I have always been interested in the extremes of galaxy properties, especially to low surface brightness (LSB). LSB galaxies are hard to find and observe, so they present an evergreen opportunity for discovery. They also expose theories built to explain bright galaxies to novel tests.
Fundamental properties of galaxies include their size and luminosity. The luminosity L is a proxy for stellar mass while the size R is one measure of how those stars are distributed. The surface brightness S is the luminosity spread over an area 2πR2, so S = L/2πR2. One may define different types of radii and corresponding surface brightnesses, but whatever the choice, only two of these three quantities are independent. At a minimum, one needs at least two parameters to quantitatively describe a galaxy, as galaxies of the same luminosity* can have their light spread over different areas.
Being composed of tens of billions of stars, it ought to take a lot more than two parameters to describe a galaxy. A useful shorthand for galaxy appearance is provided by morphological types. I’m not a huge fan (they’re not quantitative and don’t relate simply to quantitative measures), but saying a spiral galaxy is an Sa or an Sc does provide a great shorthand for evoking their appearance.
If we step back from the detailed difference in the appearance of the spiral arms of Sb and Sbc and Sc galaxies, there are some interesting physical distinctions between early type spirals (Sa – Sc) and later types (Sd on through Irr). These are all late type galaxies (LTGs) that are thin, rotationally supported disks of stars and gas. I’m not going to talk about pressure supported early type galaxies (ETGs) here, just early (Sa – Sc) and late (Sd – Irr) LTGs+.
My colleague Jim Schombert pointed out in 2006 that LTGs segregated into two sequences in size and stellar mass if not in gas mass. So early LTGs are more compact for their mass and late LTGs more diffuse.
Another distinction is in the gas fraction. This correlates with surface brightness, and early and late LTGs tend to be either star-dominated or gas dominated.
There are early LTGs with such low gas fractions that their current star formation rate risks using up all the available gas in just a Gyr or so. This seems a short time for a galaxy that has been forming stars for the past 13 Gyr, which has led to a whole subfield obsessed with how such galaxies may be resupplied with fresh gas from the IGM to keep things going. That may happen, and I’m sure it does at some level, but I think the concern with this being a terrible timing coincidence is misplaced, as there are lots of late LTGs with ample gas. The median gas fraction is 2/3 for the late LTGs above: they have twice as much gas as stars, and they can sustain their observed star formation rates for tens of Gyr, sometimes hundreds of Gyr. There are plenty of galaxies that need no injection of fresh gas. Similarly, there are genuine ETGs that are “red and dead”: some galaxies do stop forming stars. So perhaps those with short depletion times are just weary giants near the end of the road?
That paragraph may cause an existential crisis for an entire subfield, but I didn’t come here to talk about star formation winding down. No, I wanted to highlight an update to the size-mass relation provided by student Zichen Hua. No surprise, Schombert was right. Here is the new size-mass relation for gas, stars, and baryons (considering both stars and gas together):
The half-mass radius R50 is a distinct quantity for each component: gas alone, stars alone, or both$ together. All the galaxies are on the same sequence if we only look at the gas: the surface density of atomic gas is similar in all of them#. When we look at the stars, there are two clear groups: the star-dominated early LTGs (red points) and the gas-rich late LTGs (blue points). This difference in the stars persists when translated into baryons – since the stars dominate the baryonic mass budget of the early LTGs, the gas makes little difference to their baryonic size. The opposite is the case for the gas rich galaxies, and the scatter is reduced as gas is included in the baryonic size. There are some intermediate cases, but the gap between between distinct groups is real, as best we can tell. Certainly it has become more clear than it was in 2006 when Schombert had only optical data (the near-IR helps for getting at stellar mass), and the two sequences are more clearly defined in baryons than in stars alone.
A related result is that of Tully & Verheijen (1997), who found a bimodality in surface brightness. Remember above, only two of luminosity, size, and surface brightness are independent. So a bimodality in surface brightness would be two parallel lines cutting diagonally across the size-stellar mass plane. That’s pretty much what we see in the two sequences.
