Our cosmology du jour, LCDM, suffers a local missing baryon problem: we don’t detect all of the baryons we expected to find associated with the dark matter halos of individual galaxies. Should we?
Empirically, yes. The stars and cold (atomic and molecular) gas appear to be all that there is to see in late type galaxies. Having additional large reservoirs of baryons results in a fine-tuning problem: the amount of extra stuff must vary precisely with galaxy mass so as not to impact the remarkably tight mass-rotation speed relation.
In theory, no. There are lots of places to stash extra baryons in phases where they are hard to detect. Warm/hot ionized gas in the circum-galactic medium (CGM) is one obvious place to harbor hard-to-detect phase of baryonic material that might add up to a lot of mass. Indeed, in many galaxy formation simulations, lots of mass winds up in the CGM. So what should we expect in LCDM?
That depends on who you ask. I went down a deep rabbit hole about this, both covering many different types of modern hydrodynamical simulations and how what we’ve expected has varied historically. It is a mess. But there are consistent threads: we do expect that galaxies might harbor extensive CGM (for reasons that vary) or that the missing baryons might not be in galaxies at all, having been ejected to the intergalactic medium (IGM) or prevented from accreting in the first place.
Rather than attempt a systematic survey of simulations, I’ll focus here on one example, EAGLE. The reason for this choice is that Mitchell & Schaye (2022) address exactly this subject. Here is their Fig. 1, which shows the baryon content of various components as a function of dark halo mass in the top panel. The bottom panel tracks where the heavy elements are, which is interesting, but I won’t address that here.
There’s a lot going on here! For reference, our Milky Way resides in a ~1012 M☉ halo. Above M200 > 1013 M☉, most objects are groups and clusters where the distinction between centrals and satellites starts to matter. It’s complicated enough without that, so I’ll stick to individual galaxies. On the lower mass end, there’s a huge compression of the large range in stellar mass exhibited by dwarf galaxies into a relatively narrow range of halo mass, so the lower limit of M200 = 1010 M☉ captures many but not all dwarf galaxies.
That’s just the x-axis. The y-axis of the top panel shows the fraction of baryons in each component relative to the amount available in each halo (the product of the cosmic baryon fraction and the halo mass). The colored lines denote five different baryonic mass components. We readily observe two: the stars (black line) and cold gas (green line, denoted ISM in the figure legend). Additional components include gas in the CGM (cyan line) and gas that has been ejected to the IGM (red line) or was never accreted in the first place (blue line).
From this perspective, it seems hopeless to account for all the baryons on a halo-by-halo basis. Large galaxies (1011 < M200 < 1013 M☉) eject most of their baryons (the red line exceeds all others). Lower mass galaxies also eject a lot of baryons, but most of them never get accreted in the first place (the blue line). There are a couple of reasons why accretion might be precluded. One is cosmic reionization: heating of the gas in the early universe by the first UV sources makes the gas too hot to stick to low mass halos: its thermal velocity exceeds their escape speed*. Another is feedback, in which the stars that do form in a galaxy return enough energy to the surrounding gas heat it up enough to prevent it from accreting. The latter process apparently dominates in the EAGLE simulations but which effect really dominates is a topic that simulators love to debate.
The largest reservoir of baryons that sticks to its dark matter halos is the CGM. This exceeds both stars and cold (ISM) gas for all halo masses. The CGM mass fraction increases with mass, which appears to be the opposite of what we need empirically, but really we need to sum up all three of the non-observed components to compare with the unseen baryonic mass that we infer:
That seems unlikely to add up, but it isn’t really possible to check. We don’t measure the missing component (by definition); we only infer its existence from the cosmic baryon fraction. One could laboriously check each simulation to see if the various missing components that should not be detected add up in the right way to explain the data, but one could always wave away any inconsistency by tweaking how many baryons get lost to the IGM. Between ejection to the IGM, prevention of accretion in the first place, and a quasi-undetectable CGM, the prospects for rigorously testing simulations are limited. However, each of these are distinct effects that occur in combination. This exacerbates the fine-tuning problem: not only does the unaccounted-for mass have to vary just so, these different mechanisms must somehow conspire to makes it so. It does not inspire confidence that this will work out when one realizes that these different mechanisms behave differently in different simulations.
