the higher resolution simulation, so presumably provides a better handle on the star formation in individual objects. It is conceivable that TNG300 “wins” by virtue of its larger volume, but that’s just saying we have more space in which to discover very rare entities. The prediction is that massive, quenched galaxies should be exceedingly rare, but in the real universe they seem mundane.

That said, I don’t think this problem is fundamental. Hierarchical assembly is still ongoing at this epoch, bringing with it merger-induced star formation. There’s an easy fix for that: change the star formation prescription. Instead of “wet” mergers with gas that can turn into stars, we just need to form all the stars already early on so that the subsequent mergers are “dry” – at least, for those mergers that build this particular population. One winds up needing a new and different mode of star formation. In addition to what we observe locally, there needs to be a separate mode of super-efficient star formation that somehow turns all of the available baryons into stars as soon as possible. That’s basically what I advocate as the least unreasonable possibility for LCDM in our paper. This is a necessary but not sufficient condition; these early stellar nuggets also need to assemble speedy quick to make really big galaxies. While it is straightforward to mess with the star formation prescription in models (if not in nature), the merger trees dictating the assembly history are less flexible.

Putting all the data together in a single figure, we can get a sense for the evolutionary trajectory of the growth of stellar mass in galaxies across cosmic time. This figure extends from the earliest galaxies so-far known at z ~ 14 when the universe was just a few hundred million years old (of order on orbital time in a mature galaxy) to the present over thirteen billion years later. In addition to data discussed previously, it also shows recent data with spectroscopic redshifts from JWST. This is important, as the sense of the figure doesn’t change if we throw away all the photometric redshifts, it just gets a little sparse around z ~ 8.

Figure 10 from McGaugh et al. (2024): The data from Figures 4 and 6 shown together using the same symbols. Additional JWST data with spectroscopic redshifts are shown from Xiao et al. (2023; green triangles) and Carnall et al. (2024). The data of Carnall et al. (2024) distinguish between star-forming galaxies (small blue circles) and quiescent galaxies (red squares); the latter are in good agreement with the typical stellar mass determined from Schechter fits in clusters (large circles). The dashed red lines show the median growth predicted by the Illustris ΛCDM simulation (Rodriguez-Gomez et al. 2016) for model galaxies that reach final stellar masses of M* = 1010, 1011, and 1012 M☉. The solid lines show monolithic models with a final stellar mass of 9 x 1010 M☉ and ti = τ = 0.3, 0.4, and 0.5 Gyr, as might be appropriate for giant elliptical galaxies. The dotted line shows a model appropriate to a monolithic spiral galaxy with ti = 0.5 and τ = 13.5 Gyr.

The solid lines are monolithic models we built to represent classical giant elliptical galaxies that form early and quench rapidly. These capture nicely the upper envelope of the data. They form most of their stars at z > 4, producing appropriately old populations at lower redshifts. The individual galaxy data merge smoothly into those for typical galaxies in clusters.

The LCDM prediction as represented by the Illustris suite of simulations is shown as the dashed red lines for objects of several final masses. These are nearly linear in log(M*)-linear z space. Objects that end up with a typical L* elliptical galaxy mass at z = 0 deviate from the data almost immediately at z > 1. They disappear above z > 6 as the largest progenitors become tiny.

What can we do to fix this? Massive galaxies get a head start, as it were, by being massive at all epochs. But the shape of the evolutionary trajectory remains wrong. The top red line (for a final stellar masses of 1012 M☉) corresponds to a typical galaxy at z ~ 2, but it continues to grow to be atypical locally. The data don’t do that. Even with this boost, the largest progenitor is still predicted to be too small at z > 3 where there are now many examples of massive, quiescent galaxies – known both from JWST observations and from Jay Franck’s thesis before it. Again, the distribution of the data do not look like the predictions of LCDM.

One can abandon Illustris as the exemplar of LCDM, but it doesn’t really help. Other models show similar things, differing only in minor details. That’s because the issue is the mass assembly history they all share, not the details of the star formation. The challenge now is to tweak models to make them look more monolithic; i.e., change those red dashed lines into the solid black lines. One will need super-efficient star formation, if it is even possible. I’ll leave discussion of this and other obvious fudges to a future post.