Full disclosure: I was the referee of Tully & Verheijen (1997), and I didn’t want to believe it. I did not see such an effect in the data available to me, and they were looking at the Ursa Major cluster, which I suspected might be a special environment. However, they were the first to have near-IR data, something I did not have at the time. Moreover, they showed that the segregation into different groups was not apparent with optical data; it only emerged in the near-IR K-band. I had no data to contradict that, so while it seemed strange to me, I recommended the paper for publication. Turns out they were right^.
I do not understand why there are two sequences. Tully & Verheijen (1997) suggest that there are different modes of disk stability, so galaxies fall into one or the other. That seems reasonable in principle, but I don’t grasp how it works. I am not alone. There is an enormous literature on disk stability; it is largely focused on bars and spirals in star-dominated systems. It’s a fascinating and complex subject that people have been arguing about for decades. Rather less has been done for gas-dominated systems.
It is straightforward to simulate stellar dynamics. Not easy, mind you, but at least stars are very well approximated as point masses on the scale of galaxies. Not so the gas, for which one needs a hydro code. These are notoriously messy. One persistent result is that systems tend to become unstable when there is too much gas. And yet, nature seems to have figured it out as we see lots of gas rich galaxies. Their morphology is different, so there seems to be an interplay between surface brightness, gas content, and disk stability. Perhaps Tully & Verheijen’s supposition about stability modes is related to the gas content.
That brings us to other scaling relations. Whatever is going on to segregate galaxies in the size-mass plane is not doing it in the velocity-mass plane (the BTFR). There should be a dependence on radius or surface brightness along the BTFR. There really should be, but there is not. Another, related scaling relation is that of specific angular momentum with mass. These three are shown together here:
As with luminosity, size, and surface brightness, only two of these three plots are independent. Velocity and size specify the specific angular momentum j ~ V*R, so the right panel is essentially a convolution of the left and middle panels. There is very little scatter in the BTFR (left) but a lot in size-mass (middle), so you wind up with something intermediary in the j-M plane (right).
I hope that sounds trivial, because it is. It hardly warrants mention, in my opinion. However, my opinion on this point is not widely shared; there are a lot of people who make a lot of hay about the specific angular momentum of disk galaxies.
In principle this attention to j-M makes sense. Angular momentum is a conserved quantity, after all. Real physics, not just astronomical scaling relations. Moreover, one can quantify the angular momentum acquired by dark matter halos in simulations. The spin parameter thus defined seems to do a good job of explaining the size-mass relation, which appears to follow if angular momentum is conserved. In this picture, LSB galaxies form in halos with large initial spin, so they end up spread out, while HSB galaxies form in low spin halos. How far the baryons collapse just depends on that initial angular momentum.
This is one of those compelling idea that nature declined to implement. First, an objection in principle: this hinges on the baryons conserving their share of the angular momentum. The angular momentum of the whole must be conserved (absent external torques), but the whole includes both baryons and dark matter. These two components are free to exchange angular momentum with each other, and there is every reason to expect they do so. In that case, the angular momentum of the baryons need not appear to be conserved: some could be acquired from or lost to the dark matter, where it becomes invisible. As baryons collapse to form a visible galaxy at the center of a dark matter halo, it is easy for them to lose angular momentum to the dark matter. That’s exactly what happens simulations, even in the first simulations to look into this: it was an eye-opening result to me in 1993, and yet in 2025 people still pretend like baryon-only angular momentum conservation has something to do with galaxy formation. They tend to argue that it gets the size-mass relation right, so it must work out, no?
Does it though? I’ve written about this before, and the answer is not really. Models that predict about the right size-mass relation predict the wrong Tully-Fisher relation, and vice-versa. You can squeeze the toothpaste tube on one end to make it flat, but the bulge simply moves somewhere else. So I find the apparent agreement between disk sizes and angular momenta to be more illusory than compelling. Heck, even Frank van den Bosch agrees with me that you can’t get a realistic disk from the initial distribution of angular momentum j(r). Frank built his career& contradicting me, so if we agree about something y’all should take note.