We are not able to directly test the fraction of baryons that are prevented from accreting or that are ejected to the IGM. We have only the vaguest of constraints on the CGM restricted to massive galaxies. But we do measure the stellar and ISM gas mass, so we can compare the EAGLE simulation above to the data:
To the eye habituated to astronomical accuracy, the stellar mass fraction in the left panel works out pretty well. The gray band representing the simulations does more or less the same thing as the data. However, this is one of the occasions on which we can fool ourselves with log-log plots. The bands are offset from the data by a factor that is not modest. The width of the bands already accounts for the plausible variation in the velocity fudge factor. One can of course consider implausible values of fv, but the shape is also a problem. If we make an adjustment to match intermediate mass galaxies, the difference from high mass galaxies gets worse. One could make further tweaks, but this is a hopeless game as the shape problem stems from the curvature that is inevitable in abundance matching relations and the lack thereof in Tully-Fisher.
The gas content of EAGLE simulated galaxy-like objects does not compare well to the observed ISM in real galaxies (right panel). Gas is historically the hardest part to do in large magnetohydrodynamical cosmological simulations, so I’ve cut simulators a lot of slack, only occasionally pointing out that this doesn’t work out. But it really doesn’t work out, so if they want me to cut them slack then they should refrain% from asserting that everything works out. It has become a tiresome, decades-long refrain that has never panned out.
The problem for cold ISM gas in massive galaxies in EAGLE is that there isn’t enough of it. The problem in intermediate mass galaxies is that there really isn’t enough of it. The typical value is off by an order of magnitude at M200 ~ 1011 M☉. The problem in low mass galaxies is that it isn’t there at all. They typical EAGLE object with M200 < 1010.5 M☉ has no cold gas at all. Such objects should not exist, apparently. But gas rich, low masses galaxies are boilerplate examples of observational reality, so it is a substantial problem for a simulation if such things are predicted to be rare$.
There are many other LCDM simulations on the market. At most one of them can be correct. EAGLE is a reasonable example for illustrating what galaxy formation should plausibly do. Though not perfect, it is a reasonable representative of the LCDM brand. In this context, it makes sense to me that there would be all these various baryonic components and reservoirs. But reality doesn’t look like that. We add up the stars and cold gas and we’re done; anything extra involves fine-tuning. Maybe there should be more stuff associated with galaxies, but the fine-tuning problem this entails augers otherwise.
*I started to say a lot more about this here, but decided it was too deep a rabbit hole, so instead refer to a note about a conversation I had with Colin Norman on what the reionization scale should be.
%The sociology in the simulation community seems to be to assert complete success in explaining everything at all times until the next batch of simulations completes running, then point out all the improvements. Everything is explained all the time, only more so as time goes on.
$There is one caveat of comparing apples and oranges. The galaxies for which we have gas data are generally blue, late type (mostly dwarf irregular) galaxies. So we should make this comparison to similar objects in the simulation, but this distinction was not made by Mitchell & Schaye (2022). Persisting in my habit of giving the LCDM paradigm every benefit of the doubt, one can imagine that there is an as-yet undiscovered population of very low surface brightness galaxies that are red and gas poor pervading the universe, and that EAGLE is predicting these things are out there waiting to be discovered. The gas fractions are low because there are a lot of gas poor galaxies that we haven’t discovered yet. Having spent much of my career seeking low surface brightness galaxies, I’ve never been disappointed that there are more of them out there. I have, however, routinely been disappointed that there are enough of them to solve huge numerical discrepancies like this.
This is a very useful way to frame the problem. One possible conjecture is that the missing term is not primarily a hidden baryon reservoir attached to each halo, but a history-dependent response of the local gravitational medium to the baryons that actually cooled into the observed galaxy.
