A brief history of the Radial Acceleration Relation

A brief history of the Radial Acceleration Relation

In science, all new and startling facts must encounter in sequence the responses

1. It is not true!

2. It is contrary to orthodoxy.

3. We knew it all along.

Louis Agassiz (circa 1861)

This expression exactly depicts the progression of the radial acceleration relation. Some people were ahead of this curve, others are still behind it, but it quite accurately depicts the mass sociology. This is how we react to startling new facts.

For quotation purists, I’m not sure exactly what the original phrasing was. I have paraphrased it to be succinct and have substituted orthodoxy for religion, because even scientists can have orthodoxies: holy cows that must not be slaughtered.

I might even add a precursor stage zero to the list above:

0. It goes unrecognized.

This is to say, that if a new fact is sufficiently startling, we don’t just disbelieve it (stage 1); at first we fail to see it at all. We lack the cognitive framework to even recognize how important it is. An example is provided by the 1941 detection of the microwave background by Andrew McKellar. In retrospect, this is as persuasive as the 1964 detection of Penzias and Wilson to which we usually ascribe the discovery. At the earlier time, there was simply no framework for recognizing what it was that was being detected. It appears to me that P&Z didn’t know what they were looking at either until Peebles explained it to them.

The radial acceleration relation was first posed as the mass discrepancy-acceleration relation. They’re fundamentally the same thing, just plotted in a slightly different way. The mass discrepancy-acceleration relation shows the ratio of total mass to that which is visible. This is basically the ratio of the observed acceleration to that predicted by the observed baryons. This is useful to see how much dark matter is needed, but by construction the axes are not independent, as both measured quantities are used in forming the ratio.

The radial acceleration relation shows independent observations along each axis: observed vs. predicted acceleration. Though measured independently, they are not physically independent, as the baryons contribute some to the total observed acceleration – they do have mass, after all. One can construct a halo acceleration relation by subtracting the baryonic contribution away from the total; in principle the remainders are physically independent. Unfortunately, the axes again become observationally codependent, and the uncertainties blow up, especially in the baryon dominated regime. Which of these depictions is preferable depends a bit on what you’re looking to see; here I just want to note that they are the same information packaged somewhat differently.

To the best of my knowledge, the first mention of the mass discrepancy-acceleration relation in the scientific literature is by Sanders (1990). Its existence is explicit in MOND (Milgrom 1983), but here it is possible to draw a clear line between theory and data. I am only speaking of the empirical relation as it appears in the data, irrespective of anything specific to MOND.

I met Bob Sanders, along with many other talented scientists, in a series of visits to the University of Groningen in the early 1990s. Despite knowing him and having talked to him about rotation curves, I was unaware that he had done this.

Stage 0: It goes unrecognized.

For me, stage one came later in the decade at the culmination of a several years’ campaign to examine the viability of the dark matter paradigm from every available perspective. That’s a long paper, which nevertheless drew considerable praise from many people who actually read it. If you go to the bother of reading it today, you will see the outlines of many issues that are still debated and others that have been forgotten (e.g., the fine-tuning issues).

Around this time (1998), the dynamicists at Rutgers were organizing a meeting on galaxy dynamics, and asked me to be one of the speakers. I couldn’t possibly discuss everything in the paper in the time allotted, so was looking for a way to show the essence of the challenge the data posed. Consequently, I reinvented the wheel, coming up with the mass discrepancy-acceleration relation. Here I show the same data that I had then in the form of the radial acceleration relation:

The Radial Acceleration Relation from the data in McGaugh (1999). Plot credit: Federico Lelli. (There is a time delay in publication: the 1998 meeting’s proceedings appeared in 1999.)

I recognize this version of the plot as having been made by Federico Lelli. I’ve made this plot many times, but this is version I came across first, and it is better than mine in that the opacity of the points illustrates where the data are concentrated. I had been working on low surface brightness galaxies; these have low accelerations, so that part of the plot is well populated.

The data show a clear correlation. By today’s standards, it looks crude. Going on what we had then, it was fantastic. Correlations practically never look this good in extragalactic astronomy, and they certainly don’t happen by accident. Low quality data can hide a correlation – uncertainties cause scatter – but they can’t create a correlation where one doesn’t exist.

