There has been another attempt to explain away the radial acceleration relation as being fine in ΛCDM. That’s good; I’m glad people are finally starting to address this issue. But lets be clear: this is a beginning, not a solution. Indeed, it seems more like a rush to create truth by assertion than an honest scientific investigation. I would be more impressed if these papers were (i) refereed rather than rushed onto the arXiv, and (ii) honestly addressed the requirements I laid out.
This latest paper complains about IC 2574 not falling on the radial acceleration relation. This is the galaxy that I just pointed out (about the same time they must have been posting the preprint) does adhere to the relation. So, I guess post-factual reality has come to science.
Rather than consider the assertions piecemeal, lets take a step back. We have established that galaxies obey a single effective force law. Federico Lelli has shown that this applies to pressure supported elliptical galaxies as well as rotating disks.
The radial acceleration relation, including pressure supported early type galaxies and dwarf Spheroidals.
Lets start with what Newton said about the solar system: “Everything happens… as if the force between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.” Knowing how this story turns out, consider the following.
Suppose someone came to you and told you Newton was wrong. The solar system doesn’t operate on an inverse square law, it operates on an inverse cube law. It just looks like an inverse square law because there is dark matter arranged just so as to make this so. No matter whether we look at the motion of the planets around the sun, or moons around their planets, or any of the assorted miscellaneous asteroids and cometary debris. Everything happens as if there is an inverse square law, when really it is an inverse cube law plus dark matter arranged just so.
Would you believe this assertion?
I hope not. It is a gross violation of the rule of parsimony. Occam would spin in his grave.
Yet this is exactly what we’re doing with dark matter halos. There is one observed, effective force law in galaxies. The dark matter has to be arranged just so as to make this so.
Convenient that it is invisible.
Maybe dark matter will prove to be correct, but there is ample reason to worry. I worry that we have not yet detected it. We are well past the point that we should have. The supersymmetric sector in which WIMP dark matter is hypothesized to live flunked the “golden test” of the Bs meson decay, and looks more and more like a brilliant idea nature declined to implement. And I wonder why the radial acceleration relation hasn’t been predicted before if it is such a “natural” outcome of galaxy formation simulations. Are we doing fair science here? Or just trying to shove the cat back in the bag?
I really don’t know what the final answer will look like. But I’ve talked to a lot of scientists who seem pretty darn sure. If you are sure you know the final answer, then you are violating some basic principles of the scientific method: the principle of parsimony, the principle of doubt, and the principle of objectivity. Mind your confirmation bias!
That’ll do for now. What wonders await among tomorrow’s arXiv postings?
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.
Set the Wayback Machine, Mr. Peabody!
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).
The rotation curve of LSB galaxy F583-1 (filled points) as reported in McGaugh & de Blok (1998). Open points are what is left after subtracting the contribution of the stars and the gas: this is the rotation curve of the dark matter halo. Lines are example NFW halos. The data do not behave as predicted by NFW, a generic problem in LSB galaxies.
This was bad for NFW. But there is a more general problem, irrespective of the particular form of the dark matter halo. The M*-Mhalo 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:
The rotation curves of NGC 2403 (red points) and UGC 128 (open points). The top panel shows radius in physical units; the bottom panel shows the same data with the radius scaled by the scale length of the disk. This is larger for the LSB galaxies (blue lines in top panel) and has the net effect that the normalized rotation curves are practically indistinguishable.
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:
Fig. 5 from Oman et al. (2015).
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 naturalat 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.
The rotation curve of IC 2574 (left) and its location along the RAR (right).
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.
I have been musing for a while on the idea of writing about Naturalness in science, particularly as it applies to the radial acceleration relation. As a scientist, the concept of Naturalness is very important to me, especially when it comes to the interpretation of data. When I sat down to write, I made the mistake of first Googling the term.
The top Google hits bear little resemblance to what I mean by Naturalness. The closest match is specific to a particular, rather narrow concept in theoretical particle physics. I mean something much more general. I know many scientific colleagues who share this ideal. I also get the impression that this ideal is being eroded and cheapened, even among scientists, in our post-factual society.
I suspect the reason a better hit for Naturalness doesn’t come up more naturally in a Google search is, at least in part, an age effect. As wonderful a search engine as Google may be, it is lousy at identifying things B.G. (Before Google). The concept of Naturalness has been embedded in the foundations of science for centuries, to the point where it is absorbed by osmosis by students of any discipline: it doesn’t need to be formally taught; there probably is no appropriate website.
