The Milky Way and its nearest giant neighbor Andromeda (M31) are surrounded by a swarm of dwarf satellite galaxies. Aside from relatively large beasties like the Large Magellanic Cloud or M32, the majority of these are the so-called dwarf spheroidals. There are several dozen examples known around each giant host, like the Fornax dwarf pictured above.

Dwarf Spheroidal (dSph) galaxies are ellipsoidal blobs devoid of gas that typically contain a million stars, give or take an order of magnitude. Unlike globular clusters, that may have a similar star count, dSphs are diffuse, with characteristic sizes of hundreds of parsecs (vs. a few pc for globulars). This makes them among the lowest surface brightness systems known.

This subject has a long history, and has become a major industry in recent years. In addition to the “classical” dwarfs that have been known for decades, there have also been many comparatively recent discoveries, often of what have come to be called “ultrafaint” dwarfs. These are basically dSphs with luminosities less than 100,000 suns, sometimes being comprised of as little as a few hundred stars. New discoveries are being made still, and there is reason to hope that the LSST will discover many more. Summed up, the known dwarf satellites are proverbial drops in the bucket compared to their giant hosts, which contain hundreds of billions of stars. Dwarfs could rain in for a Hubble time and not perturb the mass budget of the Milky Way.

Nevertheless, tiny dwarf Spheroidals are excellent tests of theories like CDM and MOND. Going back to the beginning, in the early ’80s, Milgrom was already engaged in a discussion about the predictions of his then-new theory (before it was even published) with colleagues at the IAS, where he had developed the idea during a sabbatical visit. They were understandably skeptical, preferring – as many still do – to believe that some unseen mass was the more conservative hypothesis. Dwarf spheroidals came up even then, as their very low surface brightness meant low acceleration in MOND. This in turn meant large mass discrepancies. If you could measure their dynamics, they would have large mass-to-light ratios. Larger than could be explained by stars conventionally, and larger than the discrepancies already observed in bright galaxies like Andromeda.

This prediction of Milgrom’s – there from the very beginning – is important because of how things change (or don’t). At that time, Scott Tremaine summed up the contrasting expectation of the conventional dark matter picture:

“There is no reason to expect that dwarfs will have more dark matter than bright galaxies.” *

This was certainly the picture I had in my head when I first became interested in low surface brightness (LSB) galaxies in the mid-80s. At that time I was ignorant of MOND; my interest was piqued by the argument of Disney that there could be a lot of as-yet undiscovered LSB galaxies out there, combined with my first observing experiences with the then-newfangled CCD cameras which seemed to have a proclivity for making clear otherwise hard-to-see LSB features. At the time, I was interested in finding LSB galaxies. My interest in what made them rotate came  later.

The first indication, to my knowledge, that dSph galaxies might have large mass discrepancies was provided by Marc Aaronson in 1983. This tentative discovery was hugely important, but the velocity dispersion of Draco (one of the “classical” dwarfs) was based on only 3 stars, so was hardly definitive. Nevertheless, by the end of the ’90s, it was clear that large mass discrepancies were a defining characteristic of dSphs. Their conventionally computed M/L went up systematically as their luminosity declined. This was not what we had expected in the dark matter picture, but was, at least qualitatively, in agreement with MOND.

My own interests had focused more on LSB galaxies in the field than on dwarf satellites like Draco. Greg Bothun and Jim Schombert had identified enough of these to construct a long list of LSB galaxies that served as targets my for Ph.D. thesis. Unlike the pressure-supported ellipsoidal blobs of stars that are the dSphs, the field LSBs we studied were gas rich, rotationally supported disks – mostly late type galaxies (Sd, Sm, & Irregulars). Regardless of composition, gas or stars, low surface density means that MOND predicts low acceleration. This need not be true conventionally, as the dark matter can do whatever the heck it wants. Though I was blissfully unaware of it at the time, we had constructed the perfect sample for testing MOND.

Having studied the properties of our sample of LSB galaxies, I developed strong ideas about their formation and evolution. Everything we had learned – their blue colors, large gas fractions, and low star formation rates – suggested that they evolved slowly compared to higher surface brightness galaxies. Star formation gradually sputtered along, having a hard time gathering enough material to make stars in their low density interstellar media. Perhaps they even formed late, an idea I took a shining to in the early ’90s. This made two predictions: field LSB galaxies should be less strongly clustered than bright galaxies, and should spin slower at a given mass.