That was all before the current results. The distribution of initial spins is a continuous function that is lognormal: it has a peak and a width. Translating that% into the size distribution predicts a single size-mass relation with finite scatter. It does not predict two distinct families for gas-poor and gas-rich disk galaxies. The new results are completely at odds with this picture.
That might not be apparent to advocates of the spin-size interpretation. If one looks at the j-M (right) panel, it seems like a pretty good correlation by the standards of extragalactic astronomy. So if you’re thinking in those terms, all may seem well, and the little kink between families is no big deal. Those are the wrong terms to think in. The correlation in j-M is good because that in the BTFR plane is great. The BTFR is the more fundamental relation; j is not fundamental, it’s just the BTFR diluted by the messier size-mass relation. That’s it.
One can work out the prediction for angular momentum in MOND. That’s the dotted line in the j-M panel above. MOND gets the angular momentum right: the observed trend follows the dotted line. It is possible for galaxies to have more or less angular momentum at a given mass, so there is some scatter, as observed. Again, that’s it.
*A common assertion I frequently hear, mostly from theorists, is that mass is the only galaxy parameter that matters. This is wrong now just as it was thirty years ago. I never cease to be amazed at the extent to which a simple, compelling concept outweighs actual evidence.
+So there are “early” late types. I suppose the earliest of LTGs is the S0, which is also the latest of ETGs. There are only a few S0’s in the SPARC sample, so I’m just gonna lump them in with the other early LTGs. Morphology is reproducible – experts can train others who subsequently perform as well as the experts – but it’s not like all experts agree about all classifications, and S0 is the most confounding designation.
$I recall giving a talk about LSB galaxies at UC Santa Cruz in the ’90s. In the discussion afterwards, Sandy Faber asked whether, instead of optical scale lengths, we should be talking about baryonic scale lengths instead. Both the audience and I were like
wut?
All that we had then were measures of the scale size of the stars in optical light, so the phrasing didn’t even compute at the time. But of course she was right, and R50,bar above is such a measure.
#A result I recall from my thesis is that the dynamic range in stellar surface brightness was huge while that in the gas surface density was small: a factor of 1,000 in Σ* might correspond to a factor of 2 or maybe 3 in Σg.
^It happens a lot in astronomy that a seemingly unlikely result later proves to be correct. That’s why we need to be open-minded as referees. Today’s blasphemy is tomorrow’s obvious truth.
&Career advice for grad students: find some paper of mine from 15 – 20 years ago. Update it with a pro-LCDM spin. You’ll go far.
%There was a time when the narrow distribution of spins in simulations was alleged to explain the narrow distribution of surface brightness known as Freeman’s Law. This wasn’t right. Doing the actual math, the “narrow” spin distribution maps to a broad surface brightness distribution – not a single value, nor a bimodal distribution. Here is an example spin distribution:
Rather than a narrow Freeman’s Law, there should be galaxies of all different surface brightness, over a broad range. The spin distribution above maps into the dashed line below:
Mapping spin to surface brightness predicts galaxies that are well above the Freeman value. Such very HSB galaxies do not exist, at least not as disks, so one had to insert a cut off by hand in dark matter models that would otherwise support such galaxies.
In contrast, an upper limit to galaxy surface brightness arises naturally in MOND. Only disks with surface density less than a0/G are stable.
!OK, I guess an obvious question is how surface brightness correlates with morphological type. I didn’t want to get into how the morphological T-type does or doesn’t correlate with quantitative measures, but here is this one example. Yes, there’s a correlation, but there is also a lot of meaningless scatter. LSBs tend to be late LTGs, but can be found among the early LTGs, and vice-versa for HSBs. Despite the clear trend, a galaxy with a central baryonic surface density of 1,000 M☉ pc-2 could be in any bin of morphology.
This messy correlation is par for the course for plots involving morphology, and for extragalactic astronomy in general. This is why the small scatter in the BTFR and the RAR is so amazing – that never happens!
Hi Stacy,
Off topic, but perhaps interesting: I’ve been t(h)inkering with the idea of the Hubble constant as a (quantum?) property of space itself: every bit of space slowly generating new bits of space, so not just between galaxies but also within galaxies. I’ve calculated that for the sun this gives an increase of distance to the MW centre of 532 m/s (not as velocity, but due to space expanding). Since MOND is scale invariant, such a gradual scaling of distances is no problem for the galaxy stability in the deepMOND regime, right? In fact, since rotation curves are often flat at their max value, I wonder if it is a problem outside the deepMOND regime?
