Going in Circles

Sam: This looks strangely familiar.

Frodo: That’s because we’ve been here before. We’re going in circles!

Last year, Oman et al. published a paper entitled “The unexpected diversity of dwarf galaxy rotation curves”. This term, diversity, has gained some traction among the community of scientists who simulate the formation of galaxies. From my perspective, this terminology captures some of the story, but misses most of it.

Lets review.

It was established (by van Albada & Sancisi and by Kent) in the ’80s that rotation curves were generally well described as maximal disks: the inner rotation curve was dominated by the stars, with a gradual transition to the flat outer part which required dark matter. By that time, I had became interested in low surface brightness (LSB) galaxies, which had not been studied in such detail. My nominal expectation was that LSB galaxies were stretched out versions of more familiar spiral galaxies. As such they’d also have maximal disks, but lower peak velocities (since V² ≈ GM/R and LSBs had larger R for the same M).

By the mid-1990s, we had shown that this was not the case. LSB galaxies had the same rotation velocity as more concentrated galaxies of the same luminosity. This meant that LSB galaxies were dark matter dominated. This result is now widely known (to the point that it is often taken for granted), but it had not been expected. One interesting consequence was that LSB galaxies were a convenient laboratory for testing the dark matter hypothesis.

So what do we expect? There were, and are, many ideas for what dark matter should do. One of the leading hypotheses to emerge (around the same time) was the NFW halo obtained from structure formation simulations using cold dark matter. If a galaxy is dark matter dominated, then to a good approximation we expect the stars to act as tracer particles: the rotation curve should just reflect that of the underlying dark matter halo.

This did not turn out well. The rotation curves of low surface brightness galaxies do not look like NFW halos. One example is provided by the LSB galaxy F583-1, reproduced here from Fig. 14 of McGaugh & de Blok (1998).

This was bad for NFW. But there is a more general problem, irrespective of the particular form of the dark matter halo. The M_*-M_halo relation required by abundance matching means that galaxies of the same luminosity live in nearly identical dark matter halos. When dark matter dominates, galaxies of the same luminosity should thus have the same rotation curve.

We can test this by comparing the rotation curves of Tully-Fisher pairs: galaxies with the same luminosity and flat rotation velocity, but different surface brightness. The high surface brightness NGC 2403 and low surface brightness UGC 128 are such a pair. So for 20 years, I have been showing their rotation curves:

If NGC 2403 and UGC 128 reside in the same dark matter halo, they should have basically the same rotation curve in physical units [V(R in kpc)]. They don’t. But they do have the pretty much the same rotation curve when radius is scaled by the size of the disk [V(R/Rd)]. The dynamics “knows about” the baryons, in contradiction to the expectation for dark matter dominated galaxies.

Oman et al. have rediscovered the top panel (which they call diversity) but they don’t notice the bottom panel (which one might call uniformity). That galaxies of the same luminosity have different rotation curves remains surprising to simulations, at least the EAGLE and APOSTLE simulations Oman et al. discuss. (Note that APOSTLE was called LG by Oman et al.)  Oman et al. illustrate the point with a number of rotation curves, for example, their Fig. 5:

Oman et al. show that the rotation curves of LSB galaxies rise more slowly than predicted by simulations, and have a different shape. This is the same problem that we pointed out two decades ago. Indeed, note that the lower left panel is F583-1: the same galaxy noted above, showing the same discrepancy. The new thing is that these simulations include the effects of baryons (shaded regions). Baryons do not help to resolve the problem, at least as implemented in EAGLE and APOSTLE.

It is tempting to be snarky and say that this quantifies how many years simulators are behind observers. But that would be too generous. Observers had already noticed the systematic illustrated in the bottom panel of the NGC2403/UGC 128 in the previous millennium. Simulators are just now coming to grips with the top panel. The full implications of the bottom panel seems not yet to have disturbed their dreams of dark matter.

Perhaps that passes snarky and on into rude, but it isn’t like we haven’t been telling them exactly this for years and years and years. The initial reaction was not mere disbelief, but outright scorn. The data disagree with simulations, so the data must be wrong! Seriously, this was the attitude. I don’t doubt that it persists in some of the colder, darker corners of the communal astro-theoretical intellect.

Indeed, Ludlow et al. provide an example. These are essentially the same people as wrote Oman et al. Though Oman et al. point out a problem when comparing the simulations to data, Ludlow et al. claim that the observed uniformity is “a Natural Outcome of Galaxy Formation in CDM halos”. Seriously. This is in their title.

Well, which is it? Is the diversity of rotation curves a problem for simulations? Or is their uniformity a “natural outcome”? This is not natural at all.

Note that the lower right panel of the figure from Oman et al. contains the galaxy IC 2574. This galaxy obviously deviates from the expectation of the simulations. These predict accelerations that are much larger than observed at small radii. Yet Ludlow et al. claim to explain the radial acceleration relation.

This situation is self-contradictory. Either the simulations explain the RAR, or they fail to explain the “diversity” of rotation curves. These are not independent statements.

I can think of two explanations: either (i) the data that define the RAR don’t include diverse galaxies, or (ii) the simulations are not producing realistic galaxies. In the latter case, it is possible that both the rotation curve and the baryon distribution are off in a way that maintains some semblance of the observed RAR.

I know (i) is not correct. Galaxies like F583-1 and IC 2574 help define the RAR. This is one reason why the RAR is problematic for simulations.

That leaves (ii). Though the correlation Ludlow et al. show misses the data, the real problem is worse. They only obtain the semblance of the right relation because the simulated galaxies apparently don’t have the same range of surface brightness as real galaxies. They’re not just missing V(R); now that they include baryons they are also getting the distribution of luminous mass wrong.

I have no doubt that this problem can be fixed. Doing so is “simply” a matter of revising the feedback prescription until the desired results is obtained. This is called fine-tuning.