The first prediction follows because the collapse time of dark matter halos correlates with their larger scale environment. Dense things collapse first and tend to live in dense environments. If LSBs were low surface density because they collapsed late, it followed that they should live in less dense environments.

I didn’t know how to test this prediction. Fortunately, fellow postdoc and office mate in Cambridge at the time, Houjun Mo, did. It came true. The LSB galaxies I had been studying were clustered like other galaxies, but not as strongly. This was exactly what I expected, and I thought sure we were on to something. All that remained was to confirm the second prediction.

At the time, we did not have a clear idea of what dark matter halos should be like. NFW halos were still in the future. So it seemed reasonable that late forming halos should have lower densities (lower concentrations in the modern terminology). More importantly, the sum of dark and luminous density was certainly less. Dynamics follow from the distribution of mass as Velocity2 ∝ Mass/Radius. For a given mass, low surface brightness galaxies had a larger radius, by construction. Even if the dark matter didn’t play along, the reduction in the concentration of the luminous mass should lower the rotation velocity.

Indeed, the standard explanation of the Tully-Fisher relation was just this. Aaronson, Huchra, & Mould had argued that galaxies obeyed the Tully-Fisher relation because they all had essentially the same surface brightness (Freeman’s law) thereby taking variation in the radius out of the equation: galaxies of the same mass all had the same radius. (If you are a young astronomer who has never heard of Freeman’s law, you’re welcome.) With our LSB galaxies, we had a sample that, by definition, violated Freeman’s law. They had large radii for a given mass. Consequently, they should have lower rotation velocities.

Up to that point, I had not taken much interest in rotation curves. In contrast, colleagues at the University of Groningen were all about rotation curves. Working with Thijs van der Hulst, Erwin de Blok, and Martin Zwaan, we set out to quantify where LSB galaxies fell in relation to the Tully-Fisher relation. I confidently predicted that they would shift off of it – an expectation shared by many at the time. They did not.

The Tully-Fisher relation: disk mass vs. flat rotation speed (circa 1996). Galaxies are binned by surface brightness with the highest surface brightness galaxies marked red and the lowest blue. The lines show the expected shift following the argument of Aaronson et al. Contrary to this expectation, galaxies of all surface brightnesses follow the same Tully-Fisher relation.

I was flummoxed. My prediction was wrong. That of Aaronson et al. was wrong. Poking about the literature, everyone who had made a clear prediction in the conventional context was wrong. It made no sense.

I spent months banging my head against the wall. One quick and easy solution was to blame the dark matter. Maybe the rotation velocity was set entirely by the dark matter, and the distribution of luminous mass didn’t come into it. Surely that’s what the flat rotation velocity was telling us? All about the dark matter halo?

Problem is, we measure the velocity where the luminous mass still matters. In galaxies like the Milky Way, it matters quite a lot. It does not work to imagine that the flat rotation velocity is set by some property of the dark matter halo alone. What matters to what we measure is the combination of luminous and dark mass. The luminous mass is important in high surface brightness galaxies, and progressively less so in lower surface brightness galaxies. That should leave some kind of mark on the Tully-Fisher relation, but it doesn’t.

Residuals from the Tully-Fisher relation as a function of size at a given mass. Compact galaxies are to the left, diffuse ones to the right. The red dashed line is what Newton predicts: more compact galaxies should rotate faster at a given mass. Fundamental physics? Tully-Fisher don’t care. Tully-Fisher don’t give a sh*t.

I worked long and hard to understand this in terms of dark matter. Every time I thought I had found the solution, I realized that it was a tautology. Somewhere along the line, I had made an assumption that guaranteed that I got the answer I wanted. It was a hopeless fine-tuning problem. The only way to satisfy the data was to have the dark matter contribution scale up as that of the luminous mass scaled down. The more stretched out the light, the more compact the dark – in exact balance to maintain zero shift in Tully-Fisher.

This made no sense at all. Over twenty years on, I have yet to hear a satisfactory conventional explanation. Most workers seem to assert, in effect, that “dark matter does it” and move along. Perhaps they are wise to do so.

Working on the thing can drive you mad.

As I was struggling with this issue, I happened to hear a talk by Milgrom. I almost didn’t go. “Modified gravity” was in the title, and I remember thinking, “why waste my time listening to that nonsense?” Nevertheless, against my better judgement, I went. Not knowing that anyone in the audience worked on either LSB galaxies or Tully-Fisher, Milgrom proceeded to derive the MOND prediction:

“The asymptotic circular velocity is determined only by the total mass of the galaxy: Vf4 = a0GM.”

