[evlatests] R-L Phase Differences -- a 'simple' explanation

[Brian Svoboda]

Small erratum on my previous message: the histogram for all antennas was 
computed using (effectively) the minima and not the median values as 
advertised. A revised version is attached. The fit results CSV file in 
the FTP directory have also been revised. The plots of the fits and the 
"triangle" plots of the errors were not affected however.

Clear skies,
Brian

On 4/8/22 15:38, Brian Svoboda via evlatests wrote:
> Dear colleagues,
>
> Using the data from Rick, I have fit the RR-LL phase difference 
> measurements for hourangle and latitude for each antenna (along with a 
> phase offset nuisance parameter). Plots and fit data may be found in 
> my FTP area at:
>
>     /home/ftp/staff/bsvoboda/rl_phase_diff  (for machines with access)
>     ftp://ftp.aoc.nrao.edu/staff/bsvoboda/rl_phase_diff
>
> The fits are performed using an MCMC for one model applied to each of 
> the four targets simultaneously. Please find examples figures attached 
> for "ea03" with fit and 1-sigma errors along with a plots of the 
> covariances. Note that the statistical uncertainties of the datapoints 
> (as inferred by the MAD) likely underestimate the uncertainties 
> because of systematic effects present for some antennas that cannot be 
> captured by the model. The models appear to generally fit quite well, 
> however, and produce fairly reasonable constraints even at low SNR.
>
> Given that the E-W tilts (as measured by differences in hourangle) and 
> N-S tilts (as measured by differences in site latitude) often occur 
> together, tilts can be as high as approximately 8 arcmin. Histograms 
> are attached for the median parameter posterior ("mu_50") for the HA 
> and latitude differentials. There appears to be a rough preference for 
> positive HA and negative latitude values.
>
> With full information on the pad and antenna measurements, it would 
> likely be straightforward to compare the measured-to-expected tilt for 
> each.
>
> Clear skies,
> Brian
>
> [1] Note that the code used for the data cleaning, fitting, and 
> plotting is available at https://gitlab.nrao.edu/bsvoboda/model-rl-phases
>
> On 4/1/22 10:41, rperley via evlatests wrote:
>> There is a simple explanation for the R-L phase differentials -- a 
>> differential tilt between the two antennas.  If the two antennas' 
>> poles point in slightly different directions, the parallactic angles 
>> seen by each are different, which results in a different measured 
>> phase for the two polarizations.
>>
>> For the 'RR' correlation, the phase difference is -(delta par angle), 
>> for the 'LL' correlation, it is +(delta par angle), so the R-L 
>> difference is twice the difference is parallactic angle between the 
>> two antennas.
>>
>> This effect is independent of band -- it is purely geometrical.
>>
>> To show how these differentials vary with source declination, I 
>> generated plots for the four sources observed:  3C286 (dec = 30.5), 
>> OQ208 (dec = 28.5), 3C287 (dec = 25.2), and 3C273 (dec = 2.1).  I 
>> generated curves for a E-W tilt, and a N-S tilt.
>>
>> Attached is the resulting plot, showing the predicted R-L phase in 
>> degrees as a function of Hour Angle, for the four sources. Solid 
>> lines are for an E-W tilt, Dashed lines for N-S tilt.
>>
>> The match to the observed data is extremely good.  (To be fair, the 
>> match to the largest of the 'even' tilts is extremely good). But I 
>> bet that a suitable combination of E-W and N-S tilts would give a 
>> good fit to almost all of the data.
>>
>> There is only one problem -- the amplitude of the tilt required to 
>> give the size of the observed phase is about 5 times larger than the 
>> largest measured tilt.  The plots were generated with a tilt 
>> differential (between the two antennas) of 6 arcminutes.
>>
>> So, if this model has any relevance, it begs the question:  How do we 
>> measure the antenna tilts?  Are these tilts different than those used 
>> in the model?
>>
>> Rick
>>
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>
>
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-- 
Brian E. Svoboda, PhD
Assistant Scientist
National Radio Astronomy Observatory (NRAO)

Office: DSOC 312
Office Phone: +1 (575) 835-7246
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