Is There Evidence for Cosmic Anisotropy
In the Polarization of Distant Radio Sources?
Sean M. Carroll

Polarized radio galaxies offer a unique opportunity to test some strongly-held beliefs about cosmology and fundamental physics. These objects often have highly collimated jets, so that one may draw an axis through them and measure Psi, the angle of this axis with a line of constant declination. They are also often polarized, so that we can measure Chi, the angle described by the plane of polarization. If ordinary electromagnetism (as described by Maxwell's equations) and conventional cosmology (as described by the Roberson-Walker metric) are both valid, the relative angle Chi-Psi between the polarization of the radiation and the orientation of the source should be preserved as the light travels through space -- we should observe Chi-Psi to be whatever it was at the galaxy itself.

In 1990, George Field, Roman Jackiw and I wrote a paper (Phys. Rev. D 41, 1231; spires listing; pdf file) which used observations of these angles (collected by others) to place limits on the magnitude of non-Lorentz-invariant interactions of photons as they traveled through the universe -- i.e., to test the possibility that spacetime had a fundmentally preferred direction. To the surprise of nobody, we found that the data were consistent with no extraordinary effects. In 1997, Nodland and Ralston (Phys. Rev. Lett. 78, 3043; astro-ph/9704196) examined the same data and claimed to find evidence for an anisotropic effect -- a preferred direction in space -- closely related to the one we investigated. (More info.)

Spurred by this result, George Field and I undertook to re-examine the data. We argue that the observations are consistent with no signal, and there is no evidence for anisotropic chiral effects on the propagation of photons over cosmological distances. We wrote a paper detailing our results; it is available as astro-ph/9704263, or in an inelegant html version. A slightly condensed version appeared as Phys. Rev. Lett. 79, 2934. Similar conclusions were reached by Eisenstein and Bunn (paper at astro-ph/9704247, Phys. Rev. Lett. 79, 1957; see also this web page), and by Wright (see his cosmology tutorial).

Where they went wrong. To search for some hypothesized effect in a set of data, it is necessary to compare those data to both what one would predict in the absence of the effect, and in the presence of the effect. Nodland and Ralston essentially computed how well the data fit two different hypotheses: their "null hypothesis" (no effect) was that there is simply no relation between the polarization angle and orientation of the radio sources, and their alternative hypothesis was that the radiation is emitted with a plane of polarization aligned parallel to the source, and then rotated by an amount depending on the distance to the source and its direction in the sky. They then argued that the data fit the second possibility better. It has been known for years that their null hypothesis is untrue, and there is a relation between the polarization and orientation angles; the observed relation is that the two are perpendicular, as the first figure below indicates. This suggests a third alternative, that the polarization is emitted perpendicular to the orientation of the source, and travels to us without changing. This scenario requires no modification of conventional cosmology or electromagnetism, and is consistent with (and indeed expected from) what we know about the sources themselves. The statistical tests we performed demonstrate conclusively that this hypothesis fits the data much better than either of the two considered by Nodland and Ralston. There is, accordingly, no reason to overthrow the foundations of physics on the basis of these data.

New data and analyses. With more recent and detailed observations, one can put better limits on such effects by using small-scale information about the polarization of the radio galaxies (i.e., not coarse-graining by averaging over the source). J.P. Leahy has written a comment pointing this out (paper at astro-ph/9704285; see also his web page). There is a related preprint by John Wardle, Rick Perley and Marshall Cohen; you can look at their press release, or get the paper from astro-ph/9705142 or Phys. Rev. Lett. 79, 1801. They have a version of the second figure below, for which the data are much better and the disagreement is even more striking.

A Bayesian analysis of the original data set has been performed by Loredo, Flanagan, and Wasserman (astro-ph/9706258). The advantage to this approach is that it more or less automatically avoids the potential pitfalls of inappropriate null hypotheses and entanglement by 180-degree ambiguities in the observed quantities. They place an upper limit on possible anisotropy which is noticeably smaller than Nodland and Ralston's finding, providing additional reassurance that the effect was not present even in the original data.

