Another quick-trick simulation result

Another quick-trick simulation result

There has already been one very quick attempt to match ΛCDM galaxy formation simulations to the radial acceleration relation (RAR). Another rapid preprint by the Durham group has appeared. It doesn’t do everything I ask for from simulations, but it does do a respectable number of them. So how does it do?

First, there is some eye-rolling language in the title and the abstract. Two words: natural (in the title) and accommodated (in the abstract). I can’t not address these before getting to the science.

Natural. As I have discussed repeatedly in this blog, and in the refereed literature, there is nothing natural about this. If it were so natural, we’d have been talking about it since Bob Sanders pointed this out in 1990, or since I quantified it better in 1998 and 2004. Instead, the modus operandi of much of the simulation community over the past couple of decades has been to pour scorn on the quality of rotation curve data because it did not look like their simulations. Now it is natural?

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Accommodate. Accommodation is an important issue in the philosophy of science. I have no doubt that the simulators are clever enough to find a way to accommodate the data. That is why I have, for 20 years, been posing the question What would falsify ΛCDM? I have heard (or come up myself with) only a few good answers, and I fear the real answer is that it can’t be. It is so flexible, with so many freely adjustable parameters, that it can be made to accommodate pretty much anything. I’m more impressed by predictions that come ahead of time.

That’s one reason I want to see what the current generation of simulations say before entertaining those made with full knowledge of the RAR. At least these quick preprints are using existing simulations, so while not predictions in the strictest since, at least they haven’t been fine-tuned specifically to reproduce the RAR. Lots of other observations, yes, but not this particular one.

Ludlow et al. show a small number of model rotation curves that vary from wildly unrealistic (their NoAGN models peak at 500 km/s; no disk galaxy in the universe comes anywhere close to that… Vera Rubin once offered a prize for any that exceeded 300 km/s) to merely implausible (their StrongFB model is in the right ballpark, but has a very rapidly rising rotation curve). In all cases, their dark matter halos seem little affected by feedback, in contrast to the claims of other simulation groups. It will be interesting to follow the debate between simulators as to what we should really expect.

They do find a RAR-like correlation. Remarkably, the details don’t seem to depend much on the feedback scheme. This motivates some deeper consideration of the RAR.

The RAR plots observed centripetal acceleration, gobs, against that predicted by the observed distribution of baryons, gbar. We chose these coordinates because this seems to be the fundamental empirical correlation, and the two quantities are measured in completely independent ways: rotation curves vs. photometry. While measured independently, some correlation is guaranteed: physically, gobs includes gbar. Things only become weird when the correlation persists as gobs ≫ gbar.

The models are well fit by the functional form we found for the data, but with a different value of the fit parameter: g = 3 rather than 1.2 x 10-10 m s-2. That’s a factor of 2.5 off – a factor that is considered fatal for MOND in galaxy clusters. Is it OK here?

The uncertainty in the fit value is 1.20 ± 0.02. So formally, 3 is off by 90σ. However, the real dominant uncertainty is systematic: what is the true mean mass-to-light ratio at 3.6 microns? We estimated the systematic uncertainty to be ± 0.24 based on an extensive survey of plausible stellar population models. So 3 is only 7.5σ off.

The problem with systematic uncertainties is that they do not obey Gaussian statistics. So I decided to see what we might need to do to obtain g = 3 x 10-10 m s-2. This can be done if we take sufficient liberties with the mass-to-light ratio.

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The radial acceleration relation as observed (open points fit by blue line) and modeled (red line). Filled points are the same data with the disk mass-to-light ratio reduced by a factor of two.

Indeed, we can get in the right ball park simply by reducing the assumed mass-to-light ratio of stellar disks by a factor of two. We don’t make the same factor of two adjustment to the bulge components, because the data don’t approach the 1:1 line at high accelerations if this is done. So rather than our fiducial model with M*/L(disk) = 0.5 M/L and M*/L(bulge) = 0.7 M/L (open points in plot), we have M*/L(disk) = 0.25 M/L and M*/L(bulge) = 0.7 M/L (filled points in plot). Lets pretend like we don’t know anything about stars and ignore the fact that this change corresponds to truncating the IMF of the stellar disk so that M dwarfs don’t exist in disks, but they do in bulges. We then find a tolerable match to the simulations (red line).

