Polarimetry

Quick Start Guide

There are two components for polarization calibration:

• Determining the leakage terms (i.e., the polarization impurity between the R and L polarizations).
• Calibrating the absolute polarization angle.

There are two common approaches to determine the leakage terms:

• either observe one or more strong calibrators (> 1 Jy) over a wide range (e.g., > 60 degrees) in parallactic angle and through multiple scans,
• or observe a strong unpolarized (typically less than 1% polarized) calibrator source through at least one scan; see below for more information on determining leakage terms.

To calibrate the absolute polarization angle, observe a calibrator with a well-known polarization angle.

In the following we present detailed information on polarization calibration, including the most common calibrators for this purpose.

Guidelines

For projects requiring imaging in Stokes Q and U, the instrumental polarization can be determined through observations of a bright calibrator source spread over a range in parallactic angle. The phase calibrator chosen for the observations can also double as a polarization calibrator provided it is at a declination where it moves through enough parallactic angle during the observation (roughly Dec 15° to 50° for a few hour track). The minimum condition that will enable accurate polarization calibration from a polarized source (in particular with unknown polarization) is three observations of a bright source spanning at least 60 degrees in parallactic angle (if possible schedule four scans in case one is lost). If a bright unpolarized unresolved source is available (i.e., known to have very low polarization) then a single scan will suffice to determine the leakage terms. The accuracy of polarization calibration is generally better than 0.5% for objects small compared to the antenna beam size. However, to achieve accuracy of polarization calibration to better than a few percent, sufficient signal-to-noise for the leakage calibrator is required to be able to correct for spectral variations in instrumental polarization with typical channel widths of the order of a few MHz. The best results are achieved using an unpolarized calibrator or a bright polarized calibrator with good parallactic angle coverage. More details on different calibration strategies can be found in EVLA Memo #201. At least one observation of 3C286 or 3C138 (or another polarized calibrator with known linear polarization angle) is required to fix the absolute position angle of polarized emission. 3C48 also can be used to fix the position angle at wavelengths of 6 cm or shorter.

High sensitivity linear polarization imaging may be limited by time dependent instrumental polarization, which can add low levels of spurious polarization near features seen in total intensity and can scatter flux throughout the polarization image, potentially limiting the dynamic range. Preliminary investigation of the VLA’s new polarizers indicates that these are extremely stable over the duration of any single observation, strongly suggesting that high quality polarimetry over the full bandwidth will be possible. In addition, geometric effects appear to be limiting the absolute polarization angle calibration especially in cases where a source is observed at opposite sides of transit independent of observing band. A detailed investigation is documented in EVLA Memo #205.

The accuracy of wide field linear polarization imaging will be limited, likely at the level of a few percent at the antenna half-power width, by angular variations in the antenna polarization response. Algorithms to enable removing this angle-dependent polarization are being tested and observations to determine the antenna polarizations have begun. Circular polarization measurements will be limited by the beam squint, due to the offset secondary focus feeds, which separates the RCP and LCP beams by a few percent of the FWHM. The same algorithms noted above to correct for antenna-induced linear polarization can be applied to correct for the circular beam squint. Measurement of the beam squints, and testing of the algorithms, is ongoing.

Ionospheric Faraday rotation of the astronomical signal is always notable at 20 cm. The typical daily maximum rotation measure under quiet solar conditions is 1 or 2 radians/m2, so the ionospherically-induced rotation of the plane of polarization at these bands is not excessive – 5 degrees at 20 cm. However, under active conditions, this rotation can be many times larger, sufficiently large that polarimetry is impossible at 20 cm with correction for this effect. The AIPS program TECOR has been shown to be quite effective in removing large-scale ionospherically induced Faraday Rotation below 2 GHz. It uses currently-available data in IONEX format, which provide a global coarse correction. The effect of this ionospheric Faraday rotation on polarization angles is shown as an example in EVLA Memo #205, in particular see Fig. 3. Please consult the TECOR help file for detailed information. CASA provides a similar capability. With CASA release 4.7 it is possible to correct Faraday rotation effects using the task gencal with caltype='tecim'. The addition of dispersive delay corrections are available experimentally in CASA 5.x releases pending further verification.

Monitoring

The results of a careful monitoring program of these and other polarization calibrators can be found at http://www.vla.nrao.edu/astro/evlapolcal/ for 2011/2012. More recent monitoring data is available from the NRAO archive under project TPOL0003 for secondary calibrators and under project TCAL0009 for primary linear polarization angle calibrators. There is also a list of calibrator monitoring for VLBA observations starting with the 21A semester. If you would like to request a specific set of sources to be monitored, please submit your request to the VLA Observing department in the NRAO Science Helpdesk.

Observing Recommendations

There are several strategies for deriving the Q/U angle calibration:

• Observation of a primary polarization standard (Category A)
• Observation of a secondary polarization calibrator (Category B with Note 3) with auxiliary monitoring observations to transfer from primary.

This calibration is needed to set the polarization vector angle 0.5*arctan(U/Q) and should be done in all cases.

There are several strategies for deriving the instrumental polarization:

• Single scan observation of a zero polarization source (Category C)
• Several scans (minimum of 3 scans over 60 degrees of parallactic angle) of an unknown polarization source. These can be, but are not limited to sources listed in Category B.
• Two scans of a source of known polarization (Category A or B with transfer)

See Tables 7.4.1-7.4.4 below for Category A-D source catalogs.