If the stars and cold gas are the components that strongly set the local clock/signal-propagation state, then the tight mass-rotation relation would be expected to follow the observed baryonic disk rather than the total baryon allotment from the cosmic fraction. The CGM, expelled gas, and never-accreted gas would still exist, but they would not contribute to the same local response in the same way. That would make a halo-by-halo baryon inventory a misleading target: simulations would be forced to hide ordinary mass in just the right phase and location, while the real regularity is being controlled by the visible baryonic source geometry plus the medium response it induces.
In that picture, the EAGLE mismatch in cold gas is not just a subgrid-feedback nuisance. It may be a sign that the simulation is trying to solve a response problem as an inventory problem. The low scatter of the baryonic relation would then be telling us that the dynamically relevant “missing” piece is coupled to the local baryon distribution, not freely adjustable among CGM, IGM, and prevented-accretion channels.
There’s a structural reason for that tiresome refrain: when the unobservable reservoirs are not just empirically difficult but architecturally untestable in combination, a framework can run indefinitely without breaking visibly.
The three mechanisms you identify, CGM, IGM ejection, prevented accretion, each plausible in isolation, untestable in concert, conspiring to track galaxy mass just so, that is not a prediction, it is a description of what epicyclic rescue looks like when it has more than one lever to pull.
The BTFR’s tightness is the empirical counterargument that is already sitting on the table: stars plus cold gas closes the account, and anything extra requires these mechanisms to cancel precisely.
Frameworks that need that kind of conspiracy are usually telling you something about their regime of validity, not about the universe.
Reductionists always face a Moravec’s scenario when extending frameworks validated in simple contexts to more complex ones.
When the latency of the empirical feedback loop is relatively short, the reflex of invoking hidden entities becomes untenable fast: symbolic AI surrendered to neural networks and deep learning when it hit embodied robotics, the luminiferous ether didn’t survive Michelson-Morley, and hidden variables in quantum mechanics didn’t survive Bell.
But when empirical feedback is slow or structurally out of reach, calcification sets in instead.
Epicycles kept geocentrism alive for over a thousand years. Dark matter and dark energy have been doing the same job for decades now, and the combination of three mutually compensating unobservable reservoirs you describe here, CGM, IGM ejection, prevented accretion, suggests the patch is getting more elaborate, not more convincing.
There is no single universal framework because the very structure of any framework automatically limits its range of applicability.
What does appear to be universal are structural properties of physics that produce a layered, hierarchical reality, and the mapping between effective description and hierarchical level is becoming increasingly clear in cosmology:
Simple gravitational systems → General Relativity
Galaxies → MOND
Galaxy clusters → something else
….
A natural extension to large scales and long timeframes of the existing picture at shorter scales and timeframes already given by effective field theories. Each level demands its own effective description, valid within its regime and not beyond it. Gravity is contextual, as is anything else with physical meaning.
Some people point to Neptune or elementary particles as examples of successful predictions of hidden entities. What they omit or ignore is that those predictions were made well inside the validated domain of the theories that produced them.
The issue is not predicting unseen entities. The issue is extrapolating a framework far beyond the regime where it has been empirically validated, then treating the resulting discrepancies as evidence for new entities rather than possible evidence that the framework itself has reached its limit.
That’s a good general point about extrapolating beyond the regime of applicability. It certainly applies to dark matter, which is inferred to exist in the low acceleration regime where the only test of dynamics is the data that lead to the inference of dark matter. If one had posed galaxies as a test of inverse-square law gravity, one would say it flunks.
Neptune is a good example of an unseen entity correctly invoked to explain discrepancies within the established realm of theoretical applicability. Vulcan (the hypothetical planet perturbing Mercury’s orbit) would seem to meet that criterion as well, but in that case is turned out to be a modification of gravity, with GR causing the subtle extra perturbation.
Exactly.
The dark matter case goes even further. It does not merely invoke an unseen entity. It invokes an unseen entity with properties that have no analogue in the regimes where General Relativity has been directly validated.
