La Fin de Quoi?

Last time, I addressed some of the problems posed by the radial acceleration relation for galaxy formation theory in the LCDM cosmogony. Predictably, some have been quick to assert there is no problem at all. The first such claim is by Keller & Wadsley in a preprint titled “La Fin du MOND: LCDM is Fully Consistent with SPARC Acceleration Data.”

There are good things about this paper, bad things, and the potential for great ugliness.

The good:

  This is exactly the reaction that I had hoped to see in response to the radial acceleration relation (RAR): people going to their existing simulations and checking what answer they got. The answer looks promising. The same relation is apparent in the simulations as in the data. That’s good.

  These simulations already existed. They haven’t been tuned to match this particular observations. That’s good.  The cynic might note that the last 15+ years of galaxy formation simulations have been driven by the need to add feedback to match data, including the shapes of rotation curves. Nevertheless, I see no guarantee that the RAR will fall out of this process.

  The scatter in the simulations is 0.05 dex. The scatter in the data not explained by random errors is 0.06 dex. This agreement is good. I think the source of the scatter needs to be explored further (see below), but it is at least in the right ballpark, which is by no means guaranteed.

  The authors make a genuine prediction for how the RAR should evolve with redshift. That isn’t just good; it is bold and laudable.

The bad:

  There are only 18 simulated galaxies to compare to 153 real ones. I appreciate the difficulty in generating these simulations, but we really need a bigger sample. The large number of sampled points (1800) is less important given the simulators’ ability to parse the data as finely as their CPU allows them to resolve. I also wonder if the lowest acceleration points extend beyond the range sampled in comparable galaxies. Typically the data peter out around an HI surface density of 1 Msun/pc^2.

  The comparison they make to Fig. 3 of arxiv:1609.05917 is great.  I would like to see something like Fig. 1 and 2 from that paper as well. What range of galaxy properties do the models span? What do individual mass models looks like?

Fig. 1 from McGaugh, Lelli, & Schombert (2016) showing the range of luminosity and surface brightness covered by the SPARC data. Galaxies range over a factor of 50,000 in luminosity. The shaded region shows the range explored by the simulations discussed by Keller & Wadsley, which cover a factor of 15. Note that this is a logarithmic scale. On a linear scale, the simulations cover 0.03% of the range covered by the data along the x-axis. The range covered along the y-axis was not specified.

  My biggest concern is that there is a limited dynamic range in the simulations, which span only a factor of 15 in disk mass: from 1.7E10 to 2.7E11 Msun. For comparison, the data span 1E7 to 5E11 Lsun in [3.6] luminosity, a factor of 50,000. The simulations only sample the top 0.03% of this range.

  Basically, the simulated galaxies go from a little less massive than the Milky Way up to a bit more massive than Andromeda. Comparing this range to the RAR and declaring the problem solved is like fitting the Milky Way and Andromeda and declaring all problems in the Local Group solved without looking at any of the dwarfs. It is at lower mass scales and for lower surface brightness galaxies that problems become severe. Consequently, the most the authors can claim is a promising start on understanding a tiny fraction of bright galaxies, not a complete explanation of the RAR.

  Indeed, while the authors quantify the mass range over which their simulated galaxies extend, they make no mention of either size or surface brightness. Are these comparable to real galaxies of similar mass? Too narrow a range in size at fixed mass, as seems likely in a small sample, may act to artificially suppress the scatter.  Put another way: if the simulated galaxies only cover a tiny region of Fig. 1 above, it is hardly surprising if they exhibit little scatter.

  The apparent match between the simulated and observed scatter seems good. But the “left over” observational scatter of 0.06 dex is the same as what we expect from scatter in the mass-to-light ratio.  That is irreducible. There has to be some variation in stellar populations, and it is much easier to imagine this number getting bigger than being much smaller.

  In the simulations, the stellar mass is presumably known perfectly, so I expect the scatter has a different source. Presumably there is scatter from halo to halo as seen in other simulations. That’s natural in LCDM, but there isn’t any room for it if we also have to accommodate scatter from the mass-to-light ratio. The apparent equality of observed and simulated scatter is meaningless if they represent scatter in different quantities.

  I have trouble believing that the RAR follows simply from dissipative collapse without feedback. I’ve worked on this before, so I’m pretty sure it does not work this way. It is true that a single model does something like this as a result of dissipative collapse. It is not true that an ensemble of such models are guaranteed to fall on the same relation.

  There are many examples of galaxies with the same mass but very different scale lengths. In the absence of feedback, shorter scale lengths lead to more compression of the dark matter halo. One winds up with more dark matter where there are more baryons. This is the opposite of what we see in the data.

  This makes me suspect the dynamic range in the simulations is a problem. Not only do they cover little range in mass compared to the data, but this particular conclusion may only be reached if there is virtually no dynamic range in size at a given mass. That is hardly surprising given the small sample size.

The ugly:

  The title.

  This paper has nothing to do with MOND, nor says anything about it. Why is it in the title?

  At best, the authors have shown that, over a rather limited dynamic range, simulations in LCDM might reproduce post facto what MOND predicted a priori. If so, LCDM survives this test (as far as it goes). But in no respect can this be considered a problem for MOND, which predicted the phenomenon over 30 years ago. This is a classic problem in the philosophy of science: should we put more weight on the a priori prediction, or on the capacity of a more flexible theory to accommodate the same observation later on?

The title is revealing of a deep-rooted bias. It tarnishes what might be an important results and does a disservice to the objectivity we’re suppose to value in science.

DO OTHER SIMULATIONS AGREE?

  I am eager to see whether other simulations agree with these results. Not all simulators implement feedback in the same way, nor get the same results. The most dangerous aspect of this paper is that it may give people an excuse to think the problem is solved so they never have to think about it again. The RAR is a test that needs to be applied every time to each and every batch of simulations. If they don’t pass this test, they’re wrong. Unfortunately, there is precedent in the galaxy formation community to take reassurances such as this for granted, and not to bother to perform the test.

THE RAR TEST MUST BE PERFORMED FOR ALL SIMULATIONS. ALWAYS.