[evlatests] More on R-L phases

[Rick Perley]

Previous circulars described the curious phase differences between the 
RCP and LCP correlations.  A plausible connection with differential 
antenna tilts was suggested.

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.

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.

As will be described below, all of these expectations, *except one* are 
met.

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).

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.

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.

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:

(1) BLCHN, which does a correlator-based solution using the RR and LL 
data, and

(2) RLCAL, which solves for the R-L phase difference, based on the 
temporal change in position angle of the polarized emission.

Details are described below.

*A) Stokes I images. *

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.

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.

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).

Attached are 'before' and 'after' image pairs, for each source, in 
Stokes 'I'.  Things to note:

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.

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.

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.


*B)  Polarization Images.
*

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.

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.

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.

This program was run on the observed images for 3C286, 3C287 and 3C273 
data.  A very clear signature was seen with the following characteristics:

a) A phase signature of a few degrees (maximum 4.0 for 3C286), with 
'odd' symmetry about meridian transit.

b) Far stronger on 3C286 than the others, almost no signature at all on 
3C273.

c) Sharply dependent on parallactic angle.

d) *Independent of the reference antenna.  (!!!) *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.

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.

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.

To show the correlation with parallactic angle, here are the generated 
RL solutions for 3C286 (in degrees) , along with the actual parallactic 
angle:

RL Phase    Par Angle

0.4            -74

0.5            -74

0.5            -74

0.9            -74

0.8            -74

1.1            -72

1.6            -69

2.6            -62

4.0            -45

0.7               3

-2.8            48

-2.8            64

-2.8            64

-2.4            70

-2.0            72

-1.8            74

-1.7            74

-1.6            74

---------------------------------

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?

C) Bottom Line:

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.

All suggestion will be seriously considered!

Rick

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