In many sciences, we are often faced with messy and incomplete data. In Astronomy in particular, there are often complicated astrophysical processes well beyond our terrestrial experience that allow a broad range of interpretations. Some of these are natural while others are contrived. Usually, the most natural interpretation is the correct one. In this regard, what I mean by Naturalness is closely related to Occam’s Razor, but it is something more as well. It is that which follows – naturally – from a specific hypothesis.
An obvious astronomical example: Kepler’s Laws follow naturally from Newton’s Universal Law of Gravity. It is a trivial amount of algebra to show that Kepler’s third Law, P2 = a3, follows as a direct consequence of Newton’s inverse square law. The first law, that orbits are ellipses, follows with somewhat more math. The second law follows with the conservation of angular momentum.
It isn’t just that Newtonian gravity is the simplest explanation for planetary orbits. It is that all the phenomena identified by Kepler follow naturally from Newton’s insight. This isn’t obvious just by positing an inverse square law. But in exploring the consequences of such a hypothesis, one finds that one clue after another falls into place like the pieces of a jigsaw puzzle. This is what I mean by Naturalness.
I expect that this sense of Naturalness – the fitting together of the pieces of the puzzle – is what gave Newton encouragement that he was on the right path with the inverse square law. Let’s not forget that both Newton and his inverse square law came in for a lot of criticism at the time. Both Leibniz and Huygens objected to action at a distance, for good reason. I suspect this is why Newton prefaced his phrasing of the inverse square law with the modifier as if: “Everything happens… as if the force between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.” He is not claiming that this is right, that it has to be so. Just that it sure looks that way.
The situation with the radial acceleration relation in galaxies today is the same. Everything happens as if there is a single effective force law in galaxies. This is true regardless of what the ultimate reason proves to be.
The natural explanation for the single effective force law indicated by the radial acceleration relation is that there is indeed a unique force law at work. In this case, such a force law has already been hypothesized: MOND. Often MOND is dismissed for other reasons, though reports of its demise have repeatedly been exaggerated. Perhaps MOND is just the first approximation of some deeper theory. Perhaps, like action at a distance, we simply don’t yet understand the underlying reasons for it.
Jules: Nah, I ain’t biased, I just don’t dig MOND, that’s all.
Vincent: Why not?
Jules: MOND is an ugly theory. I don’t consider ugly theories.
Vincent: MOND makes predictions that come true. Fits galaxy data gooood.
Jules: Hey, MOND may fit every galaxy in the universe, but I’d never know ’cause I wouldn’t consider the ugly theory. MOND has no generally covariant extension. That’s an ugly theory. I ain’t considering nothin’ that ain’t got a proper cosmology.
Vincent: How about ΛCDM? ΛCDM has lots of small scale problems.
Jules: I don’t care about small scale problems.
Vincent: Yeah, but do you consider ΛCDM to be an ugly theory?
Jules: I wouldn’t go so far as to call ΛCDM ugly, but it’s definitely fine-tuned. But, ΛCDM’s got the CMB. The CMB goes a long way.
Vincent: Ah, so by that rationale, if a theory of modified dynamics fit the CMB, it would cease to be an ugly theory. Is that true?
Jules: Well, we’d have to be talkin’ about one charming eff’n theory of modified dynamics. I mean, it’d have to be ten times more charmin’ than MOND, you know what I’m sayin’?
So the always humorous, unabashedly nerdy xkcd recently published this comic:
This hits close to home for me, in many ways.
First, this is an every day experience for me. Hardly a day goes by that I don’t get an email, or worse, a phone call, from some wanna-be who has the next theory of everything. I try to be polite. I even read some of what I get sent. Mostly this is a waste of my time. News flash: at most, only one of you can be right. If the next Einstein is buried somewhere amongst these unsolicited, unrefereed, would-be theories, I wouldn’t know, because I do not have the time to sort through them all.
Second, it is true – it is a logical possibility that what we call dark matter is really just a proxy for a change in the law of gravity on galactic scales. It is also true that attempts to change the law of gravity on large scales do not work to explain the dark matter problem. (Attempts to do this to address the dark energy problem are a separate matter.)
Third, it is a logical fallacy. The implication of the structure of the statement is that the answer has to be dark matter. One could just as accurately turn the statement on its head and say “Yes, everybody has already had the idea, maybe it isn’t modified gravity – there’s just a lot of invisible mass on large scales!’ It sounds good but it doesn’t really fit the data.”
The trick is what data we’re talking about.