This result was certainly startling if not as new as I then thought. That’s why I used the title How Galaxies Don’t Form. This was contrary to our expectations, as I had explained in exhaustive detail in the long paper and revisit in a recent review for philosophers and historians of science.

I showed the same result later that year (1998) at a meeting on the campus of the University of Maryland where I was a brand new faculty member. It was a much shorter presentation, so I didn’t have time to justify the context or explain much about the data. Contrary to the reception at Rutgers where I had adequate time to speak, the hostility of the audience to the result was palpable, their stony silence eloquent. They didn’t want to believe it, and plenty of people got busy questioning the data.

Stage 1: It is not true.

I spent the next five years expanding and improving the data. More rotation curves became available thanks to the work of many, particularly Erwin de Blok, Marc Verheijen, and Rob Swaters. That was great, but the more serious limitation was how well we could measure the stellar mass distribution needed to predict the baryonic acceleration.

The mass models we could build at the time were based on optical images. A mass model takes the observed light distribution, assigns a mass-to-light ratio, and makes a numerical solution of the Poisson equation to obtain the the gravitational force corresponding to the observed stellar mass distribution. This is how we obtain the stellar contribution to the predicted baryonic force; the same procedure is applied to the observed gas distribution. The blue part of the spectrum is the best place in which to observe low contrast, low surface brightness galaxies as the night sky is darkest there, at least during new moon. That’s great for measuring the light distribution, but what we want is the stellar mass distribution. The mass-to-light ratio is expected to have a lot of scatter in the blue band simply from the happenstance of recent star formation, which makes bright blue stars that are short-lived. If there is a stochastic uptick in the star formation rate, then the mass-to-light ratio goes down because there are lots of bright stars. Wait a few hundred million years and these die off, so the mass-to-light ratio gets bigger (in the absence of further new star formation). The time-integrated stellar mass may not change much, but the amount of blue light it produces does. Consequently, we expect to see well-observed galaxies trace distinct lines in the radial acceleration plane, even if there is a single universal relation underlying the phenomenon. This happens simply because we expect to get M*/L wrong from one galaxy to the next: in 1998, I had simply assumed all galaxies had the same M*/L for lack of any better prescription. Clearly, a better prescription was warranted.

In those days, I traveled through Tucson to observe at Kitt Peak with some frequency. On one occasion, I found myself with a few hours to kill between coming down from the mountain and heading to the airport. I wandered over to the Steward Observatory at the University of Arizona to see who I might see. A chance meeting in the wild west: I encountered Eric Bell and Roelof de Jong, who were postdocs there at the time. I knew Eric from his work on the stellar populations of low surface brightness galaxies, an interest closely aligned with my own, and Roelof from my visits to Groningen.

As we got to talking, Eric described to me work they were doing on stellar populations, and how they thought it would be possible to break the age-metallicity degeneracy using near-IR colors in addition to optical colors. They were mostly focused on improving the age constraints on stars in LSB galaxies, but as I listened, I realized they had constructed a more general, more powerful tool. At my encouragement (read their acknowledgements), they took on this more general task, ultimately publishing the classic Bell & de Jong (2001). In it, they built a table that enabled one to look up the expected mass-to-light ratio of a complex stellar population – one actively forming stars – as a function of color. This was a big step forward over my educated guess of a constant mass-to-light ratio: there was now a way to use a readily observed property, color, to improve the estimated M*/L of each galaxy in a well-calibrated way.

Combining the new stellar population models with all the rotation curves then available, I obtained an improved mass discrepancy-acceleration relation:

The Radial Acceleration Relation from the data in McGaugh (2004); version using Bell’s stellar population synthesis models to estimate M*/L (see Fig. 5 for other versions). Plot credit: Federico Lelli.

Again, the relation is clear, but with scatter. Even with the improved models of Bell & de Jong, some individual galaxies have M*/L that are wrong – that’s inevitable in this game. What you cannot know is which ones! Note, however, that there are now 74 galaxies in this plot, and almost all of them fall on top of each other where the point density is large. There are some obvious outliers; those are presumably just that: the trees that fall outside the forest because of the expected scatter in M*/L estimates.

I tried a variety of prescriptions for M*/L in addition to that of Bell & de Jong. Though they differed in texture, they all told a consistent story. A relation was clearly present; only its detailed form varied with the adopted prescription.