Finally, note that there are a bunch of galaxies with JWST spectroscopic redshifts from 3 < z < 4 that are not exceptionally high mass (the small blue points). These are expected in any paradigm. They can be galaxies that are intrinsically low mass and won’t grow much further, or galaxies that may still grow a lot, just with a longer fuse on their star formation timescale. Such objects are ubiquitous in the local universe as spiral and irregular galaxies. Their location in the diagram above is consistent with the LCDM predictions, but is also readily explained by monolithic models with long star formation timescales. The dotted line shows a monolithic model that forms early (ti = 0.5) but converts gas into stars gradually (τ = 13.5 Gyr rather than < 1 Gyr). This is a boilerplate model for a spiral that has been around for as long as the short-τ model for giant ellipticals. So while these lower mass galaxies exist, their location in the M*-z plane doesn’t really add much to this discussion as yet. It is the massive galaxies that form early and become quiescent rapidly that most challenge LCDM.

Measuring the growth of the stellar mass of galaxies over cosmic time

Measuring the growth of the stellar mass of galaxies over cosmic time

This post continues the series summarizing our ApJ paper on high redshift galaxies. To keep it finite, I will focus here on the growth of stellar mass. The earlier post discussed what we expect in theory. This depends both on mass assembly (slow in LCDM, fast in MOND), how the assembled mass is converted into stars, and how those stars shine in light we can detect. We know a lot about stars and their evolution, so for this post I will assume we know how to convert a given star formation history into the evolution of the light it produces. There are of course caveats to that which we discuss in the paper, and perhaps will get to in a future post. It’s exhausting to be exhaustive, so not today, Satan.

The principle assumption we are obliged to make, at least to start, is that light traces mass. As mass assembles, some of it turns into stars, and those stars produce light. The astrophysics of stars and the light they produce is the same in any structure formation theory, so with this basic assumption, we can test the build-up of mass. In another post we will discuss some of the ways in which we might break this obvious assumption in order to save a favored theory. For now, we assume the obvious assumption holds, and what we see at high redshift provides a picture of how mass assembles.

Before JWST

This is not a new project; people have been doing it fo for decades. We like to think in terms of individual galaxies, but there are lots out there, so an important concept is the luminosity function, which describes the number of galaxies as a function of how bright they are. Here are some examples:

Figure 3. from Franck & McGaugh (2017) showing the number of galaxies as a function of their brightness in the 4.5 micron band of the Spitzer Space Telescope in candidate protoclusters from z = 2 to 6. Each panel notes the number of galaxies contributing to the Schechter luminosity function+ fit (gray bands), the apparent magnitude m* corresponding to the typical luminosity L*, and the redshift range. The magnitude m* is characteristic of how bright typical galaxies are at each redshift.

One reason to construct these luminosity functions is to quantify what is typical. Hundreds of galaxies inform each fit. The luminosity L* is representative of the typical galaxy, not just anecdotal individual examples. At each redshift, L* corresponds to an observed apparent magnitude m*, which we plot here:

Figure 3 from McGaugh et al. (2024): The redshift dependence of the Spitzer [4.5] apparent magnitude m* of Schechter function fits to populations of galaxies in clusters and candidate protoclusters; each point represents the characteristic brightness of the galaxies in each cluster. The apparent brightness of galaxies gets fainter with increasing redshift because galaxies are more distant, with the amount they dim depending also on their evolution (lines). The purple line is the monolithic exponential model we discussed last time. The orange line is the prediction of the Millennium simulation (the state of the art at the time Jay Franck wrote his thesis) and the Munich galaxy formation model based on it. The open squares are the result of applying the same algorithm to the simulation as used on the data; this is what we would have observed if the universe looked like LCDM as depicted by the Munich model. The real universe does not look like that.

We plot faint to bright going up the y-axis; the numbers get smaller because of the backwards definition of the magnitude scale (which dates to ancient times in which the stars that appeared brightest to the human eye were “of the first magnitude,” then the next brightest of the second magnitude, and so on). The x-axis shows redshift. The top axis shows the corresponding age of the universe for vanilla LCDM parameters. Each point shows the apparent magnitude that is typical as informed by observations of dozens to hundreds of individual galaxies. Each galaxy has a spectroscopic redshift, which we made a requirement for inclusion in the sample. These are very accurate; no photometric redshifts are used to make the plot above.