In a few lines, he derived rather trivially what I had been struggling to understand for months. The lack of surface brightness dependence in Tully-Fisher was entirely natural in MOND. It falls right out of the modified force law, and had been explicitly predicted over a decade before I struggled with the problem.

I scraped my jaw off the floor, determined to examine this crazy theory more closely. By the time I got back to my office, cognitive dissonance had already started to set it. Couldn’t be true. I had more pressing projects to complete, so I didn’t think about it again for many moons.

When I did, I decided I should start by reading the original MOND papers. I was delighted to find a long list of predictions, many of them specifically to do with surface brightness. We had just collected fresh data on LSB galaxies, which provided a new window on the low acceleration regime. I had the data to finally falsify this stupid theory.

Or so I thought. As I went through the list of predictions, my assumption that MOND had to be wrong was challenged by each item. It was barely an afternoon’s work: check, check, check. Everything I had struggled for months to understand in terms of dark matter tumbled straight out of MOND.

I was faced with a choice. I knew this would be an unpopular result. I could walk away and simply pretend I had never run across it. That’s certainly how it had been up until then: I had been blissfully unaware of MOND and its perniciously successful predictions. No need to admit otherwise.

Had I realized just how unpopular it would prove to be, maybe that would have been the wiser course. But even contemplating such a course felt criminal. I was put in mind of Paul Gerhardt’s admonition for intellectual honesty:

“When a man lies, he murders some part of the world.”

Ignoring what I had learned seemed tantamount to just that. So many predictions coming true couldn’t be an accident. There was a deep clue here; ignoring it wasn’t going to bring us closer to the truth. Actively denying it would be an act of wanton vandalism against the scientific method.

Still, I tried. I looked long and hard for reasons not to report what I had found. Surely there must be some reason this could not be so?

Indeed, the literature provided many papers that claimed to falsify MOND. To my shock, few withstood critical examination. Commonly a straw man representing MOND was falsified, not MOND itself. At a deeper level, it was implicitly assumed that any problem for MOND was an automatic victory for dark matter. This did not obviously follow, so I started re-doing the analyses for both dark matter and MOND. More often than not, I found either that the problems for MOND were greatly exaggerated, or that the genuinely problematic cases were a problem for both theories. Dark matter has more flexibility to explain outliers, but outliers happen in astronomy. All too often the temptation was to refuse to see the forest for a few trees.

The first MOND analysis of the classical dwarf spheroidals provides a good example. Completed only a few years before I encountered the problem, these were low surface brightness systems that were deep in the MOND regime. These were gas poor, pressure supported dSph galaxies, unlike my gas rich, rotating LSB galaxies, but the critical feature was low surface brightness. This was the most directly comparable result. Better yet, the study had been made by two brilliant scientists (Ortwin Gerhard & David Spergel) whom I admire enormously. Surely this work would explain how my result was a mere curiosity.

Indeed, reading their abstract, it was clear that MOND did not work for the dwarf spheroidals. Whew: LSB systems where it doesn’t work. All I had to do was figure out why, so I read the paper.

As I read beyond the abstract, the answer became less and less clear. The results were all over the map. Two dwarfs (Sculptor and Carina) seemed unobjectionable in MOND. Two dwarfs (Draco and Ursa Minor) had mass-to-light ratios that were too high for stars, even in MOND. That is, there still appeared to be a need for dark matter even after MOND had been applied. One the flip side, Fornax had a mass-to-light ratio that was too low for the old stellar populations assumed to dominate dwarf spheroidals. Results all over the map are par for the course in astronomy, especially for a pioneering attempt like this. What were the uncertainties?

Milgrom wrote a rebuttal. By then, there were measured velocity dispersions for two more dwarfs. Of these seven dwarfs, he found that

“within just the quoted errors on the velocity dispersions and the luminosities, the MOND M/L values for all seven dwarfs are perfectly consistent with stellar values, with no need for dark matter.”

Well, he would say that, wouldn’t he? I determined to repeat the analysis and error propagation.

Mass-to-light ratios determined with MOND for eight dwarf spheroidals (named, as published in McGaugh & de Blok 1998). The various symbols refer to different determinations. Mine are the solid circles. The dashed lines show the plausible range for stellar populations.