Polarization Calibrator Catalog and Selection

The following sources are known to be useable for polarization calibration. These consist of a few "pol standard" sources with known stable polarization (for Q/U angle calibration), plus a number of "bright" sources with "monitored" variable flux densities and polarization. Some of these are seen to have only "moderate variability" and could be used as secondary angle calibrators if you can transfer the angle from the monitoring observations. Assume others (particularly "flat spectrum") are highly variable. There are also a few "bright, low pol" sources available as leakage calibrators (but they can have measurable polarization at high frequencies).

NOTE: Be sure to use the VLA OPT Source catalog to obtain the standard J2000 positions and approximate flux densities.

Calibration Selection Procedure:

• Select Polarization Standard (to calibrate polarization angle Q/U) - optimally select one Category A source and observe at least one scan. The percentage polarization and angle for the known stable calibrators as a function of frequency is tabulated in Table 7.2.6 below. Alternative: use a "moderately variable" Category B calibrator and use monitoring information (would need to request monitoring observations, and may have to submit your own SB for this) to transfer from a primary.
• Select Leakage Calibrator (to determine instrumental polarization) - optimally select one Category C low-polarization source or Category B secondary source in optimal Dec range (see the notes of Tables 7.2.1 and 7.2.2) for PA coverage during run (if long enough). Single scans ok for Category C. Alternative: try a Category D CSO if no other options available.

Table 7.2.1 Notes:

• A1. Polarized fraction and angle values for these sources is given in Table 7.2.6 below.
• A2. 3C48 is weak at high frequency and somewhat resolved in larger configurations. Depolarized below 4GHz.
• A3. 3C48 has been undergoing a major event since 2016 affecting its polarization and flux density properties, especially above 5 GHz. For accurate polarization angle calibration, care should be taken that a current model of its polarization properties is available and applied during calibration.
  
• A4. 3C138 has been undergoing a major event since 2021 that could be affecting its polarization and flux density properties, especially above 5 GHz. For accurate polarization angle calibration, care should be taken that a current model of its polarization properties is available and applied during calibration. This can be obtained from monthly monitoring observations available from the NRAO archive with the project code TCAL0009.
  
• A5. 3C286 is our foremost primary calibrator and should be used if available.

Table 7.2.2 Notes:

• B1. In optimal Declination range to be used as leakage calibrator with PA coverage. Recommended as calibrators and if necessary can be used as secondary standards with monitoring.
• B2. Low polarization at low frequencies (L, sometimes S,C), do not use as angle calibrator.
• B3. Highly variable and interesting in its own right.

Table 7.2.3 Notes:

• C1. Very bright and low polarization (<1%), but variable flux density. Approaches 1% polarized at 43 GHz.
• C2. Steep spectrum and resolved, low polarization below 10GHz (best <4.5GHz). Stable polarization above. About 6% polarized at 43 GHz See Table 7.2.6 below.
• C3. Weak at high frequency, but stable flux and very low polarization.
• C4. Very weak at high frequency, bright and low polarization below 9GHz.

The following northern sources are known to be CSO (Compact Symmetric Objects) and are characteristically unpolarized. They can be used over a range of frequencies (Gugliucci, N.E. et al. 2007, ApJ 661, 78) as "low pol" leakage calibrators. CSOs tend to be on the weak side and should be used with care at higher frequencies. We have not used these with the VLA and thus rate them as "secondary" unpolarized calibrators. Let us know if you use these so we can evaluate their performance.

Another potential set of unpolarized sources (verified only for S band) below 34 degree declination near 3C 48 and 3C 286 are listed in Table 7.2.5. However, like in the case of sources listed in Table 7.2.4, we strongly encourage to let us know before using these secondary unpolarized calibrators due to potential source variability.

Final Recommendations:

• at least one "pol standard" (ideally from Category A) should be included for angle calibration
• "bright" sources are easily useable as leakage calibrators with PA coverage (and probably good for bandpasses to boot!)
• "monitored" sources can be found at http://www.vla.nrao.edu/astro/calib/polar/ (for VLA 1999–2009) and http://www.vla.nrao.edu/astro/evlapolcal (for VLA 2010-2012), as well as in the NRAO archive under project code TCAL0009, with regular observations since 2016.
• "steep spectrum" sources are likely weak at high frequencies
• "flat spectrum" sources are likely bright at high frequencies but variable
• "moderately variable" sources may be useable in a pinch if you can get a nearby (in time) monitoring observation
  
  

Primary Polarization Calibrator Information

At least one observation of 3C286 or 3C138 is recommended to fix the absolute position angle of polarized emission. 3C48 also can be used for this at frequencies of ~3 GHz and higher, or 3C147 at frequencies above ~10 GHz. Table 7.2.6 shows the measured fractional polarization and intrinsic angle for the linearly polarized emission for these four sources in December 2010. Note that 3C138 and 3C48 are variable—the polarization properties are known to be changing significantly over time, most notably at the higher frequencies. See the "Integrated Polarization Properties of 3C48, 3C138, 3C147, and 3C286" (2013, ApJS 206, 2) by Perley and Butler for more details.

Since 3C48, 3C138, and 3C147 are variable above 10 GHz, we have performed new observations of these calibrators across the band January 31/February 1st, 2019. The updated values from this observation are listed below.

Link to Flux Density Scale, Polarization Leakage, and Polarization Angle text files.

Summary of Polarization Calibrator Monitoring

More details and up-to-date information on the regular and ad-hoc VLA polarization calibrator monitoring observations can be found on this confluence page.