One thing that impressed me when Jay made the initial version of this plot is how well the models match the evolution of m* at z < 2, which is most of cosmic time (the past ten billion years). This encourages one that the assumption adopted above, that we understand the evolution of stars well enough to do this, might actually be correct. I was, and remain, especially impressed with how well the monolithic model with a simple exponential star formation history matches these data. It’s as if the inferences the community had made about the evolution of giant elliptical galaxies from local observations were correct.

The new thing that Jay’s work showed was that the evolution of typical cluster galaxies at z > 2 persists in tracking the monolithic model that formed early (zf = 10). There is a lot of scatter in the higher redshift data even though there is little at lower redshift. This is to be expected for both observational reasons – the data get rattier at larger distances – and theoretical ones: the exponential star formation history we assume is at best a crude average; at early times when short-lived but bright massive stars are present there will inevitably be stochastic variation around this trend. At later times the law of averages takes over and the scatter should settle down. That’s pretty much what we see.

What we don’t see is the decline in typical brightness predicted by contemporaneous LCDM models. The specific example shown is the Munich galaxy formation model based on the Millennium simulation. However, the prediction is generic: galaxies get faint at high redshift because they haven’t finished assembling yet. This is not a problem of misunderstanding stellar evolution, it is a failure of the hierarchical assembly paradigm.

In order to identify [proto]clusters at high redshift, Jay devised an algorithm to identify galaxies in close proximity on the sky and in redshift space, in excess of the average density around them. One question we had was whether the trend predicted by the LCDM model (the orange line above) would be reproduced in the data when analyzed in this way. To check, Jay made mock observations of a simulated lookback cone using the same algorithm. The results (not previously published) are the open squares in the plot above. These track the “right” answer known directly in the form of the orange line. Consequently, if the universe had looked as predicted, we could tell. It doesn’t.

The above plot is in terms of apparent magnitude. It is interesting to turn this into the corresponding stellar mass. There has also been work done on the subject after Jay’s, so I wanted to include it. An early version of a plot mapping m* to stellar mass and redshift to cosmic time that I came up with was this:

The stellar mass of L* galaxies as a function of cosmic age. Data as noted in the inset. The purple/orange lines represent the monolithic/hierarchical models, as above.

The more recent data (which also predate JWST) follow the same trend as the preceding data. All the data follow the path of the monolithic model. Note that the bulk of the stars are formed in situ in the first few billion years; the stellar mass barely changes after that. There is quite a bit of stellar evolution during this time, which is why m* in the figure above changes in a complicated fashion while the stellar mass remains constant. This again provides some encouragement that we understand how to model stellar populations.

The data in the first billion years are not entirely self-consistent. For example, the yellow points are rather higher in mass than the cyan points. This difference is not one in population modeling, but rather in how much of a correction is made for non-stellar, nebular emission. So as not to go down that rabbit hole, I chose to adopt the lowest stellar mass estimates for the figure that appears in the paper (below). Note that this is the most conservative choice; I’m trying to be as favorable to LCDM as is reasonably plausible.

Figure 4 from McGaugh et al. (2024): The characteristic stellar mass as a function of time with the corresponding redshift noted at the top.

There were more recent models as well as more recent data, so I wanted to include those. There are, in fact, way too many models to illustrate without creating a confusing forest of lines, so in the end I chose a couple of popular ones, Illustris and FIRE. Illustris is the descendant of Millennium, and shows identical behavior. FIRE has a different scheme for forming stars, and does so more rapidly than Illustris. However, its predictions still fall well short of the data. This is because both simulations share the same LCDM cosmology with the same merger tree assembly of structure. Assembling the mass promptly enough is the problem; it isn’t simply a matter of making stars faster.

I’ll show one more version of this plot to illustrate the predicted evolutionary trajectories. In the plots above, I only show models that end up with the mass of a typical local giant elliptical. Galaxies come in a variety of masses, so what does that look like?

The stellar mass of galaxies as a function of cosmic age. Data as above. The orange lines represent the hierarchical models that result in different final masses at z = 0.