The prescription that minimized the scatter in the relation was the M*/L obtained in MOND fits. That’s a tautology: by construction, a MOND fit finds the M*/L that puts a galaxy on this relation. However, we can generalize the result. Maybe MOND is just a weird, unexpected way of picking a number that has this property; it doesn’t have to be the true mass-to-light ratio in nature. But one can then define a ratio Q

Equation 21 of McGaugh (2004).

that relates the “true” mass-to-light ratio to the number that gives a MOND fit. They don’t have to be identical, but MOND does return M*/L that are reasonable in terms of stellar populations, so Q ~ 1. Individual values could vary, and the mean could be a bit more or less than unity, but not radically different. One thing that impressed me at the time about the MOND fits (most of which were made by Bob Sanders) was how well they agreed with the stellar population models, recovering the correct amplitude, the correct dependence on color in different bandpasses, and also giving the expected amount of scatter (more in the blue than in the near-IR).

Fig. 7 of McGaugh (2004). Stellar mass-to-light ratios of galaxies in the blue B-band (top) and near-IR K-band (bottom) as a function of BV color for the prescription of maximum disk (left) and MOND (right). Each point represents one galaxy for which the requisite data were available at the time. The line represents the mean expectation of stellar population synthesis models from Bell et al. (2003). These lines are completely independent of the data: neither the normalization nor the slope has been fit to the dynamical data. The red points are due to Sanders & Verheijen (1998); note the weak dependence of M*/L on color in the near-IR.

The obvious interpretation is that we should take seriously a theory that obtains good fits with a single free parameter that checks out admirably well with independent astrophysical constraints, in this case the M*/L expected for stellar populations. But I knew many people would not want to do that, so I defined Q to generalize to any M*/L in any (dark matter) context one might want to consider.

Indeed, Q allows us to write a general expression for the rotation curve of the dark matter halo (essentially the HAR alluded to above) in terms of that of the stars and gas:

Equation 22 of McGaugh (2004).

The stars and the gas are observed, and μ is the MOND interpolation function assumed in the fit that leads to Q. Except now the interpolation function isn’t part of some funny new theory; it is just the shape of the radial acceleration relation – a relation that is there empirically. The only fit factor between these data and any given model is Q – a single number of order unity. This does leave some wiggle room, but not much.

I went off to a conference to describe this result. At the 2006 meeting Galaxies in the Cosmic Web in New Mexico, I went out of my way at the beginning of the talk to show that even if we ignore MOND, this relation is present in the data, and it provides a strong constraint on the required distribution of dark matter. We may not know why this relation happens, but we can use it, modulo only the modest uncertainty in Q.

Having bent over backwards to distinguish the data from the theory, I was disappointed when, immediately at the end of my talk, prominent galaxy formation theorist Anatoly Klypin loudly shouted

“We don’t have to explain MOND!”

It stinks of MOND!

But you do have to explain the data. The problem was and is that the data look like MOND. It is easy to conflate one with the other; I have noticed that a lot of people have trouble keeping the two separate. Just because you don’t like the theory doesn’t mean that the data are wrong. What Anatoly was saying was that

2. It is contrary to orthodoxy.

Despite phrasing the result in a way that would be useful to galaxy formation theorists, they did not, by and large, claim to explain it at the time – it was contrary to orthodoxy so didn’t need to be explained. Looking at the list of papers that cite this result, the early adopters were not the target audience of galaxy formation theorists, but rather others citing it to say variations of “no way dark matter explains this.”

At this point, it was clear to me that further progress required a better way to measure the stellar mass distribution. Looking at the stellar population models, the best hope was to build mass models from near-infrared rather than optical data. The near-IR is dominated by old stars, especially red giants. Galaxies that have been forming stars actively for a Hubble time tend towards a quasi-equilibrium in which red giants are replenished by stellar evolution at about the same rate they move on to the next phase. One therefore expects the mass-to-light ratio to be more nearly constant in the near-IR. Not perfectly so, of course, but a 2 or 3 micron image is as close to a map of the stellar mass of a galaxy as we’re likely to get.