Nodland and Ralston are sticking to their original position, as indicated by two responses (astro-ph/9705190 and astro-ph/9706126) to their critics, and a subsequent update (astro-ph/9708114). Eisenstein and Bunn, and Leahy, have appended additional material to their papers, mentioned above, to reply to these responses -- their original points remain unchanged. A preprint by Ralston, Jain, and Nodland (astro-ph/9707326), suggesting an explanation for the ``corkscrew effect'' using geometrical phases, has been submitted to PRL. In March 1998, Jain and Ralston submitted a paper (astro-ph/9803164) claiming to once again detect anisotropy, this time in a different data set.

Although a consensus has arisen that the effect does not exist in the data, there have also been attempts to offer theoretical explanations by Moffat, Obukhov, Korotky, and Hehl, Dobado and Maroto, Kühne, Mansouri and Nouzari, Sachs, and Bracewell and Eshleman.

On the other hand, there are perfectly respectable phenomena that do alter the relationship between polarization and orientation angles, and observations such as those discussed here can be used to investigate such effects. An example is the paper by Surpi and Harari, which discusses the role of weak gravitational lensing on these angles. (Earlier related work appears in two papers by Kronberg et al.: 1, 2.) Another example is contained in a paper of mine, ``Quintessence and the Rest of the World' . I point out that models of slowly-rolling scalar fields, proposed as sources of dynamical vacuum energy, have a good chance of interacting with electromagnetism in just the right way to rotate the polarization vectors of distant objects (in a sense independent of the direction on the sky).

Popular accounts. Additional accounts are available from Associated Press, The New York Times, the American Institute of Physics, Science News, and Time. Follow-up articles, concerning some of the refutations of the original Nodland and Ralston paper, have appeared in Science News, Physics World, Popular Science, the LA Times, and Scientific American. (Or at least their respective web pages.) For a less nuanced discussion, see Tabloid.

Diffusion into the culture continues apace. The preferred direction has made the funny pages, courtesy of Hilary Price's Rhymes With Orange. Equally amusingly, it turns out that Lyndon LaRouche knew it all along. It has also been used as evidence for creationism. (And now there's a follow-up to that last piece. I would offer an opinion, but as a member of the evolutionist/big-bang establishment, my views are inevitably tainted.) Arianna Huffington takes cosmic anisotropy as providing support for moral absolutes. (I couldn't make this stuff up.) And you knew this would happen sooner or later: it's a sign of extraterrestrial intelligence.

Here are some figures which illustrate our findings.

This is a histogram of the number of galaxies with a given difference between Chi, the angle of their plane of polarization, and Psi, their orientation in the sky, for distant galaxies (redshifts greater than or equal to 0.3). These angles are only defined up to a rotation of 180 degrees, so on this graph 0 and 180 degrees are to be identified. There is clearly a peak at 90 degrees, with some outlying points; this correlation is understood on astrophysical grounds in terms of magnetic fields in the source galaxies. If there were a significant change in the polarization angle between the source and us, it would be very hard to explain this sharp peak. If Nodland and Ralston are correct, this peak is a statistical fluke; they suggest that the polarization is intrinsically parallel (rather than perpendicular) to the source axis, and that a combination of random errors and cosmic anisotropy conspire to create the distribution shown here.

This is a plot of Chi-Psi vs. r cos(theta), which Nodland and Ralston claim should be linearly related (with a nonzero slope). Here r is the distance traveled by the photon, and theta is the angle between the direction to the source and the preferred direction in the sky picked out by the hypothetical anisotropic effect. (Once again, only galaxies with redshifts greater than 0.3 are plotted.) Their best fit is denoted by the dashed diagonal line, which wraps around a cylinder since 0 and 180 degrees are equivalent. The solid horizontal line represents no effect other than random fluctuations around the value of 90 degrees. Statistical tests reveal that this is a better fit to these data points.

Here is a plot of the positions of the radio galaxies in the sky, this time including all redshifts. The symbols indicate deviations from the peak at 90 degrees; squares denote less than 90, and x's denote greater than 90. The size of the symbol depends on the amount of deviation; smaller symbols are sources whose polarization angle is very close to perpendicular to their position angle. Although this figure does not tell us anything directly about the question of redshift-dependent anisotropies, it gives an idea of the distribution of angles, as well as highlighting the fact that more data is needed in the southern hemisphere (a problem which is even more acute at high redshifts).

Sean Carroll
carroll [at]