The curves of stellar growth predicted by LCDM have pretty much the same shape, just different amplitude. The most massive case illustrated above is reasonable insofar as there are real galaxies that massive, but they are rare. They are also rare in simulations, which make the predicted curve a bit jagged as there aren’t enough examples to define a smooth trajectory as there are for lower mass objects. More importantly, the shape is wrong. One can imagine that the galaxies we see at high redshift are abnormally massive, but even the most massive galaxies don’t start out that big at high redshift. Moreover, they continue to grow hierarchically in LCDM, so they wind up too big. In contrast, the data look like the monolithic model that we made on a lark, no muss, no fuss, no need to adjust anything.

This really shouldn’t have come as a surprise. We already knew that galaxies were impossibly massive at z ~ 4 before JWST discovered that this was also true at z ~ 10. The a priori prediction that LCDM has made since its inception (earlier models show the same thing) fails. More recent models fail, though I have faith that they will eventually succeed. This is the path theorists has always taken, and the obvious path here, as I remarked previously, is to make star formation (or at least light production) artificially more efficient so that the hierarchical model looks like the monolithic model. For completeness, I indulge in this myself in the paper (section 6.3) as an exercise in what it takes to save the phenomenon.

A two year delay

Regular readers of this blog will recall that in addition to the predictions I emphasized when JWST was launched, I also made a number of posts about the JWST results as they started to come in back in 2022. I had also prepared the above as a science paper that is now sections 1 to 3 of McGaugh et al. (2024). The idea was to have it ready to go so I could add a brief section on the new JWST results and submit right away – back in 2022. The early results were much as expected, but I did not rush to publish. Instead, it has taken over two years since then to complete what turned into a much longer manuscript. There are many reasons for this, but the scientific reason is that I didn’t believe many of the initial reports.

JWST was new and exciting and people fell all over themselves to publish things quickly. Too quickly. To do so, they relied on a calibration of the telescope plus detector system made while it was on the ground prior to launch. This is not the same as calibrating it on the sky, which is essential but takes some time. Consequently, some of the initial estimates were off.

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 galaxies shouldn’t exist; the darker region is a where they cannot exist.

In the example above, all of the galaxies had both their initial mass and redshift estimates change with the updated calibration. So I was right to be skeptical, and wait for an improved analysis. I was also right that while some cases would change, the basic interpretation would not. All that happened in the example above was that the galaxies moved from the “can’t exist in LCDM” region (dark blue) into the “really shouldn’t exist in LCDM” region (light blue). However, the widespread impression was that we couldn’t trust photometric redshifts at all, so I didn’t see what new I could justifiably add in 2022. This was, after all, the attitude Jay and I had taken in his CCPC survey where we required spectroscopic redshifts.

So I held off. But then it became impossible to keep up with the fire hose of data that ensued. Every time I got the chance to update the manuscript, I found some interesting new result had been published that I had to include. New things were being discovered faster than I could read the literature. I found myself stuck in the Red Queen’s dilemma, running as fast as possible just to stay in place.

Ultimately, I think the delay was worthwhile. Lots new was learned, and actual spectroscopic redshifts began to appear. (Spectroscopy takes more telescope time than photometry – spreading out the light reduces the signal-to-noise per pixel, necessitating longer exposure times, so it always lags behind. One also discovers the galaxies in the same images that are used for photometry, so it also gets a head start.) Consequently, there is a lot more in the paper than I had planned on. This is another long blog post, so I will end it where I had planned for the original paper to end, with the updated version of the plot above.

Massive galaxies at high redshift from JWST

The stellar masses of galaxies discovered by JWST as a function of redshift is shown below. Unlike most of the plots above, these are individual galaxies rather than typical L* galaxies. Many are based on photometric redshifts, but those in solid black have spectroscopic redshifts. There are many galaxies that reside in a region they should not, at least according to LCDM models: their mass is too large at the observed redshift.