When a framework is pushed across eight orders of magnitude beyond the scales on which it was tested, then rescued by an invisible, non interactive, non dissipative substance alleged to constitute 85% of all matter, it is no longer making a prediction. It is introducing an exception designed to shield the framework from falsification.
Cold dark matter seems to require epicycle machinations to simulate any observations.
The argument for it has usually been that LCDM explains so much of the data that competing ideas can’t. Yet it doesn’t really explain the data, does it?
“Epicycles” is exactly what I thought to myself as I tried very hard to save CDM thirty+ years ago, before I had even considered MOND. So no, it doesn’t explain the dynamical data for galaxies and it never did. When you hear people assert that LCDM explains so much, they are usually referring to cosmological data. Even there, there is a pronounced tendency to simply disregard discrepant data.
There’s a way to tell the difference between an idea that fits the data well and an idea that doesn’t (obviously the less adjustable an idea is the better) – the difference is about an order of magnitude. I’ve found that with a wrong idea, a few things click into place. With a right idea, a few tens of things click into place. (btw, I posted an incorrect interpolation function was working on last time, got there afterwards, thanks for your help.)
Yep. That’s the experience I had with MOND once I allowed myself to consider it. One never has that experience if one doesn’t allow oneself.
What do you all think about Neil Turok’s ideas? As Jonathan suggested, he seems to feel many (if not 10s?) of things are clicking into place.
Which things? That’s ever the issue – people often talk about “dark matter” like it’s a monolithic subject when its more like a dozen different gremlins wrestling underneath the hood.
Well, he claims no new physics is needed, and that dark matter is not cold, but possibly a signal for right handed neutrinos. Some things clicking into place for him I suppose are that we would no longer need inflation, and the hierarchy problem may go away. I’m sure I am not doing his theory justice by trying to summarize it that way.
Personally, I think the discussion from looking very closely at what he suggests could be valuable for MOND theories, even if he is missing talking about it.
I can tell you what I think about his overview ideas about physics, which I very much agree with, rather than his present theories. I talked to Neil Turok for two hours at Cambridge University in 2017, they were filming for a documentary about my interpretation for QM. The British documentary maker sent him a paper of mine, he got interested, and invited us to the Perimeter Institute in Canada, which he was director of at the time. The film people didn’t have the money to cover everything and get the film crew out there, we were wondering about sleeping at the airport, then he said he was visiting his old place of work in Cambridge soon, so we did it there.
We agreed about a lot, disagreed about a lot, he was good to talk to. We agreed about the wood more than the trees – but really got to grips with some issues, and went way off the track I’d been told to keep it on. One issue was the vacuum catastrophe, which he said he saw as the greatest problem in physics at present, and that the next generation of physicists must solve it. I have a good explanation for it, but we weren’t meant to talk about gravity, so I could only discuss the question, not possible answers.
He mentioned that he’d had a new idea, about the big bang being like a mirror, with two offshoots from it. He’s developed that a lot further since then – I don’t know his present work. But the reason we got in touch (apart from the fact the he and Carlo Rovelli both take the ‘interactions, not measurements’ view of QM) was that he’s often called for simplicity in physics, and for putting more effort into the search for an underlying conceptual framework. He speaks his mind, whether you agree or not, and he’s described a ‘crisis in physics’ as being partly due to our theories having got more complicated than the universe they describe. He gave a talk called ‘The astonishing simplicity of everything’, and says simplicity in our theories is now a need, rather than a preference. He saw me as a kind of ‘idiot savant’, except without the savant (only joking), we talked about how both Einstein and Wheeler had predicted an underlying conceptual basis for physics would be found in the future. It’s true that finding a simple explanation is often harder than creating a complicated one.
Thanks for providing that insight. Turok is still developing the mirror universe idea. I think his last paper reintroduces quadratic gravity to support that picture.
A lot of those ideas are really fascinating, and I wonder if his boundary condition where the “big bang” is a mirror isn’t perhaps interchangeable with the boundary condition where the observer is a mirror, after suitable transformation.