Around this time, the University of Maryland had begun a collaboration with Kitt Peak to build a big infrared camera, NEWFIRM, for the 4m telescope. Rob Swaters was hired to help write software to cope with the massive data flow it would produce. The instrument was divided into quadrants, each of which had a field of view sufficient to hold a typical galaxy. When it went on the telescope, we developed an efficient observing method that I called “four-shooter”, shuffling the target galaxy from quadrant to quadrant so that in processing we could remove the numerous instrumental artifacts intrinsic to its InSb detectors. This eventually became one of the standard observing modes in which the instrument was operated.

NEWFIRM in the lab in Tucson. Most of the volume is for cryogenics: the IR detectors are heliumcooled to 30 K. Partial student for scale.

I was optimistic that we could make rapid progress, and at first we did. But despite all the work, despite all the active cooling involved, we were still on the ground. The night sky was painfully bright in the IR. Indeed, the thermal component dominated, so we could observe during full moon. To an observer of low surface brightness galaxies attuned to any hint of scattered light from so much as a crescent moon, I cannot describe how discombobulating it was to walk outside the dome and see the full fricking moon. So bright. So wrong. And that wasn’t even the limiting factor: the thermal background was.

We had hit a surface brightness wall, again. We could do the bright galaxies this way, but the LSBs that sample the low acceleration end of the radial acceleration relation were rather less accessible. Not inaccessible, but there was a better way.

The Spitzer Space Telescope was active at this time. Jim Schombert and I started winning time to observe LSB galaxies with it. We discovered that space is dark. There was no atmosphere to contend with. No scattered light from the clouds or the moon or the OH lines that afflict that part of the sky spectrum. No ground-level warmth. The data were fantastic. In some sense, they were too good: the biggest headache we faced was blotting out all the background galaxies that shown right through the optically thin LSB galaxies.

Still, it took a long time to collect and analyze the data. We were starting to get results by the early-teens, but it seemed like it would take forever to get through everything I hoped to accomplish. Fortunately, when I moved to Case Western, I was able to hire Federico Lelli as a postdoc. Federico’s involvement made all the difference. After many months of hard, diligent, and exacting work, he constructed what is now the SPARC database. Finally all the elements were in place to construct an empirical radial acceleration relation with absolutely minimal assumptions about the stellar mass-to-light ratio.

In parallel with the observational work, Jim Schombert had been working hard to build realistic stellar population models that extended to the 3.6 micron band of Spitzer. Spitzer had been built to look redwards of this, further into the IR. 3.6 microns was its shortest wavelength passband. But most models at the time stopped at the K-band, the 2.2 micron band that is the reddest passband that is practically accessible from the ground. They contain pretty much the same information, but we still need to calculate the band-specific value of M*/L.

Being a thorough and careful person, Jim considered not just the star formation history of a model stellar population as a variable, and not just its average metallicity, but also the metallicity distribution of its stars, making sure that these were self-consistent with the star formation history. Realistic metallicity distributions are skewed; it turn out that this subtle effect tends to counterbalance the color dependence of the age effect on M*/L in the near-IR part of the spectrum. The net results is that we expect M*/L to be very nearly constant for all late type galaxies.

This is the best possible result. To a good approximation, we expected all of the galaxies in the SPARC sample to have the same mass-to-light ratio. What you see is what you get. No variable M*/L, no equivocation, just data in, result out.

We did still expect some scatter, as that is an irreducible fact of life in this business. But even that we expected to be small, between 0.1 and 0.15 dex (roughly 25 – 40%). Still, we expected the occasional outlier, galaxies that sit well off the main relation just because our nominal M*/L didn’t happen to apply in that case.

One day as I walked past Federico’s office, he called for me to come look at something. He had plotted all the data together assuming a single M*/L. There… were no outliers. The assumption of a constant M*/L in the near-IR didn’t just work, it worked far better than we had dared to hope. The relation leapt straight out of the data:

The Radial Acceleration Relation from the data in McGaugh et al. (2016). Plot credit: Federico Lelli.

Over 150 galaxies, with nearly 2700 resolved measurements within each galaxy, each with their own distinctive mass distribution, all pile on top of each other without effort. There was plenty of effort in building the database, but once it was there, the result appeared, no muss, no fuss. No fitting or fiddling. Just the measurements and our best estimate of the mean M*/L, applied uniformly to every individual galaxy in the sample. The scatter was only 0.12 dex, within the range expected from the population models.