I have reviewed this problem many times (e.g., McGaugh & de Blok 1998, Sanders & McGaugh 2002, McGaugh 2006, Famaey & McGaugh 2012, McGaugh 2015). Some of the data favor dark matter, some favor modified gravity. Which is preferable depends on how we weigh the different lines of evidence. If you think the situation is clear cut, you are not well informed of all the facts.* Most of the data that we cite to require dark matter are rather ambiguous and can usually be just as well interpreted in terms of modified gravity. The data that isn’t ambiguous points in opposite directions – see the review papers.
Note that I was careful above to say “galactic scales.” The scale that turns out to matter is not a size scale but an acceleration scale. Galaxies aren’t just big. The centripetal accelerations that hold stars in their orbits are incredibly low: about one part in 1011 of what we feel on the surface of the Earth. The only data that test gravity on this acceleration scale are the data that evince the missing mass problem. We only infer the need for dark matter at these very low accelerations. So while it is not possible to construct an empirically successful theory that modifies gravity on some large length scale, it remains a possibility that a modification can be made on an acceleration scale.
That the mass discrepancy problem occurs on an acceleration scale and not at some length scale has been known for many years. Failing to make the distinction between a length scale and an acceleration scale is fine for a comic strip. It is not OK for scientists working in the field. And yet I routinely encounter reasonable, intelligent scientists who are experts in some aspect of the dark matter problem but are unaware of this essential fact.
To end with another comic, the entire field is easily mocked:
The astute scientific reader will recognize that Mr. Breathed is conflating dark matter with dark energy. Before getting too dismissive, consider how you would go about explaining to him that our cosmic paradigm requires not just invisible mass to provide extra gravity, but also dark energy to act like antigravity. Do you really think that doubling down on ad hoc hypotheses makes for a strong case?
*Or worse, you may fall prey to cognitive dissonance and confirmation bias.
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?
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.
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.
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?
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.
One reason we have posed it as a law of nature is that it is interpretation-free. It is a description of how nature works – in this case, a rule for how galaxies rotate. Why nature behaves thus is another matter.
Some people have been saying the RAR (I tire of typing out “radial acceleration relation”) is a problem for dark matter, while others seem to think otherwise. Lets examine this.
The RAR has a critical scale g† = 1.2 · 10-10 m s-2. At high acceleration, above this scale, we don’t need dark matter: systems like the solar system or the centers of high surface brightness galaxies are WYSIWYG. At low accelerations, below this scale, we begin to need dark matter. The lower the acceleration, the more dark matter we need.
OK, so this means there is little to no dark matter when the baryons are dense (high gbar), but progressively more as gbar becomes smaller than the critical scale g†. Low gbar happens when the surface density of baryons is low. So the amount of dark matter scales inversely with baryonic surface density.
That’s weird.
This is weird for a number of reasons. First, there is no reason for the dark matter to care what the baryons are doing when dark matter dominates. When gobs ≫ gbar the dark matter greatly outweighs the baryons, which simply become tracer particles in the gravitational potential of the dark matter halo. There is no reason for the dark matter to know or care about what the baryonic tracer particles are doing. And yet the RAR persists as a tight correlation well into this regime. It is as if the baryonic tail wags the dark matter dog.
Second, there should be more dark matter where there are more baryons. Galaxies form by baryons falling into dark matter halos. As they do so, they dissipate energy and sink to the center of the halo. In this process, the drag some of the dark matter along with them in a process commonly referred to as “adiabatic compression.” In practice, the process need not be adiabatic, but the dark matter must respond to the rearrangement of the gravitational potential caused by the dissipative infall of the baryons.
These topics have been discussed at great length in the galaxy formation literature. Great arguments have erupted time and again about how best to implement the compression in models, and how big the effect is in practice. These details need not concern us here. What matters is that they are non-negotiable fundamentals of the dark matter paradigm.
Galaxies form by baryonic infall within dark matter halos. The halos form first while the baryons are still coupled to the photons prior to last scattering. This is one of the fundamental reasons we need non-baryonic cold dark matter that does not interact with photons: to get a jump on structure formation. Without it, we cannot get from the smooth initial condition observed in the cosmic microwave background to the rich amount of structure we see today.
As the baryons fall into halos, they must sink to the center to form galaxies. Why? Dark matter halos are much bigger than the galaxies that reside within them. All tracers of the gravitational potential say so. Initially, this might seem odd, as the baryons might to just track the dominant dark matter. But baryons are different: they can dissipate energy. By so doing, they can sink to the center – not all baryons need to sink to the centers of their dark matter halos, but enough to make a galaxy. This they must do in order to form the galaxies that we observe – galaxies that are more centrally condensed than their dark matter halos.
