Observational Evidence Against Birefringence over Cosmological Distances

In a recent paper, Nodland and Ralston [1] claim to find a systematic rotation of the plane of polarization of electromagnetic waves propagating over cosmological distances. Their claimed effect is large, requiring the plane of polarization from high redshift objects to be rotated by as much as 3.0 radians – an easily detectable signature. Here we report new optical data taken with the Keck Telescope, and radio observations made with the Very Large Array (VLA) which show that any such rotation is less than 3 degrees out to redshifts in excess of two. The data used by Nodland and Ralston consisted of radio measurements of the integrated polarization of extragalactic radio sources. After correcting for Faraday rotation, they compare the intrinsic angle of polarization, χ, to the major axis of the radio source, ψ. They suggest that “On symmetry grounds χ would be expected to align with the major axis angle ψ of the galaxy.” High resolution observations of extragalactic radio sources [2,3] show that such an expectation is optimistic. The integrated polarization of a radio source is the vector sum of the polarized radiation from several different emission regions, which have different angles of polarization. The resulting degree of polarization is generally low, with a net angle only weakly related to the major axis of the radio source. Nodland and Ralston fit the misalignment angle β = χ − ψ to a dipole anisotropy of the form β = 12Λ −1 s r cos(γ). Here, r is a distance which they define as r = 6.17 × 10[1 − (1 + z)− 3 2 ] meters for a Hubble constant of 100 km/sec/Mpc, and Λs is a scale length which they find to be about 0.9× 10 meters, or nearly one billion light years. γ is the angle between the direction to the radio source and a pole direction ~s, whose coordinates are 20± 2 hours in right ascension, and −10± 20 degrees in declination. Thus, the Nodland and Ralston relation states that the plane of polarization of emission from cosmological objects should be seen to be rotated by an amount: β = 31.8r cos(γ) degrees. Note that in their paper, Nodland and Ralston arbitrarily add ±π to the measured β values such that β is constrained to be positive for positive cos γ, and negative for negative cos γ. It is this procedure which leads at first sight to the apparently strong correlation in their Fig. 1d. In fact, judgements of the significance must be based on the data within each quadrant separately, as is pointed out by NR. We shall not discuss the statistical or theoretical arguments in their paper. Problems with their statistical methods have been discussed by Carroll and Field [4], Eisenstein and Bunn [5], and Loredo, Flanagan and Wasserman [6]. Here we will appeal directly to recent high resolution polarization observations of distant objects with well defined structural axes against which we can test the claimed rotation. A cosmological rotation of this type has already been rejected by Cimatti et al. [7] based on polarized UV light from the distant radio galaxy MRC 2025-218 (z = 2.63). The polarized light is due to electron or dust scattering of light emanating from the galaxy nucleus, and the observed electric vectors are nearly exactly perpendicular to the axis of extended UV and Lyα emission, as is often found in high redshift radio galaxies [7–9]. Cimatti et al. [7] show that the angle χ− ψ = 87± 10◦, and state that “the plane of polarization is not rotated by more than ten degrees when the radiation travels from z = 2.63 to us.” The rotation predicted from the relation of Nodland and Ralston for this object is 163◦ – close to a π ambiguity, however. The presence of such an ambiguity can be confidently ruled out by the results of optical polarimetry for lower redshift radio galaxies, [8,9], which show a strong tendency for the misalignment angles to cluster near 90◦. With a large optical telescope, a polarization image of a faint, distant radio galaxy can be made, and this directly gives the polarization distribution of the radiation from the extended emission regions. When this is done, the polarization vectors typically show a centro-symmetric pattern, with the E-vectors perpendicular to the radius to the nucleus. This is the signature of scattering (whether by dust or from electrons) of radiation from a point source. A