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<p>Previous circulars described the curious phase differences
between the RCP and LCP correlations. A plausible connection with
differential antenna tilts was suggested. <br>
</p>
<p>If this is indeed the case, we should see the effects of the R-L
phase differentials in the cross-hand data for highly polarized
sources. Three of the four objects observed in this study are
indeed strongly polarized, so I have looked closely for the
expected signature. <br>
</p>
<p>Since we have circularly polarized systems, the expected
signature is a change in the apparent position angle of the
linearly polarized flux of the polarized sources. The magnitude
should be about the same as the observed R-L phase, and it should
be greatest for those sources which transit nearest the zenith
(i.e., largest for 3C286, and least for 3C273). Finally, it
should change with difference reference antennas, as the effect of
calibration is to put all antennas into the phase frame of the
reference antenna. <br>
</p>
<p>As will be described below, all of these expectations, *except
one* are met. <br>
</p>
<p>To do these tests, I extracted a single spectral window from the
data (to speed up the rather laborious processing). I chose a
frequency (4936) for which there was both a 3-bit SPW and an
identical 8-bit SPW (identical means the same center frequency,
wiodth, resolution, and observation time). <br>
</p>
<p>To check on the effect of changing reference antennas, I
calibrated, and imaged, with three different reference antennas,
chosen for having very different R-L profiles in the prior work:
ea01, ea02, and ea19. <br>
</p>
<p>Data were calibrated with standard techniques, and self-cal,
using an excellent model, performed on each. R-L phase plots were
made, and confirmed what has been reported before. <br>
</p>
<p>Images in I, Q, and U were then generated (to be shown below). I
have two special tricks which were performed to improve the
images: <br>
</p>
<p>(1) BLCHN, which does a correlator-based solution using the RR
and LL data, and <br>
</p>
<p>(2) RLCAL, which solves for the R-L phase difference, based on
the temporal change in position angle of the polarized emission.
<br>
</p>
<p>Details are described below. <br>
</p>
<p><b>A) Stokes I images. </b><br>
</p>
<p>The observing duration for each source in this run was about the
same for each: about 15 minutes (a bit more on OQ208). Hence,
each should have about the same noise limit. The initial
'dynamic range' for all four sources was about the same -- about
25,000:1 (peak to rms) -- somewhat less for 3C273 (which will be
explained below). The expected rms noise is about 35 microJy/beam
-- the observed limits were much higher: 76, 133, 275 and 1440
microJy/beam for OQ208, 3C287, 3C286 and 3C273, respective. <br>
</p>
<p>No amount of self-cal can improve on these results. The source
of the problem lies in the failure of the correlator gains to be
described in terms of product as antenna gain fluctuations. The
effect on the imaging is easily seen in the images themselves.
See below. <br>
</p>
<p>AIPS has a couple of nifty programs to solve for and utilize
correlator-based gains. BLCHN solves for these on a
channel-by-channel basis. I used the program to find and apply
these gains. BLCHN uses a model (clean components) and the
self-calibrated data. For this application, I solved for a single
solution, for each baseline, averaging over the entire observation
duration. (BLCHN is a very dangerous program -- were we to use a
short time interval, it will happily make the data match the model
*exactly* -- no matter how far the model is from reality). <br>
</p>
<p>Attached are 'before' and 'after' image pairs, for each source,
in Stokes 'I'. Things to note:</p>
<p>a) For OQ208, 3C286 and 3C287, the application of this constant
correlator-based correction has greatly improved the images. The
grey scales in each change in proportion to the peak brightness:
-0.1 to 1 mJy for OQ208, -0.2 to 2 mJy for 3C287, -0.4 to 4 mJy
for 3C286, and -1.4 to 14 mJy for 3C273. </p>
<p>b) The 'closure perturbations' for 3C273 are much more prominent
than the other sources -- this is because this object is at +2
declination, so the u-v tracks are nearly perfectly horizontal,
which results, in the transform, with the error effect primarily
seen in the N-S bar. <br>
</p>
<p>c) The factor of improvement is quite large: a factor of 4.5 for
3C286, 3.5 for 3C286, 2.0 for OQ208, and 2.5 for 3C273. The noise
in OQ 208 is near thermal (it is the weakest source) -- all the
others are still well above thermal, especially 3C273.