No MOND was involved in the construction of this relation. It may look like MOND, but we neither use MOND nor need it in any way to see the relation. It is in the data. Perhaps this is the sort of result for which we would have to invent MOND if it did not already exist. But the dark matter paradigm is very flexible, and many papers have since appeared that claim to explain the radial acceleration relation. We have reached

3. We knew it all along.

On the one hand, this is good: the community is finally engaging with a startling fact that has been pointedly ignored for decades. On the other hand, many of the claims to explain the radial acceleration relation are transparently incorrect on their face, being nothing more than elaborations of models I considered and discarded as obviously unworkable long ago. They do not provide a satisfactory explanation of the predictive power of MOND, and inevitably fail to address important aspects of the problem, like disk stability. Rather than grapple with the deep issues the new and startling fact poses, it has become fashionable to simply assert that one’s favorite model explains the radial acceleration relation, and does so naturally.

There is nothing natural about the radial acceleration relation in the context of dark matter. Indeed, it is difficult to imagine a less natural result – hence stages one and two. So on the one hand, I welcome the belated engagement, and am willing to consider serious models. On the other hand, if someone asserts that this is natural and that we expected it all along, then the engagement isn’t genuine: they’re just fooling themselves.

Early Days. This was one of Vera Rubin’s favorite expressions. I always had a hard time with it, as many things are very well established. Yet it seems that we have yet to wrap our heads around the problem. Vera’s daughter, Judy Young, once likened the situation to the parable of the blind men and the elephant. Much is known, yes, but the problem is so vast that each of us can perceive only a part of the whole, and the whole may be quite different from the part that is right before us.

So I guess Vera is right as always: these remain Early Days.

A Stellar Population Mystery in a Low Surface Brightness Galaxy

A Stellar Population Mystery in a Low Surface Brightness Galaxy

“Galaxies are made of stars.”

Bob Schommer, quoted by Dave Silva in his dissertation on stellar populations

This tongue-in-cheek quote is a statement of the obvious, at least for the 90+ years since Hubble established that galaxies are stellar systems comparable to and distinct from the Milky Way. There’s interstellar gas and dust too, and I suppose for nearly half that time, people have also thought galaxies to be composed of dark matter. But you can’t see that; the defining characteristic of galaxies is the stars by whose amalgamated light they shine.

The spiral galaxy NGC 7757 (left) and a patch of adjacent sky (right). Both images are 1/4 degree on a side. Most of the sky looks like the patch at right, populated only by scattered stars. You know a galaxy when you see one. These images are based on photographic data obtained using the Oschin Schmidt Telescope on Palomar Mountain as part of the Palomar Observatory Sky Survey-II (POSS-II).

Stellar populations is the term astronomers use to describe the generations of stars that compose the galaxies we observe. The concept was introduced by Walter Baade in a 1944 paper in which he resolved individual stars in Andromeda and companion galaxies, aided by war time blackouts. He noted that some of the stars he resolved had color-magnitude diagrams (CMDs – see below) that resembled that of the solar neighborhood, while others were more like globular clusters. Thus was born Population I and Population II, the epitome of astronomical terminology.

More generally, one can imagine defining lots of populations by tracing groups of stars with a common origin in space and time to the event in which they formed. From this perspective, the Milky Way is the composite of all the star forming events that built it up. Each group has its own age, composition, and orbital properties, and it would be good to have a map that is more detailed than “Pop I” and “Pop II.” Many projects are working to map out these complex details, including ESA’s Gaia satellite, which is producing many spectacular and fundamental results, like the orbit and acceleration of the sun within the Milky Way.

