People often ask for a straight up comparison between ΛCDM and MOND. This is rarely possible because the two theories are largely incommensurable. When one is eloquent the other is mute, and vice-versa.

It is possible to attempt a comparison about how bad the missing baryon problem is in each. In CDM, we expect a relation between dynamical mass and rotation speed of the form Mvir ∝ Vvir3. In MOND the equivalent relation has a different power law, Mb ∝ Vf4.

In CDM we speak of virial quantities – the total mass of everything, including dark matter, and the circular speed way out at the virial radius (typically far outside the luminous extent of a galaxy). In MOND, we use the observed baryonic mass (stars and gas) and the flat rotation speed. These are not the same, so strictly speaking, still incommensurable. But they provide a way to compare the baryonic mass with the total inferred mass.


This plot shows the detected baryon fraction as a function of mass. The top panel is identical to last time. In ΛCDM we see most of the baryons in the most massive systems, but progressively less in smaller systems. In MOND the situation is reversed. The check-sum is complete in galaxies, but falls short in clusters of galaxies. (Note that the error bars have been divided by an extra power of velocity in the lower panel, which amplifies their appearance.) The reader may judge for himself which of these problems is more serious.

Critics of MOND frequently cite the bullet cluster as having falsified MOND. Period. No room for debate. See the linked press release from NASA: dark_matter_proven.

OK, what kind of dark matter? As discussed previously, we need at least two kinds of dark matter in ΛCDM: non-baryonic cold dark matter (some entirely novel particle) and dark baryons (normal matter not yet detected). Unfortunately, “dark matter” is a rather generic, catch-all term that allows these two distinct problems to be easily confused. We see the need for unseen mass in objects like the bullet cluster, and make the natural leap to conclude that we are seeing the non-baryonic cold dark matter that we expect in cosmology. There it is, case closed.

This is an example of a logical fallacy. There is nothing about the missing mass problem suffered by MOND in clusters that demands the unseen mass be non-baryonic. Indeed, even in ΛCDM we suffer some missing baryon problem on top of the need for non-baryonic cold dark matter. In both theories, there is a missing baryon problem in clusters. In both cases, this missing baryon problem is more severe at small radii, suggestive of a connection with the also-persistent cooling flow problem. Basically, the X-ray emitting gas observed in the inner 200 kpc or so of clusters have time to cool, so it ought to be condensing into – what? Stars? MACHOs? Something normal but as yet unseen.

It is not obvious that cooling flows can solve MOND’s problem in clusters. The problem is both serious and persistent. It was first pointed out in 1988 by The & White, and is discussed in this 2002 Annual Review. A factor or two (or even a bit more) of the expected baryons in clusters are missing (the red portion of the plot above). Note, however, that this problem was known long before the bullet cluster was discovered. From this perspective, it would have been very strange had the bullet cluster not shown the same discrepancy as every other cluster in the sky.

I do not know if the missing mass in clusters is baryonic. I am at a loss to suggest a plausible form that the missing baryons might be lurking in. Certainly others have tried. But lets take a step back and as if it is plausible.

As seen above, we have a missing baryon problem in both theories. It just manifests in different places. Advocates of ΛCDM do not, by and large, seem to consider the baryon discrepancy in galaxies to be a problem. The baryons were blown out, or are there but just not detected yet. No Problem. I’m not as lenient, but if we are to extend that grace to ΛCDM, why not also to MOND?

Recall that Shull et al. found that about 30% of baryons remain undetected in the local universe. In order to solve the problem MOND suffers in clusters, we need a mass in baryons about equal to the ICM wedge in this pie chart:


Note that the missing wedge is much larger than the ICM wedge. There are more than enough baryons out there to solve this problem. Indeed, it hardly makes a dent in the global missing baryon problem. Those baryons “must” be somewhere, so why not some in clusters of galaxies?

The short answer is cognitive dissonance. If one comes to the problem sure of the answer, then one sees in the data what one expects to see. MOND fits rotation curves? That’s just a fluke: it bounces off the wall of cognitive dissonance without serious consideration. MOND needs dark matter in clusters? Well of course – we knew that it had to be wrong in the first place.

I understand this perspective exceedingly well. It is where I started from myself. But the answer I wanted is not the conclusion that a more balanced evaluation of the evidence leads one to. The challenge is not in the evidence – it is to give an unorthodox idea a chance in the first place.

6 thoughts on “Missing baryons in LCDM and MOND

  1. a small typo: “… and as if it is plausible”

    Your debunking of the bullet cluster’s “smoking gun” status (hum) in light of the missing baryon problem is especially useful I think.

    The first figure is rather compelling. But if I understand correctly, the use of a fraction in Y axis, as well as a log scale on the X axis, puts the emphasis away from the sum total missing mass. This quantity is probably larger in MOND than in lCDM, since MOND fails on large scales. You are giving a similar importance to all scales – which sounds reasonable though.


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