The Bullet Cluster

A sufficient number of inquiries have been generated by the press release concerning the "direct proof of dark matter" (August 2006) that I am posting some comments here.

To start with the bottom line, I am inclined to agree with the authors that there is likely to be more mass in the bullet cluster than meets the eye - even in modified gravity theories. I am not entirely sure this has to be the case, because it is a non-symmetric, non-equilibrium situation. Relativistic extensions of MOND theory (like TeVeS) can have a strong non-linear response to off axis elements in the mass-energy tensor. It would take a very involved, detailed modeling exercise to check that - to my knowledge that exercise has yet to be done. It has been my experience that when we use our Newtonian intuition to say "modified theories surely can not do X" we often go wrong, so this is not a trivial concern.

Nevertheless, the most straightforward interpretation is that there is indeed unseen mass. Unfortunately, that doesn't really tell us anything we didn't already know. While MOND has had more successes than most astronomers seem to realize (it doesn't do just rotation curves - see, e.g., McGaugh & de Blok 1998; Sanders & McGaugh 2002), the one type of system for which it persistently comes up short is rich clusters of galaxies (e.g., Aguirre et al.; Sanders 2003). That is, even after taking MOND into account, we infer more mass from dynamical measures than we currently see in all known baryonic components. Is this bad for the theory? Yes. Is it worse than the problems with CDM? Not obviously. [Don't know what those are? Read the literature. A summarry is given here and in this table.] But one is obliged to say, in MOND, that there must still be more mass to be discovered in clusters. (Consider it a prediction.) I'd be more upset about this if it hadn't already happened before - there was a time, in my memory, when it was believed that all the baryons were in the stars, before we appreciated how much mass was in the X-ray gas. Early on, MOND failed in clusters by an over order of magnitude (one reason I paid it scant attention until much later); after the X-ray gas was discovered that dropped to a factor of 2 or 3. (Indeed, in his original papers, Milgrom suggested the X-ray gas could represent more mass than was then widely appreciated.)

The observations of the bullet cluster simply reaffirm the need for more mass in rich clusters. It doesn't tell us what form that mass is in; it certainly doesn't demand that that mass be CDM (tempting as that might be). It does add something new, and that is that whatever that mass is, it is not collisional. So not gas. Could be WIMPS, yes, but it could also be black holes or brown dwarfs or massive neutrinos or very small rocks [*] or any of the other ideas we've had about hiding mass.

If MOND is to survive, the extra mass in clusters must eventually be discovered. By the same token, if CDM is correct, there must be a legitimate explanation for MOND. [There have been some unconvincing assertions to this effect, but little real progress. There have also been denials: as one prominent theorist put it to me, "We don't have to explain MOND!" MOND encapsulates an empirical phenomenology - so yes, yes you do have to explain it.] An interesting corallary is that if substantially more mass is discovered in clusters, this may falsify CDM. Currently, the baryon fraction in clusters (unlike that in galaxies [**]) is in good agreement with the cosmological mass fraction and BBN. That falls apart if there are a lot more baryons there. Things would be even worse if it turns out to be massive neutrinos (~ 1eV would do it), as this would negate the structure forming motivation for CDM. So it should eventually be possible to distinguish the theories. There is a lot more evidence (both pro and con) to weigh than a single odd cluster.

*This is a joke. It could not really be very small rocks. So much mass in very small rocks would lead to an optically opaque system with huge far-IR emission.

**This is not a joke. While the baryon mass budget more or less adds up in clusters, it falls short in individual galaxies. (I've been saying this for a long time, though the only upshot seems to be the addition of another free parameter to galaxy formation models.) For a given halo mass, the fraction of baryons you actually see declines systematically with the characteristic velocity of the system. That fraction may be near unity in clusters, but it is only about 40% in the Milky Way. That's a serious problem because our inventory of Milky Way baryons is as complete as astronomy gets. The problem gets worse as you go to smaller systems; typically in dwarfs the number of detected baryons is only a few percent of those that should be associated with a dark halo of the observed mass. There are many outs - the baryons have been blown away, or they are there in some unobserved form... Sound familiar? CDM suffers the same problem in galaxies that MOND suffers in clusters: there is some missing baryonic mass. If we attempt to be objective (never really part of the value system in cosmology), the missing baryon problem is bad for both theories. Some put it to me that it is worse for MOND, since it seeks to do away with dark matter, so it shouldn't ever need dark matter. I think that is a fair point, but neither should we be overconfident of having detected all baryons, especially when we all believe that BBN requires there to be a lot more baryons out there than we have directly accounted for. (Or as Bob Sanders puts it - "There is nothing in MOND that requires all baryons to shine with M/L ~ 1.") And it is a very serious problem for CDM as well. We have two missing mass problems here - in each galaxy there is the dynamical missing mass (presumably CDM) and additionally missing baryons (which must be in some dark form). Worse, getting the baryon content of each galaxy right requires considerable fine tuning. Since the existence of invisible mass is not a rigorously falsifiable idea, such fine-tuning problems are about the worst problem the theory can face.

Below is a figure illustrating the baryon deficit in MOND and CDM. The red line is MOND, the orange line is CDM. The latter does better in clusters (green triangles) while the former does better in spiral galaxies (blue circles) and dwarfs (blue squares). The difference between the line and the points is the deficit in each case. The red line overshoots the cluster data, meaning that MOND wants more mass than is seen in clusters. The orange line overshoots the blue point, meaning that CDM should have a lot more baryons associated with each galaxy halo than are observed.

A funny thing is that the lines cross at about 1000 km/s. If you look on scales bigger than this, the universe looks like LCDM. If you look at scales smaller than this, the universe looks like MOND.

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