Figure 6 from McGaugh et al. (2024): Mass estimates for high-redshift galaxies from JWST. Colored points based on photometric redshifts are from Adams et al. (2023; dark blue triangles), Atek et al. (2023; green circles), Labbé et al. (2023; open squares), Naidu et al. (2022; open star), Harikane et al. (2023; yellow diamonds), Casey et al. (2024; light blue left-pointing triangles), and Robertson et al. (2024; orange right-pointing triangles). Black points from Wang et al. (2023; squares), Carniani et al. (2024; triangles), Harikane et al. (2024; circles) and Castellano et al. (2024; star) have spectroscopic redshifts. The upper limit for the most massive galaxy in TNG100 (Springel et al. 2018) as assessed by Keller et al. (2023) is shown by the light blue line. This is consistent with the maximum stellar mass expected from the stellar mass–halo mass relation of Behroozi et al. (2020; solid blue line). These merge smoothly into the trend predicted by Yung et al. (2019b) for galaxies with a space density of 10−5 dex−1 Mpc−3 (dashed blue line), though L. Yung et al. (2023) have revised this upward by ∼0.4 dex (dotted blue line). This closely follows the most massive objects in TNG300 (Pillepich et al. 2018; red line). The light gray region represents the parameter space in which galaxies were not expected in LCDM. The dark gray area is excluded by the limit on the available baryon mass (Behroozi & Silk 2018; Boylan-Kolchin 2023). [Note added: I copied this from the caption in our paper, but the links all seem to go to that rather than to each of the cited papers. You can get to them from our reference list if you want, but it’ll take some extra clicks. It looks like AAS has set it up this way to combat trawling by bots.]

One can see what I mean about a fire hose of results from the number of references given here. Despite the challenges of keeping track of all this, I take heart in the fact that many different groups are finding similar results. Even the results that were initially wrong remain problematic for LCDM. Despite all the masses and redshifts changing when the calibration was updated, the bulk of the data (the white squares, which are the black squares in the preceding plot) remain in the problematic region. The same result is replicated many times over by others.

The challenge, as usual, is assessing what LCDM actually predicts. The entire region of this plot is well away from the region predicted for typical galaxies. To reside here, a galaxy must be an outlier. But how extreme an outlier?

The dark gray region is the no-go zone. This is where dark matter halos do not have enough baryons to make the observed mass of stars. It should be impossible for galaxies to be here. I can think of ways to get around this, but that’s material for a future post. For now, it suffices to know that there should be no galaxies in the dark gray region. Indeed, there are not. A few straddle the edge, but nothing is definitively in that region given the uncertainties. So LCDM is not outright falsified by these data. This bar is set very low, as the galaxies that do skirt the edge require that basically all of the available baryons have been converted into starts practically instantaneously. This is not a reasonable.

Not with ten thousand simulations could you do this.

So what is a reasonable expectation for this diagram? That’s hard to say, but that’s what the white and light gray region attempts to depict. Galaxies might plausibly be in the white region but should not be in the light gray region for any sensible star formation efficiency.

One problem with this statement is that it isn’t clear what a sensible star formation efficiency is. We have a good idea of what it needs to be, on average, at low redshift. There is no clear indication that it changes as a function of redshift – at least until we hit results like this. Then we have to be on guard for confirmation bias in which we simply make the star formation efficiency be what we need it to be. (This is essentially what I advocate as the least unreasonable option in section 6.3 of the ApJ paper.)

OK, but what should the limit be? Keller et al. (2023) made a meta-analysis of the available simulations; I have used his analysis and my own reading of the literature to establish the lower boundary of the light gray area. It is conceivable that you would get the occasional galaxy this massive (the white region is OK), but not more so (the light gray region is not OK). The boundary is the most extreme galaxy in each simulation, so as far from typical as possible. The light gray region is really not OK; the only question is where exactly it sets in.

The exact location of this boundary is not easy to define. Different simulations give different answers for different reasons. These are extremal statistics; we’re asking what the one most massive galaxy is in an entire simulation. Higher resolution simulations perceive the formation of small structures like galaxies sooner, but large simulations have more opportunity for extreme events to happen. Which “wins” in terms of making the rare big galaxy early is a competition between these effects that appears, in my reading, to depend on details of simulation implementation that are unlikely to be representative of physical reality (even assuming LCDM is the correct underlying physics).