What such an analysis implies is a scaling factor of ~1.07/Gyr which multiplies to 2.5 over ~13.5 Gyr. Thus the radius of galaxies is expected to be 2.5 times as small at z ~ 10. Assuming they host the same amount of stars as close by, that increases the surface brightness by a factor 6.25 which comes quite close to 1+z. Would it be possible that this explains partly why Tolman test results fall short one factor of (1+z)?
In LCDM however, the slow upscaling of distances within a galaxy would be a runaway effect: if in a few years an orbit radius increases with 1 km, that decreases gravity towards the centre. That makes the object spiral outward, first slightly but since that decreases gravity further it will pretty quickly leave the galaxy. Solving this issue by adding a little velocity towards the galaxy centre does not work: after half an orbit that added velocity still points in the wrong direction! And I don’t know exactly how to analyze adding dark matter, but one needs a delicate balance between spiraling in (2nd derivative) versus space expansion (which affects the orbit as 1st derivative, assuming a stable orbit). I wouldn’t bet on that being realized for so many galaxies.
Do you know has MOND ever been used to model the formation of the Moon? Although strongly in the Newtonian regime, could the billions of years of evolution reveal some statistically significant distinctions in MOND for something that is now so well studied and constrained?
Specifically the moon, no, not that I’m aware of. People have looked into other solar system effects, especially in the outer solar system. There are some analyses that indicate that MOND could be responsible for the signal that leads to the inference of Planet 9. There are also analyses of the orbits of long term comets that say no way, now how is MOND going on in the outer solar system. So shruggy emoticon.
What stands out in your new analysis is how the size–mass scatter contrasts with the tightness of the BTFR: only the extended, rotation-supported systems settle onto the low-acceleration branch so cleanly. Those galaxies seem to have crossed the characteristic acceleration scale a₀, at which point the baryonic disk stops exchanging substantial angular momentum with other baryonic components and begins to behave as if its own j were conserved. The more compact or disturbed systems, where internal torques still dominate, remain above that threshold and scatter accordingly. The bifurcation you highlight looks very much like galaxies occupying different dynamical phases depending on how far they’ve progressed along that threshold.
Yes, that’s similar to what Tully & Verheijen argued.
What do you think about this paper from earlier this month, it seems important: https://academic.oup.com/mnras/article/544/1/975/8281988
They found a new correlation between Sn brightness and host galaxy age, in which dimmer SNe are in younger galaxies, with high significance. The sample was much larger than the work in the ’90s that suggested an accelerating expansion, and the finding seems to remove that conclusion, and instead suggests the expansion is decelerating.
The corrected curve it leads to lands very close to the unexplained DESI curve from earlier this year (figure 9). Both show the expansion first decelerating as far as 6.65 Gyr, then accelerating to 11.8 Gyr, then decelerating again. These two curves landing almost on top of each other, which came from different methods, mean we may have finally got the universe’s expansion history, after a century of trying. One section of the paper’s title includes the phrase ‘a new concordance’, which is partly about the fact that the LCDM curve goes way off elsewhere.
So it’s now even harder to make dark energy just lambda. To fill this hole in the jigsaw, we’ve already cut a detailed fake piece of the puzzle, that fits the hole mathematically. But we have no explanation, and it seems that for the curve to vary as it does, at least two things must be varying. There’s also no explanation for the correlation between Sn brightness and host galaxy age, which tends to be linear. To me these are new places where the data is crying out for conceptual progress, and a new conceptual approach to make that possible.
So, yes, I think we’re just throwing free parameters around at this point. First it was CDM, then Lambda, now the dark energy equation of state. There’s enough freedom now to fit any monotonic set of redshift-distance data.