A simple stellar population is a group of stars that all share the same composition and age: they were born of the same material at the same time. Even such a simple stellar population can be rather complicated, as stars form with a distribution of masses (the IMF, for Initial Mass Function) from tiny to massive. The lowest mass stars are those that just barely cross the threshold for igniting hydrogen fusion in their core, which occurs at about 7% of the mass of the sun. Still lower mass objects are called brown dwarfs, and were once considered a candidate for dark matter. Though they don’t shine from fusion like stars, brown dwarfs do glow with the residual heat of their formation through gravitational contraction, and we can now see that there are nowhere near enough of them to be the dark matter. At the opposite end of the mass spectrum, stars many tens of times the mass of the sun are known, with occasional specimens reaching upwards of 100 solar masses. These massive stars burn bright and exhaust their fuel quickly, exploding as supernovae after a few million years – a mere blink of the cosmic eye. By contrast, the lowest mass stars are so faint that they take practically forever to burn through their fuel, and are expected to continue to shine (albeit feebly) for many tens of Hubble times into the future. There is a strong and continuous relation between stellar mass and lifetime: the sun is expected to persist as-is for about 10 billion years (it is just shy of halfway through its “main sequence” lifetime). After a mundane life fusing hydrogen and helium as a main sequence star, the sun will swell into a red giant, becoming brighter and larger in radius (but not mass). This period is much shorter-lived, as are the complex sequence of events that follow it, ultimately leaving behind the naked core as an earth-sized but roughly half solar mass white dwarf remnant.

Matters become more complicated when we consider galaxies composed of multiple generations and different compositions. Nevertheless, we understand well enough the evolution of individual stars – a triumph of twentieth century astronomy – to consider the complex stellar populations of external galaxies. A particular interest of mine are the stellar populations of low surface brightness galaxies. These are late morphological types (often but not always irregular galaxies) that tend to be gas rich and very blue. This requires many young stars, but also implies a low metallicity. This much can be inferred from unresolved observations of galaxies, but the effects of age and composition are often degenerate. The best way to sort this out is to do as Baade did and resolve galaxies into individual stars. This was basically impossible for all but the nearest galaxies before the launch of the Hubble Space Telescope. The resolution of HST allows us to see farther out and deeper into the color-magnitude diagrams of external galaxies.

The low surface brightness galaxy F575-3, as discovered on a POSS-II sky survey plate (left) and as seen by HST (right). Both images are negatives. Only a tiny fraction of the 6.6 degree square POSS-II plate is shown as the image at left covers a mere 1/13 degree on a side. The pink outline shows the still smaller area of sky observed by HST, which visited the object at different roll angles: the differing orientation of the satellite causes the slight twist in the rectangular shape that is imaged. HST resolves individual stars, allowing construction of a color-magnitude diagram. It also resolves background galaxies, which are the majority of the extended objects in this image. Some even shine right through the foreground LSB galaxy!

Collaborator Jim Schombert has long been a leader in studying low surface brightness galaxies, discovering many examples of the class, and leading their study with HST among many stellar contributions. He is one of the unsung heroes without whom the field would be nowhere near where it is today. This post discusses a big puzzle he has identified in the stellar populations of low surface brightness galaxies: the case of the stars with inexplicable[?] IR excesses. Perhaps he has also solved this puzzle, but first we have to understand what is normal and what is weird in a galaxy’s stellar population.

When we resolve a galaxy into stars in more than one filter, the first thing we do is plot a color-magnitude diagram (CMD). The CMD quantifies how bright a star is, and what its color is – a proxy for its surface temperature. Hot stars are blue; cooler ones are red. The CMD is the primary tool by which the evolution of stars was unraveled. Normal features of the CMD include the main sequence (where stars spend the majority of their lives) and the red giant branch (prominent since giant stars are bright if rare). This is what Baade recognized in Populations I and II – stars with CMDs like those near the sun (lots of main sequence stars and some red giants) and those like globular clusters (mostly red giants at bright magnitudes and fainter main sequence stars).

In actively star forming galaxies like F415-3 below, there are plenty of young, massive, bright stars. These evolve rapidly, traipsing across the CMD from blue to red and back to blue and then red again. We can use what we know about stellar evolution to deduce the star formation history of a galaxy – how many stars formed as a function of time. This works quite well for short time periods as massive stars evolve fast and are easy to see, but it becomes increasingly hard for older stars. A galaxy boasts about its age when it is young but becomes less forthcoming as it gets older.

Color-magnitude diagram (CMD) of the low surface brightness galaxy F415-3 observed by HST (Schombert & McGaugh 2015). Each point is one star. The x-axis is color, with bluer stars to the left and redder stars to the right. The y-axis is magnitude: brighter stars are higher; fainter stars are lower. There are many, many stars fainter than those detected here; these observations only resolve the brightest stars that populate the top of the CMD. The lines demarcate the CMD into regions dominated by stars in various evolutionary phases. Counting stars in each box lets us trace out the recent star formation history, which is found to vary stochastically over the past few tens of millions of years while remaining roughly constant when averaged over the age of the universe (13+ billion years).