That’s enough, in return, to affect the dark matter. As the baryons dissipate, the gravitational potential is non-stationary. The dark matter distribution must respond to this change in the total gravitational potential. The net result is a further concentration of the dark matter towards the center of the halo: in effect, the baryons drag some dark matter along with them.
Dark matter halos formed in numerical simulations illustrating the effect of adiabatic compression. One the left is a pristine halo without baryons. In the middle is a halo after formation of a disk galaxy. On right is a halo after formation of a more compact disk.
One can see by eye the compression caused by the baryons. The more dense the baryons become, the more dark matter they drag towards the center with them.
The fundamental elements of the dark matter paradigm, galaxy formation by baryonic infall and dissipation accompanied by the inevitable compression of the dark matter halo, inevitably lead us to expect that more baryons in the center means more dark matter as well. We observe the exact opposite in the RAR. As baryons become denser, they become the dominant component, to the point where they are the only component. Rather than more dark matter as we expect, more baryons means less dark matter in reality.
Third, the RAR correlation is continuous and apparently scatter-free over all accelerations. The data map from the regime of no dark matter at high accelerations to lots of dark matter at low accelerations in perfect 1:1 harmony with the distribution of the baryons. If we observe the distribution of baryons, we know the corresponding distribution of dark matter. The tail doesn’t just wag the dog. It tells it to sit, beg, and roll over.
Fourth, there is a critical scale in the data, g†. That’s the scale where the mass discrepancy sets in. This is a purely empirical statement.
Cold dark matter is scale free. Being scale free is fundamental to its nature. It is essential to fitting the large scale structure, which it does quite well.
So why is there this ridiculous acceleration scale in the data?!? Who ordered this?! It should not be there.
So yes, the radial acceleration relation is a problem for the cold dark matter paradigm.
Flat rotation curves were the first clear evidence that the dynamics of galaxies do not follow the same rules as planetary systems. But they do follow rules. These include asymptotic flatness, Tully-Fisher, the luminosity-size-rotation curve shape relation (aka the `universal‘ rotation curve), Renzo’s rule, and the central density relation.
Rotation curves color coded by the characteristic surface density of stars and gas, ranging from low surface brightness galaxies (blue) to those of high surface brightness (red).
These various relations sound like a hodge-podge of random astronomical effects. This is misleading. There is a great deal of organization in the data. The surface density of stars and gas, and the acceleration (gbar) determined by their gravitational potential, plays a defining role. Indeed, the known relations are all manifestations of a single, more fundamental relation, the radial acceleration relation.
The radial acceleration relation. The centripetal acceleration measured by the rotation curve (gobs) correlates with that predicted by the observed distribution of stars and gas (gbar). The data consist of 2,693 resolved points along the rotation curves of 153 rotating galaxies from the SPARC database. All galaxies fall along the same relation, within the uncertainties. Red squares are binned data. The lower panel shows residuals from a fit to the data. The dashed lines are the scatter in the data; the red lines are the amount of scatter expected from measurement uncertainties.
The radial acceleration relation connects what you see in galaxies with what you get for the gravitational force. This would be a trivial statement if galaxies behave as planetary systems do. They would follow the 1:1 dotted line in the figure. Instead, they bend away from that line.
Indeed, the data are consistent with a single effective force law, which can be written
Other functional forms could also work. But they would all necessarily have a critical acceleration scale g† ≈ 10-10 m s-2. This is an important scale that is ubiquitous in extragalactic astronomy. It seems to be a new fundamental scale in physics.
The critical acceleration marks the onset of the missing mass problem. Above this scale, there is no need for dark matter. Below it, the difference between the 1:1 line and the data is what we attribute to dark matter. The more the observed acceleration exceeds that which can be explained by the stars and gas, the larger the mass discrepancy.
Irrespective of interpretation, the data establish the radial acceleration relation in a purely empirical way. There is nothing but data here. The axes are independent: one is measured from rotation curves, the other from photometry. These need not be well connected – the dark matter could cause any sort of acceleration independently of the stars and gas. But they are intimately coupled.
There are no deviations from the radial acceleration relation beyond those attributable to experimental error. The residuals do not correlate with mass, size, surface brightness, color, environment, how many intelligent civilizations a galaxy hosts, or anything else. The scale that matters is not luminosity or halo mass or size. It is the acceleration determined from the surface density of stars and gas.
The radial acceleration relation is a fundamental relation. In effect, it is a law of nature. Third in our counting, but first in importance, as both flat rotation curves and the Tully-Fisher relation follow from it. It must be explained by any theory that claims to provide a satisfactory description of galaxy dynamics.
Triton Station 