Do we need to go there? Meh. It is easy for me to believe there is a systematic in SNIa peak luminosities that may evolve over time. This one looks really big to me, and feels like it may be an artifact. DESI by itself I found more convincing, and I didn’t really find that particularly convincing. Which is to say, I don’t think LCDM is really in extra trouble from these observations, even if I also think LCDM is already it’s own trouble as both the L and the CDM are already fudge factors.
Your remark that “ΛCDM is already its own trouble” strongly resonates: once the free parameters begin to dominate the “explanatory” content, the line between explanation and curve-fitting starts to blur. At that point, the question isn’t whether a new observation adds “extra” trouble, but that the model has accumulated enough adjustable structure to absorb almost any tension by construction—drifting into the territory of being, in the Pauli sense, not even wrong.
So if both Lambda and CDM are fudge factors of such magnitude how is it possible to cling to GR as a valid cosmological theory? I mean it seems the only coherent reaction would either be to pathetically (given the observations) keep endorsing the fudge factors as real as the majority of the community or reject GR its cosmological validiry, no rational middle ground except for associated psychosocial compromises otherwise understandable.
Is the possible empirical success of “smoothed matter overdensity” likely to be an effect due to MOND?
“Galaxy assembly bias in cosmological hydrodynamical simulations: a comparison between SIMBA and IllustrisTNG” by Hong-Gang Yang, Marcos Pellejero, John Peacock, Romeel Davé, 2025
https://arxiv.org/abs/2511.01441
https://en.wikipedia.org/wiki/Halo_occupation_distribution
At a basic level, structure on galaxy scales correlates with structure on larger scales – that’s a property of Gaussian statistics, which hold in either DM or MOND. I presume by “smoothed matter overdensity” they mean the larger scale structure in which a galaxy finds itself, so sure – at this very basic level. I’d have to read it to know if I interpret those words right, which I’m not about to do. All they claim to be doing in the abstract is comparing two LCDM simulations that I know to fail in basic ways. TNG is the simulation I referred to in https://tritonstation.com/2024/12/20/on-the-timescale-for-galaxy-formation/ for describing the redshift evolution; it is too slow in making galaxies at high redshift. Simba I looked at briefly because it showed some rotation curves, but these were so unrealistic that I immediately lost interest.
So whatever they’re talking about, it is just rearranging deck chairs on the Titanic.
Hi Stacy, well this is a bit off topic. By the time I read your posts and read the links I often find that comments are closed. I was thinking of writing to you, but that is a bit intrusive. Anyway here goes.
I’ve been looking at the discrepancy you see in MoND for galaxy clusters. I know you don’t like the idea of MoND and DM, but let’s use this discrepancy as a prediction of a DM mass. So a prediction from MoND of the mass. Now I tried some very stupid ways of doing this, (like escape velocity from a galaxy cluster) but it didn’t work… escape from where in the cluster. And following some of your recent posts I think this calculation is much more difficult. It should not be treated as some steady state but a transient in galaxy formation. I would need to do some calculation like R.H. Sanders did in ‘Cosmology with MoND. And to be honest I only understood ~1/2 of that paper. So First I wonder if anyone else has done such a calculation/ prediction. And second I did a stupid estimate of my own. So I took the cluster mass where MoND starts to deviate to be about 10^12 solar masses. I then calculated the terminal velocity of that size mass in MoND (v^4 = a_0 * G * M) and equated that velocity to the velocity of some primordial particle from the big bang 1/2 m * v^2 = k*T, for the temperature I took 2K (I think that’s the right number) and I got a mass of something like 100eV. (I’ll have to check again, I did this silly calc a few times and …) OK this is a silly equivalence, but there may be a bit of truth in it. Mostly I think that MoND predicts that if a DM particle exists it should be light. In the 10 to 1000 eV range.
Thanks for you blog and attention.
Indeed. Something similar was suggested by Garry Angus https://arxiv.org/abs/0805.4014 who posits an 11eV sterile neutrino as a candidate for the unseen mass in clusters. This has inspired a fair amount of work no the so-called nuHDM model, e.g., https://arxiv.org/abs/2506.19196. Other possibilities along these lines remain to be explored.