Most late type, irregular galaxies have been perking along, forming stars at a modest but fairly steady rate for most of the history of the universe. That’s a very broad-brush statement; there are many puzzling details in the details. F415-3 seems to be deficient in AGB stars. These are asymptotic giants, the phase of evolution after the phase after the first-ascent red giant branch. This may be challenging the limits of our understanding of the modeling of stellar evolution. The basics are well-understood, but stars are giant, complicated, multifaceted beasts: just as understanding that terrestrial planets are basically metallic cores surrounded by mantles of rocky minerals falls short of describing the Earth, so too does a basic understanding of stellar evolution fall short of explaining every detail of every star. That’s what I love about astronomy: there is always something new to learn.

Below is the CMD of F575-3, now in the near infrared filters available on HST rather than the optical filters above. There is not such a rich recent star formation history in this case; indeed, this galaxy has been abnormally quiescent for its class. There are some young stars above the tip of the red giant branch (the horizontal blue line), but no HII regions of ionized gas that point up the hottest, youngest stars (typically < 10 Myr old). Mostly we see a red giant branch (the region dark with points below the line) and some main sequence stars (the cloud of points to the left of the red giant branch). These merge into a large blob at faint magnitudes as the uncertainties smear everything together at the limits of the observation.

Color-magnitude diagram of the stars in F575-3 observed by HST (left) and the surrounding field (right). The typical size of the error bars is shown in the right panel; this causes the data to smear into a blob at fainter magnitudes. One can nevertheless recognize some of the main features, as noted: the main sequence of young stars, the red giant branch below the horizontal line, and a region of rapidly evolving stars above the line (mostly asymptotic giants with some helium burning stars and a few red supergiants). There are also a number of stars to the right of the giant branch, in a region of the CMD that is not explained by models of stellar evolution. There shouldn’t be any stars here, but there are more than can be explained by background contamination. What are they?

One cool thing about F575-3 is that it has the bluest red giants known. All red giants are red, but just how red depends sensitively on their metallicity – the fraction of their composition that isn’t hydrogen or helium. As stars evolve, they synthesize heavy elements that are incorporated into subsequent generations of stars. After a while, you have a comparatively metal-rich composition like that of the sun – which is still not much: the mass of the elements in the sun that are not hydrogen or helium is less than 2% of the total. I know that sounds like a small fraction – it is a small fraction – but it is still rather a lot by the standards of the universe in which we live, which started as three parts hydrogen and one part helium, and nothing heavier than lithium. Stars have had to work hard for generation upon generation to make everything else in the periodic table from carbon on up. Galaxies smaller than the Milky Way haven’t got as far along in this process, so dwarf galaxies are typically low metallicity – often much less than 1% by mass.

F575-3 is especially low metallicity. Or so it appears from the color of its red giant stars. These are the bluest reds currently known. Here are some other dwarfs for comparison, organized in order of increasing metallicity. The right edge of the red giant branch in F575-3 is clearly to the left of everything else.

Color-magnitude diagrams of some of the dwarf galaxies that have been observed by HST. Colored lines illustrate the sequence expected for red giants of different metallicities. These are all well below the solar composition, as measured by the logarithmic ratio of the iron abundance relative to hydrogen relative to that in the sun: solar [Fe/H] = 0; [Fe/H] = -1 is one tenth of the solar metal abundance. The lines illustrate the locations of giant branches with [Fe/H] = -2.3 (blue), -1.5 (green) and -0.7 (red). That’s 0.5%, 3%, and 20% of solar, respectively. Heavy elements make up less than 0.4% of the mass of the stars in these galaxies.

But that’s not what I wrote to tell you about. I already knew LSB galaxies were low metallicity; that’s what I did part of my thesis on. That was based on the gas phase abundances, but it makes sense that the stars would share this property – they form out of the interstellar gas, after all. Somebody has to be the bluest of them all. That’s remarkable, but not surprising.