Amusingly, the data are now more linear than the functional form we assumed. If this is what we thought stars did, we wouldn’t have picked the functional form the simulations apparently reproduce. We would have drawn a straight line through the data – at least most of it.

That much isn’t too much of a problem for the models, though it is an interesting question whether they get the shape of the RAR right for the normalization they appear to demand. There is a serious problem though. That becomes apparent in the lowest acceleration points, which deviate strongly below the red line. (The formal error bars are smaller than the size of the points.)

It is easy to understand why this happens. As we go from high to low accelerations, we transition from bulge dominance to stellar disk dominance to gas dominance. Those last couple of bins are dominated by atomic gas, not stars. So it doesn’t matter what we adopt for the stellar mass-to-light ratio. That’s where the data sit: well off the simulated line.

Is this fatal for these models? As presented, yes. The simulations persist in predicting higher accelerations than observed. This has been the problem all along.

There are other issues. The scatter in the simulated RAR is impressively small. Much smaller than I expected. Smaller even than the observational scatter. But the latter is dominated by observational errors: the intrinsic relation is much tighter, consistent with a δ-function. The intrinsic scatter is what they should be comparing their results to. They either fail to understand, or conveniently choose to gloss over, the distinction between intrinsic scatter and that induced by random errors.

It is worth noting that some of the same authors make this same mistake – and it is a straight up mistake – in discussing the scatter in the baryonic Tully-Fisher relation. The assertion there is “the scatter in the simulated BTF is smaller than observed”. But the observed scatter is dominated by observational errors, which we have taken great care to assess. Once this is done, there is practically no room left over for intrinsic scatter, which is what the models display. This is important, as it completely inverts the stated interpretation. Rather than having less scatter than observed, the simulations exhibit more scatter than allowed.

Can these problems be fixed? No doubt. See the comments on accommodation above.

The Grand Observational Challenge for Galaxy Formation Simulations

After writing the commentary on the latest fin du MOND, it occurred to me that there are many issues that I consider to be obvious. But I’ve been thinking about them for a quarter century, so perhaps they may need to be clearly elucidated for those who don’t share that background. I am thinking, in particular, of galaxy formation modelers and theorists.

There are now many sophisticated galaxy formation simulations by many independent groups. They use different codes (sometimes with overlap) to implement the same physics with different algorithms. Well, sometimes it isn’t entirely clear that they’re talking about the same physics, or just using the same words to mean different things. But they all seek to form realistic galaxies in numerical simulations.

The observed radial acceleration relation (RAR) provides a strong test of simulated galaxy models. To claim that a suite of model galaxies is realistic, they must match the RAR. If they do, great. If they don’t, then they are not an adequate representation of observed reality.

What needs to happen now is for every group that performs these simulations to test their models against the data. We have provided the necessary observational data. All they need to do is make the same straightforward query of their simulation results. This is the Grand Observational Challenge for Galaxy Simulations.

Some requests:

  • Please be explicit: show your work.
    • Show us the RAR from your models. Don’t hide anything.
    • Show us the parameter space covered by your models (Mh, M*, R, Σ, etc.)
    • Show us the mass models of individual simulated galaxies.
    • Don’t just assert everything works out and expect me to believe it.
  • Start with what you’ve got.
    • I want to see what the current generation of models shows before you go and run more and more simulations until you find some that match the data.
    • When seeking models that do match, quantify the failure rate. How much parameter space do you have to hunt through before it works? How plausible were those not-quite-right parameters, independent of knowledge of the RAR?
  • Don’t claim more than you actually demonstrate.
    • If you have simulations that span only 0.03% of the observed mass range, then only claim to explain (at most) 0.03% of the problem.
  • Pay careful attention to the scatter.
    • How much intrinsic scatter should we expect?
    • What are the sources of scatter? Are they irreducible?
    • Are there residual correlations?
      • That is, at fixed mass (say) do galaxies fall systematically on one or the other side of the RAR depending on scale length or some other parameter?
  • Don’t fudge it.
    • I can tell.