Maybe he’s got half the story correct, but the reason it appears so simple is because it isn’t locally real in the same way as you and I are. The complexity doesn’t exactly emerge from a simpler quantum gravity description so much as it disappears from a locally real description of the universe.
So if that is at least half true, what do you all think about the potential validity of this paradox that I came up with? Is it the ramblings of an idiot?
Braun’s Paradox:
The closer we look at the early universe, the more it looks our own age.
Background:
JWST observations appear to be breaking the standard model of cosmology.
Resolution:
Cosmic time is measured by a clock comoving with the expansion of the universe, and determined by applying General Relativity to the FLRW metric, with the boundary conditions where the universe is homogeneous and isotropic on large scales.
We find the age of our local patch of the universe to be about 13.8 Gyr by rewinding the expansion and cosmic clock, and this age is supported by local measurements of structure and evolution of galaxies and stars. At the other end of the scale from our local patch of the universe we expect to see the origin (or at least up to the cosmic horizon).
Now consider that when making measurements of the inhomogeneous and anisotropic structures of galaxies close to our cosmic horizon (as with JWST for example), we must remove all influence on the measurements of our local patch in spacetime, such that what was our locally evolving structure becomes essentially a homogeneous and isotropic background.
Therefore, in order to look closely at the early universe, our local patch should take on the character of the cosmic horizon. As a result, our cosmic clock time (or age) should be reset to the age of the horizon.
The extremely distant galaxies and structures that we then resolve with the oldest light now appear to be about 13.8 Gyr old, as if the scale was flipped the other way.
I don’t want to go outside my field (or down a rabbit hole underneath it), I’m not an astronomer, don’t know much about the measurement process. But it’s great when people engage with your ideas, I felt that when I talked to NT, it was a rare oasis in a desert really. Looking at what you say, I’m seeing some large leaps, which it might not be too possible to make. Like transforming from the big bang being a mirror to the observer being one – that might need more support.
When you say ‘the closer we look at the early universe, the more it looks our own age’, it seems you’re saying the observed age of structures varies depending on the resolution of the observation – that I don’t get. If instead you mean observed age depends on redshift, that comes nearer to something I’m working on – I have a curve where time rate and mass come down in proportion over history for specific reasons, it homgenises galaxy formation times across many eras when you allow for the different contributions of time and mass, so galaxies land on or near it.
Then you say that to correct the JWST measurements, we have to remove all differences between the early universe and present conditions, and that this makes major alterations to a lot of things. But just because time isn’t understood, it doesn’t mean we can use it in a loose way to remove anomalies. It might remove them, but without a cross-corroborated basis for how time works, it gets a bit hit and miss. Perhaps you have more to support those ideas. It’s true there might be an evolving cosmological time rate – there certainly could be undiscovered time rate effects. Time varies its rate in two real local effects that have no explanation, but which give us detailed clues, suggesting more to discover. Like that in one of them matter’s energy is proportional to the time rate, in the other it’s inversely proportional to it. Any explanation for time needs to explain that.
What happens in clusters then, please?
I’m assuming that in these models, galaxies are spherical cows – a lot of symmetry is used to make the maths manageable. Also, that for material is ejected to beyond R200 or for material that is not incorporated relative a particular galaxy, that doesn’t mean it’s not available for the whole cluster.
Am I correct then, in guessing that a cluster would be an amorphous blob, and the ratio of baryonic matter in different places would take eons to settle down? Would not the scatter of a plot of different types of matter in clusters be all over the place?
One advantage of numerical simulations is that nothing needs to be a spherical cow. Particles go where the modeled physics tells them to go. So they’re usually a mess.
The distinction between central and satellites matters for clusters: the “central” galaxy represents the whole cluster; the satellites are all the other objects within it. So I imagine you are correct that if the central ejects stuff it is gone but if satellites eject it some of it might still be available for the whole cluster. Simply doing the book keeping in these sims is a challenge.
Clusters are indeed amorphous blobs, with the settling time depending – short near the center, but perhaps approaching a Hubble time in the outskirts. A related concern is that clusters grow by the infall of groups which is ongoing, so no cluster is ever really settled down.