What is surprising is that F575-3 has an excess of stars with an IR-excess – their colors are too red in the infrared part of the spectrum. These are the stars to the right of the red giant branch. We found it basically impossible to populate this portion of the CMD without completely overdoing it. Plausible stellar evolution tracks don’t go there. Nature has no menu option for a sprinkling of high metallicity giant stars but hold the metals everywhere else: once you make those metals, there are ample numbers of high metallicity stars. So what the heck are these things with a near-IR excess?

The CMD of F575-3 in near-IR (left) and optical colors (right). Main sequence stars are blue, rapidly evolving phases like asymptotic giants are red, and most of the black points are red giant stars. There is a population of mystery stars colored purple. These have a near-IR excess: very red colors in the infrared, but normal colors in the optical.

My first thought was that they were bogus. There are always goofy things in astronomical data; outliers are often defects of some sort – in the detector, or the result of cosmic ray strikes. So initially they were easy to ignore. However, this kept nagging at us; it seemed like too much to just dismiss. There are some things like this in the background, but not enough to explain how many we see in the body of the diagram. This argued against things not associated with the galaxy itself, like background galaxies with redshifted colors. When we plotted the distribution of near-IR excess objects, they were clearly associated with the galaxy.

The distribution of sources with a near-IR excess (red) compared to objects of similar apparent magnitude. They’re in the same place as the galaxy that the eye sees in the raw image. Whatever they are, they’re clearly part of F575-3.

The colors make no sense for stars. They aren’t the occasional high metallicity red giant. So our next thought was extinction by interstellar dust. This has the net effect of making things look redder. But Jim did the hard work of matching up individual stars in both the optical and near-IR filters. The optical colors are normal. The population that stands out in the near-IR CMD mixes in evenly with the rest of the stars in the optical CMD. That’s the opposite of what dust does. Dust affects the optical colors more strongly. Here the optical colors are normal, but the near-IR colors are too red – hence an IR-excess.

There, I was stumped. We had convinced ourselves that we couldn’t just dismiss the IR-excess population as artifacts. They had the right spatial distribution to be part of the galaxy. They had the right magnitudes to be stars in the galaxy. But that had really weird IR colors that were unexplained by any plausible track of stellar evolution.

Important detail: stellar evolution models track what happens in the star, up to its surface, but not in the environment beyond. Jim thought about it, and came back to me with an idea outside my purview. He remembered a conversation he had had long ago with Karl Rakos while observing high redshift clusters with custom-tailored filters. Rakos had previously worked on Ap and Be stars – peculiar stars. I had heard of these things, but they’re rare and don’t contribute significantly to the integrated light of the stellar population in a galaxy like the Milky Way. They seemed like an oddity of little consequence in a big universe.

Be stars – that’s “B” then “e” for B-type stars (the second hottest spectral classification) with emission lines (hence the e). Stars mostly just have absorption lines; emission lines make them peculiar. But Jim learned from his conversations with Rakos that these stars also frequently had IR-excesses. Some digging into the literature, and sure enough, these types of stars have the right magnitudes and colors to explain the strange population we can’t otherwise understand.

It is still weird. There are a lot of them. Not a lot in an absolute sense, but a lot more than we’d expect from their frequency in the Milky Way. But now that we know to look for them, you can see a similar population in the some other dwarfs. Maybe they become more frequent in lower metallicity galaxies. The emission lines and the IR excess come from a disk of hot gas around the star; maybe such disks are more likely to form when there are fewer metals. This makes at least a tiny amount of sense, as B stars have a lot of energy to emit and angular momentum to transport. The mechanisms by which that can happen multiply when there are metals to make dust grains that can absorb and reprocess the abundance of UV photons. In their absence, when the metallicity is low, nature has to find another way. So maybe – maybe – Be stars are more common in lower metallicity environments because the dearth of dust encourages the formation of gas disks. That’s entirely speculative (a fun but dangerous aspect of astronomy), so maybe not.

I don’t know if ultimately Be stars are the correct interpretation. It’s the best we’ve come up with. I really don’t know whether metallicity and dust play the role I just speculatively described. But it is a new and unexpected thing – and that’s the cool thing about the never-ending discovery space of astronomy. Even when you know what to expect, the universe can still surprise you – if you pay attention to the data.