To make my own assessment, I reviewed the accessible simulations (they don’t all provide the necessary information) to fine the very most massive simulated galaxy as a function of redshift. As ever, I am looking for the case that is most favorable to LCDM. The version I found comes from the large-box, next generation Illustris simulation TNG300. This is the red line a bit into the gray area above. Galaxies really, really should not exist above or to the right of that line. Not only have I adopted the most generous simulation estimate I could find, I have also chosen not to normalize to the area surveyed by JWST. One should do this, but the area so far surveyed is tiny, so the line slides down. Even if galaxies as massive as this exist in TNG300, we have to have been really lucky to point JWST at that spot on a first go. So the red line is doubly generous, and yet there are still galaxies that exceed this limit.

The bottom line is that yes, JWST data pose a real problem for LCDM. It has been amusing watching this break people’s brains. I’ve seen papers that say this is a problem for LCDM because you’d have to turn more than half of the available baryons into stars and that’s crazy talk, and others that say LCDM is absolutely OK because there are enough baryons. The observational result is the same – galaxies with very high stellar-to-dark halo mass ratios, but the interpretation appears to be different because one group of authors is treating the light gray region as forbidden while the other sets the bar at the dark gray region. So the difference in interpretation is not a conflict in the data, but an inconsistency in what [we think] LCDM predicts.

That’s enough for today. Galaxy data at high redshift are clearly in conflict with the a priori predictions of LCDM. This was true before JWST, and remains true with JWST. Whether the observations can be reconciled with LCDM I leave as an exercise for scientists in the field, or at least until another post.

+A minor technical note: the Schechter function is widely used to describe the luminosity function of galaxies, so it provides a common language with which to quantify both their characteristic luminosity L* and space density Φ*. I make use of it here to quantify the brightness of the typical galaxy. It is, of course, not perfect. As we go from low to high redshift, the luminosity function becomes less Schechter-like and more power law-like, an evolution that you can see in Jay Franck’s plot. We chose to use Schechter fits for consistency with the previous work of Mancone et al. (2010) and Wylezalek et al. (2014), and also to down-weight the influence of the few very bright galaxies should they be active galactic nuclei or some other form of contaminant. Long story short, plausible contaminants (no photometric redshifts were used; sample galaxies all have spectroscopic redshifts) cannot explain the bulk of the data; our estimates of m* are robust and, if anything, underestimate how bright galaxies typically are.

A few videos for the new year

A few videos for the new year

Happy new year to those who observe the Gregorian calendar. I will write a post on the observations that test the predictions discussed last time. It has been over a quarter century since Bob Sanders correctly predicted that massive galaxies would form by z = 10, and three years since I reiterated that for what JWST would see on this blog. This is a testament to both the scientific method and the inefficiency of communication.

Here I provide links to some recent interviews on the subject. These are listed in chronological order, which happen to flow in order of increasing technical detail.

The first entry is from my colleague Federico Lelli. It is in Italian rather than English, but short and easy on the ears. If nothing else, appreciate that Dr. Lelli did this on the absence of sleep afforded a new father.

Next is an interview I did with EarthSky. I thought this went well, and should be reasonably accessible.

Next is Scientific Sense:

Most recently, there is the entry from the AAS Journal Author Series. These are based on papers published in the journals of the American Astronomical Society in which authors basically narrate their papers, so this goes through it at an appropriately high (ApJ) level.

We discuss the “little red dots” some, which touches on the issues of size evolution that were discussed in the comments previously. I won’t add to that here beyond noting again that the apparent size evolution is proportional to (1+z), in the sense that high redshift galaxies are apparently smaller than those of similar stellar mass locally. This (1+z) is the factor that relates the angular diameter distance of the Robsertson-Walker metric to that of Euclidean geometry. Consequently, we would not infer any size evolution if the geometry were Euclidean. It’s as if cosmology flunks the Tolman test. Weird.

There is a further element of mystery towards the end where the notion that “we don’t know why” comes up repeatedly. This is always true at some deep philosophical level, but it is also why we construct and test hypotheses. Why does MOND persistently make successful predictions that LCDM did not? Usually we say the reason why has to do with the successful hypothesis coming closer to the truth.

That’s it for now. There will be more to come as time permits.