Apparently, a (constant) closure correction is not enough to
remove all the errors. the noise in 3C273, in particular, remains
a factor of about 20 higher than thermal. <br>
</p>
<p><br>
</p>
<p><b>B) Polarization Images. <br>
</b></p>
<p>Stokes Q and U images were made for all sources. OQ208 is nearly
completely unpolarized -- the images have what appears to be
noise-limited appearance. <br>
</p>
<p>For the other sources, there is significant polarized emission:
3.5% for 3C287, 11,.5% for 3C286, and nearly 10% for 3C273.
Examination of the Q and U images for 3C286 in particular, clearly
showed the effect of a change in R-L phase for some of the scans.
<br>
</p>
<p>Some years ago, I asked Eric to generate a program to solve for
R-L phase changes -- RLCAL. This is essentially a polarization
positional angle self-calibration program: It compares the
observed RL and LR phases to that predicted by a model, and finds
the changes in the RL and LR phases which best matches the model.
<br>
</p>
<p>This program was run on the observed images for 3C286, 3C287 and
3C273 data. A very clear signature was seen with the following
characteristics:</p>
<p>a) A phase signature of a few degrees (maximum 4.0 for 3C286),
with 'odd' symmetry about meridian transit. <br>
</p>
<p>b) Far stronger on 3C286 than the others, almost no signature at
all on 3C273. <br>
</p>
<p>c) Sharply dependent on parallactic angle. <br>
</p>
<p>d) <b>Independent of the reference antenna. (!!!) </b>I
repeated this full operation (calibration, imaging,
self-calibration) with three different reference antennas, chosen
because they have starkly different R-L phases as seen by the
earlier work. They all gave the same signatures to the RLCAL
program. <br>
</p>
<p>Attached are three figures, showing the effect of applying the RL
and LR phase changes to the data. OQ 208 has no polarization, so
is omitted. These are in Stokes 'Q' only -- the 'U' images show
the same effects. <br>
</p>
<p>The 3C286 and 3C287 images are greatly improved, although clear
residuals remain. However 3C273 is hardly improved at all -- no
surprise as the observed RL and LR phase solutions from RLCAL are
nearly constant. <br>
</p>
<p>To show the correlation with parallactic angle, here are the
generated RL solutions for 3C286 (in degrees) , along with the
actual parallactic angle:</p>
<p>RL Phase Par Angle</p>
<p>0.4 -74</p>
<p>0.5 -74 <br>
</p>
<p>0.5 -74</p>
<p>0.9 -74</p>
<p>0.8 -74</p>
<p>1.1 -72</p>
<p>1.6 -69</p>
<p>2.6 -62</p>
<p>4.0 -45</p>
<p>0.7 3</p>
<p>-2.8 48</p>
<p>-2.8 64</p>
<p>-2.8 64</p>
<p>-2.4 70</p>
<p>-2.0 72</p>
<p>-1.8 74</p>
<p>-1.7 74</p>
<p>-1.6 74</p>
<p>---------------------------------</p>
<p>A similar, but much smaller range in phase correction, is seen in
3C287. For 3C273, the range in parallactic angle is 79 degrees
(-31 to +48 degrees), but the range in RL phase correction is only
1.4 degrees. So the correlation of phase correction with
parallactic angle is far from perfect. Perhaps the correlation is
better with elevation? but then, why do the profiles have very
clear odd symmetry w.r.t. transit? <br>
</p>
<p>C) Bottom Line:</p>
<p>I'm puzzled, perplexed, and completely devoid of a proposed
solution which matches both the R-L and the RL phase effects.
They are similar, yet different. <br>
</p>
<p>All suggestion will be seriously considered! <br>
</p>
<p>Rick<br>
</p>
<p><br>
</p>
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