Thanks, I think I’ve read the Garry Angus paper, but I’ve got a printer now and should do it again. The other is new to me so thanks. (I just want to make sure MoND sticks it’s flag in the light DM prediction :^)
Professor Milgrom states, “I have argued on many occasions … that understanding and formulating MOND in a relativistic framework may require completely new concepts that are, at present, beyond our ken. For example, the “coincidence” of the MOND constant, a0, with cosmologically significant accelerations, makes cosmology the only strong-gravity relativistic system in the MOND regime. This may point to MOND having to be understood together with cosmology as inseparable aspects of the same FUNDAMOND, and not as some relativistic meta-theory for which cosmology is only a special solution.”
Milgrom, Mordehai. “The deep-MOND limit–a study in Primary vs secondary predictions.” arXiv preprint arXiv:2510.16520 (2025). page 2 of https://arxiv.org/abs/2510.16520
Professor Witten states, “A dream would be to get a concrete clue from experiment about what is the energy scale for new physics beyond the Higgs particle.”
“Witten reflects.” CERN Courier, 21 December 2021, page 3 of 6
https://www.ias.edu/sites/default/files/Witten%20reflects%20–%20CERN%20Courier.pdf
My guess is that a hybrid of FUNDAMOND with one or more types of dark matter particles will fail due to group theoretical problems — in other words, there might be no plausible stringy dark-matter-particle groups between U(!) X SU(2) X SU(3) and SO(32). My opinion is that Guendelman’s “Dynamical String Tension Theories with target space scale invariance SSB and restoration” solves string theory’s swampland problem & suggests that there might be 3 different types of inertia (Newton-Einstein, FUNDAMOND, and another related to dark energy) based on 3 different types of string tension. However, my guesses and opinions might be completely worthless. I think pro-MOND astronomers & astrophysicists should try to identify the world’s most talented, young theoretical physicists and convince them to work on FUNDAMOND.
Well, yes – physicists seeking experimental motivation for fundamentally new physics have proven adept at ignoring evidence that’s right in front of them. Only it’s not – the string community starts from the premise that all fundamental physics stems from symmetry groups of the sort you note. The corollary of that attitude is that all other fields are not fundamental, so there can not possibly be any indication of new fundamental physics from mere astronomy.
What do you think about this claim which runs contrary to the mainstream? (How it might relates to MOND I have speculated a bit on in previous post comments.)
What seems obvious is that, as an active observer, we have to actively remove the objective reality to arrive at such (i.e. Rovelli) subjective or relational perspective. The universe doesn’t start off quantum and emerge into the classical. The opposite is true. It is classical, and only by removing the classical interactions can our perspective reveal something so physically relational. Reality doesn’t emerge from QM, rather it disappears from view when actively shielded. It is the opposite of emergent. Our perspective is what is emergent. Same holds true for cosmology, we will be left with our perspective and subjective experience after shielding out the objective reality.
I don’t really have a strong opinion on this.
does MOND better than dm explains why
arXiv:2511.19736 (gr-qc)
[Submitted on 24 Nov 2025]
General relativity, early galaxy formation and the JWST observations
Christos G. Tsagas
The James Webb Space Telescope has recently detected massive, fully formed, galaxies at redshifts corresponding to few hundred million years after the Big-Bang. However, our current cosmological model cannot produce such massive systems so early in the lifetime of the universe.
Yes, MOND explains early galaxy formation better than LCDM.
I have no idea what this chap is on about with peculiar velocities. That is a subject that has been thoroughly discussed in the literature, contrary to his assertion that it has been ignored. Perhaps it simply hasn’t been rehashed recently enough.
maybe the two baryonic size–mass sequences are actually hysteresis: once a disk drops below some critical gas surface density it falls into a compact, star-dominated attractor and can’t climb back without a violent gas-rich accretion event.
I was thinking something similar, that galaxies form a condensation sequence. They’re hung up at low surface density, without the ability to form lots of stars (low gas density, low metallicity, low dust content, so little molecular gas) but if they manage to exceed some density threshold then it all snowballs, they form a lot of stars, and you get a high surface brightness stellar disk. There are hints of a third clump of galaxies with dense bulges, but there aren’t enough data here to speculate on whether that is a third step in condensation.