Wednesday, October 19, 2005

Revisiting the evidence for dark matter

Recently, the CERN Courier, a usually reliable source, came out with this article: General relativity versus exotic dark matter.
Determinations of the rotation speed of stars in galaxies (galactic rotation curves) based on the assumption that Newtonian gravity is a good approximation have led to the inference that a large amount of dark matter must be present - more than can be accounted for by non-luminous baryonic matter. While there are plenty of attractive theoretical candidates for the additional dark matter, such as a lightest supersymmetric particle (LSP), it is also interesting to look into the details of the calculations that suggest the need for such exotica. Now F I Cooperstock and S Tieu of the University of Victoria have reworked the problem using general relativity in place of Newtonian gravity, and they find no need to assume the existence of a halo of exotic dark matter to fit the observed rotation curves.
This is based on a July arXiv preprint: General Relativity Resolves Galactic Rotation Without Exotic Dark Matter.

Then only a week ago Space.com jumped on the story: Dark Matter: Invisible, Mysterious and Perhaps Nonexistent. However, it does caution, "The new analysis has been submitted to the Astrophysical Journal but has yet to be reviewed by other scientists."

It seems that more than a few people are skeptical about dark matter, and eager to tout anything that seems to explain it away. Unfortunately for them, the Cooperstock-Tieu paper was reviewed by other scientists, who'd already thrown cold water on it in another arXiv preprint from August, Singular disk of matter in the Cooperstock and Tieu galaxy model.

Cosmologist Sean Carroll at Cosmic Variance explains in some detail where Cooperstock and Tieu seem to have gone wrong: Escape from the clutches of the dark sector.
To be honest, there are a bunch of problems with this paper. For example, equations (1) and (2) seem mutually inconsistent — they have chosen one coordinate system in which to express the spacetime metric, and another in which to express the spacetime velocity of the particles in the galaxy. Ordinarilly, you have to pick one coordinate system and stick to it. More importantly, Korzynski has analyzed their solution carefully and noticed that they have secretly included not only the mass of the stars, but a completely imaginary thin sheet of infinite density in the galactic plane. So the fact that the rotation curves don’t decay as they should is really no surprise.


Sean also writes some interesting stuff about problems using perturbation theory to "solve" the Einstein equations, and this may be relevant to work of Kolb and others (see this) that attempts to explain accelerating cosmic expansion without dark energy or quintessence. (See here for my overview of those topics.) But we're getting too far off course, so put this on the shelf for now.

Anyhow, problems with choice of coordinate systems are one of the most common sources of error in general relativity. Even Einstein himself had managed to screw up at times on this account. In fact, such a lapse led him to cease submitting papers to a leading physics journal, the Physical Review, as explained in this article: Einstein Versus the Physical Review. It seems that in 1936 Einstein had written a paper with his assistant Nathan Rosen disproving the possibility of gravity waves. He was miffed that the journal had put the paper out for peer review, and a referee discovered that a problem with choice of coordinate systems invalidated the result. Although Einstein soon recognized his mistake and published a revised paper a few months later in another journal, he never again submitted work to the Physical Review.

So both the CERN Courier and Space.com missed the doubts of other cosmologists about the Cooperstock-Tieu paper. But there's something much more important that they missed: There is a huge amount of other evidence for "exotic" dark matter which is independent of galactic rotation curves. (This is sometimes known as the "galaxy rotation problem".) Recall that there are two types of dark matter: baryonic dark matter (made mostly of protons and neutrons) and exotic dark matter (all other gravitating matter that's not visible). Here's some of the evidence:

  1. The average velocities of galaxies in large galaxy clusters allows one to calculate the mass of the cluster -- and it's much too high to be accounted for by the visible (baryonic) matter. (This comes from the "virial theorem".)
  2. X-ray observations of galaxy clusters show the presence of a lot of hot gas that could not persist in the cluster without much more mass due to exotic dark matter. See: Scientists Find Missing Matter.
  3. Gravitational lensing caused by large galaxy clusters affecting objects behind the cluster (on the same line of sight) also implies much more mass in the cluster.
  4. Clusters of clusters ("superclusters") could not have formed to the extent that they have without exotic dark matter. A couple of recent surveys of many thousands of galaxies supports this. This is all part of the issue of cosmological structure formation, which is easiest to explain if there is a large amount of exotic dark matter.
  5. The amplitudes of temperature fluctuations in the cosmic microwave background require much more mass than available as baryonic matter.
  6. Various anomalous objects have been detected that appear to have the mass of a galaxy but little or no visible matter -- "low surface brightness galaxies" and "dark galaxies". See: Astronomers claim first 'dark galaxy' find, and Have we seen the first "dark galaxy"?.
  7. New calculations of star velocities in elliptical galaxies are consistent with large amounts of exotic dark matter. See: here, here, here, here.


The bottom line is: if exotic dark matter didn't exist, cosmologists would need to come up with new explanations for a whole lot of other fairly well-established phenomena.

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Other references:

Experimental Searches for Dark Matter - survey/review article from 2002

Dark matter - survey and many additional references on dark matter

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