Polarimetry

by Tony Perreault last modified Aug 28, 2017 by Frank Schinzel

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. At least one observation of 3C286 or 3C138 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. The results of a careful monitoring program of these and other polarization calibrators can be found at http://www.aoc.nrao.edu/~smyers/evlapolcal/polcal_master.html

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.

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 corrrection for this effect. The AIPS program TECOR has been shown to be quite effective in removing large-scale ionospherically induced Faraday Rotation. It uses currently-available data in IONEX format. Please consult the TECOR help file for detailed information. In the future CASA will provide 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 under development and will be available in future releases of CASA.

 

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 auxilary 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 7.5.1 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 7.4.2 and 7.4.3) 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 7.4.1: Category A - primary polarization standards
SourceOther nameCommentsNotes
J0137+3309 B0134+329 (3C48) pol standard (>4GHz) A1,A2
J0521+1638 B0518+165 (3C138) pol standard A1
J1331+3030 B1328+307 (3C286) pol standard A1,A3

Table 7.2.1 Notes:

  • A1. Polarized fraction and angle values for these sources is given in Table 7.5.1 below.
  • A2. 3C48 is weak at high frequency and somewhat resolved in larger configurations. Depolarized below 4GHz.
  • A3. 3C286 is our foremost primary calibrator and should be used if available.

 

Table 7.4.2: Category B - secondary polarization calibrators
SourceOther nameCommentsNotes
J0359+5057 B0355+508 (NRAO150) bright, flat spectrum, monitored upon request, moderate variability B1
J0555+3948 B0552+398 bright, flat spectrum, monitored upon request, moderate variability B1,B2
J0854+2006 B0851+202 bright, flat spectrum, monitored upon request, moderate variability B1
J0927+3902 B0923+392 bright, flat spectrum, monitored upon request, moderate variability B1,B2
J1310+3220 B1308+326 monitored upon request
J2136+0041 B2134+004 bright, flat spectrum, monitored upon request, moderate variability
J2202+4216 B2200+420 (BLLac) bright, flat spectrum, monitored upon request, moderate variability B1
J2253+1608 B2251+158 (3C454.3) bright, flat spectrum, monitored upon request B3

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 7.4.3: Category C - primary low polarization leakage calibrators
SourceOther nameCommentsNotes
J0319+4130 B0316+413 (3C84) low pol, bright, flat spectrum, monitored upon request C1
J0542+4951 B0538+498 (3C147) low pol <10GHz, steep spectrum, resolved C2
J0713+4349 B0710+439 low pol, CSO, monitored upon request C3
J1407+2827 B1404+286 (OQ208) low pol, steep spectrum C4
J2355+4950 B2352+495 low pol, CSO, monitored upon request C3

Table 7.2.3 Notes:

  • C1. Very bright and low polarization (<1%), but variable flux density. Approaches 1% polarized at 43GHz.
  • C2. Steep spectrum and resolved, low polarization below 10GHz (best <4.5GHz). Stable polarization above. See Table 7.5.1 below.
  • C3. Weak at high frequency, but stable flux and very low polarization.
  • C4. 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.

WARNING: the positions given in Table 7.4.4 are B1950, use the Source names in the VLA OPT to get the J2000 positions.

 

Table 7.4.4: Category D - secondary (unverified) low polarization sources
SourceRA (1950)DEC (1950)B1950 Name'Comments
J0029+3456 00 26 34.8386 34 39 57.586 0026+346 CSO
J0111+3906 01 08 47.2595 38 50 32.691 0108+388 CSO
J0410+7656 04 03 58.60 76 48 54.0 0404+768 CSO
J1035+5628 10 31 55.9562 56 44 18.284 1031+567 CSO
J1148+5924 11 46 10.4160 59 41 36.834 1146+596 CSO
J1400+6210 13 58 58.310 62 25 08.40 1358+624 CSO
J1815+6127 18 15 05.4851 61 26 04.496 1815+614 CSO
J1823+7938 18 26 43.2676 79 36 59.943 1826+796 CSO
J1944+5448 19 43 22.6729 54 40 47.955 1943+546 CSO
J1945+7055 19 46 12.0492 70 48 21.397 1946+708 CSO
J2022+6136 20 21 13.3005 61 27 18.157 2021+614 CSO

Table 7.2.4 Comments:

  • 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.aoc.nrao.edu/~smyers/evlapolcal/polcal_master.html (for VLA 2010-2012)
  • "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 (Table 7.2.5)

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 7.5.1 shows the measured fractional polarization and intrinsic angle for the linearly polarized emission for these four sources in December 2010. Note that 3C138 is 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.

Table 7.5.1: Polarization Properties of Four Calibrators
Freq.3C48Pol3C48Ang3C138Pol3C138Ang3C147Pol3C147Ang3C286Pol3C286Ang
GHz % Deg. % Deg. % Deg. % Deg.
1.05 0.3 25 5.6 −14 <0.05 8.6 33
1.45 0.5 140 7.5 −11 <0.05 9.5 33
1.64 0.7 −5 8.4 −10 <0.04 9.9 33
1.95 0.9 −150 9.0 −10 <0.04 10.1 33
2.45 1.4 −120 10.4 −9 <0.05 10.5 33
2.95 2.0 −100 10.7 −10 <0.05 10.8 33
3.25 2.5 −92 10.0 −10 <0.05 10.9 33
3.75 3.2 −84 <0.04 11.1 33
4.50 3.8 −75 10.0 −11 0.1 −100 11.3 33
5.00 4.2 −72 10.4 −11 0.3 0 11.4 33
6.50 5.2 −68 9.8 −12 0.3 −65 11.6 33
7.25 5.2 −67 10.0 −12 0.6 −39 11.7 33
8.10 5.3 −64 10.4 −10 0.7 −24 11.9 34
8.80 5.4 −62 10.1 −8 0.8 −11 11.9 34
12.8 6.0 −62 8.4 −7 2.2 43 11.9 34
13.7 6.1 −62 7.9 −7 2.4 48 11.9 34
14.6 6.4 −63 7.7 −8 2.7 53 12.1 34
15.5 6.4 −64 7.4 −9 2.9 59 12.2 34
18.1 6.9 −66 6.7 −12 3.4 67 12.5 34
19.0 7.1 −67 6.5 −13 3.5 68 12.5 35
22.4 7.7 −70 6.7 −16 3.8 75 12.6 35
23.3 7.8 −70 6.6 −17 3.8 76 12.6 35
36.5 7.4 −77 6.6 −24 4.4 85 13.1 36
43.5 7.5 −85 6.5 −27 5.2 86 13.2 36