We consider the same set of data as was used in [10], with
the corrections noted above. This set includes 160 sources,
with redshifts as high as 2.012. The first step is to establish
the existence of a reliable correlation between 
and 
,
so that we may test its behavior for distant galaxies. Following
[24], we have divided the data into distant and nearby
objects, with the division drawn at z=0.3; there are 89 sources
with z<0.3, and 71 with 
. In Figures One and Two, we
have plotted histograms of 
for these two sets. We have
for the purposes of these figures
defined so that it lies between 
and 
,
and grouped the data into bins which are 
wide.
Figure 1: Histogram of number of galaxies vs. , for
galaxies with z<0.3.
Figure 2: Histogram of number of galaxies vs. , for
galaxies with .
In Figure One, representing nearby galaxies, there appears to be
evidence for a narrow enhancement at 
, and
a broader peak at 
. However, the
correlation is evidently not very strong. The most likely explanation
for this fact is that many of these galaxies are members of a
different population than those at high redshift, which
can be observed only if they are of high luminosity,
and the lower-luminosity galaxies demonstrate a weaker correlation
between polarization and position angle. For the more distant
galaxies shown in Figure Two, there is a very clear peak at
. There is no noticeable peak at
in this sample; again, this may be
explained if the galaxies with are
members of a lower-luminosity population. (See [2, 3] for
discussion of these correlations and their interpretation in
terms of models of the sources.)
It is reasonable to suppose that the galaxies with a higher degree
of maximum polarization would show any effect more strongly than
those that are polarized only weakly. We therefore show in Figures
Three and Four the same plots as in Figures One and Two, this time
limited only to those sources with maximum polarization greater than
or equal to 
. These are the sources that were analyzed in
[10].
Figure 3: Histogram of number of galaxies vs. , for
galaxies with z<0.3 and maximum polarization 
.
Figure 4: Histogram of number of galaxies vs. , for
galaxies with and maximum polarization .
The peaks found in the previous plots, at and 
at low redshifts and more dramatically at in the
high-redshift sample, are also
evident in Figure Three and Figure Four, arguably more convincingly.
However, any increased correlation is offset to some degree by the
smaller number of data points. Therefore, in the remainder of this
paper we will not discard those sources with maximum polarization
; we will thus use precisely the same data as were analyzed
in [24].
The crux of our disagreement with [24] can be found in Figure
Two, the distribution of for sources with .
As noted in [10], this plot constitutes vivid evidence that
the polarization angle in these sources is intrinsically perpendicular
to the position angle on the sky. If the claim of [24] is true,
it is necessary to believe that the peak at is an accident,
and these data are actually drawn from a distribution which is
intrinsically centered at , with position- and redshift-dependent
contributions of order . We will argue in the next section
that this is not the simplest interpretation of these data.