The net result: they were both right. M/L was still too high for Draco and Ursa Minor, and still too low for Fornax. But this was only significant at the 2σ level, if that – hardly enough to condemn a theory. Carina, Leo I, Leo II, Sculptor, and Sextans all had fairly reasonable mass-to-light ratios. The voting is different now. Instead of going 2 for 5 as Gerhard & Spergel found, MOND was now 5 for 8. One could choose to obsess about the outliers, or one could choose to see a more positive pattern.  Either a positive or a negative spin could be put on this result. But it was clearly more positive than the first attempt had indicated.

The mass estimator in MOND scales as the fourth power of velocity (or velocity dispersion in the case of isolated dSphs), so the too-high M*/L of Draco and Ursa Minor didn’t disturb me too much. A small overestimation of the velocity dispersion would lead to a large overestimation of the mass-to-light ratio. Just about every systematic uncertainty one can think of pushes in this direction, so it would be surprising if such an overestimate didn’t happen once in a while.

Given this, I was more concerned about the low M*/L of Fornax. That was weird.

Up until that point (1998), we had been assuming that the stars in dSphs were all old, like those in globular clusters. That corresponds to a high M*/L, maybe 3 in solar units in the V-band. Shortly after this time, people started to look closely at the stars in the classical dwarfs with the Hubble. Low and behold, the stars in Fornax were surprisingly young. That means a low M*/L, 1 or less. In retrospect, MOND was trying to tell us that: it returned a low M*/L for Fornax because the stars there are young. So what was taken to be a failing of the theory was actually a predictive success.


And Gee. This is a long post. There is a lot more to tell, but enough for now.

*I have a long memory, but it is not perfect. I doubt I have the exact wording right, but this does accurately capture the sentiment from the early ’80s when I was an undergraduate at MIT and Scott Tremaine was on the faculty there.

12 thoughts on “Dwarf Satellite Galaxies and Low Surface Brightness Galaxies in the Field. I.

  1. hello,

    in light of Positron Annihilation into Dark Matter Experiment, and searches for fifth forces and dark photons,

    is there any papers and research that a new fifth force, long range like gravity, acting only on baryons, could reproduce MOND, and even CMB third peak and large scale structure?

    so “dark matter” isn’t a fermion but a boson that creates a new long range force that acts on baryons. perhaps it is only noticeable when acceleration goes below Ao


    1. There have been various suggestions to the effect that the dark matter could be a boson with an extremely long (galaxy scale) de Broglie wavelength that would behave as required, hopefully on all scales.
      I think we need to pass through a period of chaos in which many such ideas are tried and most discarded. But first we have to get out of the mindset that ordinary CDM will succeed where it has persistently failed. We also have to be cautious of overselling such ideas (SIDM being the poster child for excessive enthusiasm at present).


      1. I’ve head that, and Sabine Hossfelder’s most recent post is on the related idea of superfluid dark matter, an idea of dark matter that mimics MOND. maybe all your research will live on as superfluid dark matter?


  2. You mention, “Problem is, we measure the velocity where the luminous mass still matters. In galaxies like the Milky Way, it matters quite a lot. It does not work to imagine that the flat rotation velocity is set by some property of the dark matter halo alone.”
    Could dark matter in the background of all observations explain this?


  3. Not quite sure what you mean… a background of dark matter? In any case, no – the point is that the luminous mass contributes a substantial fraction of the budget of the rotation curve. Rearranging that mass should thus affect the amplitude thereof. It doesn’t.


    1. The concept of a background of dark matter would suggest to me that space has higher curvature. So I am wondering if MOND can be viewed as a spacetime transformation in light of the curvature imposed by a dark matter background.
      However, this concept may require either a reinterpretation or a dualistic interpretation of the Cosmological Principle.


      1. Sorry, I should explain that I consider the “dark matter background” to imply mass located beyond the observable universe, like a singular primordial black hole or Cosmic Black Hole.


  4. I had to look SIDM up. Pretty funny. Our theoretical physicists, who seem congenitally incapable of imagining a world without their beloved dark matter, are hard at work trying to gin up a model of gravitational viscosity for dm that might resuscitate their dying, imaginary friend.

    These theorists have never, AFAIK, made a credible effort to model gravitational viscosity for the actual, observable, baryonic matter in galaxies. In that regard, they seem like the man who crosses the street without looking because he doesn’t want to see something that scares him.


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