Unless noted otherwise, this is about polarisation of the pulsar and not about the nebula. This generally means that the long baselines are analysed.

There is a discussion thread on this subject in the USG forum.

description of data set¹⁾

Polarisation properties of the pulsar are discussed by Ger de Bruyn in the LSM 29 Oct 2008. The linear polarisation seems to be variable, but sometimes very strong with several Jy polarised flux in the HBA range.

A first search for linear polarisation did not show any strong evidence, see LSM 23 Feb 2011 by Olaf Wucknitz. Sarod checked with MeqTrees and found about 10% polarisation with about the right RM (as reported by Ger de Bruyn).

Here are AIPS POSSM plots (postscript version here) of all Stokes parameters as function of frequency. Each page is averaged over 30min, only a good time range is shown. Only good subbands are shown, the highest block is discarded because of weak signal in DE603. The image above shows only one time interval.

The data were converted to a circular basis in own software, then fringe-fitted and amplitude-calibrated for RR and LL in AIPS. This removes differential but not absolute Faraday rotation. The latter is hopefully constant within each 30min interval. Plots with shorter intervals show more noise but no signal either. Description of the plots: From upper left to lower right they show Stokes IQUV for baseline FR606-RS306. The upper half of each panel shows the imaginary part, the lower one the real part. Note that the real part of Stokes I is not within the range and cannot be seen. It was set to 10 Jy. The true flux may be a factor of 2 higher.

With perfect calibration, all imaginary parts should be zero. This is not quite true, but deviations are not strongly frequency-dependent. Stokes V is close to zero as expected. This is not a result of the calibration strategy, because the amplitude calibration was forced to be the same for R and L.

Linear polarisation would be seen in Q and U. There are indeed residuals, but they are probably just calibration errors (leakage terms). The rotation measure (RM) of the pulsar is known to be about -45, which would mean that the signal oscillates between Q and U with a period of roughly 1 MHz in this frequency range. No hint of this is seen in the plots down to a level << 1 Jy (i.e. << 10%).

Instead of Q and U, we can also check RL and LR that are related like follows (modulo sign conventions and possible factors of 2):

RL = Q + i U
LR = Q - i U

If Q and U are strictly real, the real and imaginary parts of RL (or LR provide) the same information as Q and U. With the leakage terms, this is not true anymore. Depending on the leakage terms, the RL/LR plots may be clearer than Q and U. No signal is seen here either:

Postscript version here

— Olaf Wucknitz 06-Mar-2011 18:24

I do not have a full RM synthesis code, but on the long baselines it is easy enough to analyse the Faraday dispersion function on single baselines. I averaged the calibrated data in 30min blocks (total ionospheric Faraday rotation is pretty constant over 30min) and Fourier-transformed Q+iU in lambda² space (→ RM). There is usually a strong peak at RM near zero, which is a result of the large leakage terms. I then subtracted the peak (one iteration of Clean with gain=1) and plotted the residual spectrum to be able to see any real signal. Only the long baseline FR606-RS306 is shown.

The left panel shows the dispersion function in blocks of 30min, the right panel is averaged incoherently over the full time range. The first two hours in the afternoon are skipped. Only the lower 30 subbands were used, because a coherent combination of all good blocks is not allowed by the calibration strategy. There is a strong peak near zero. A secondary peak near -45 (the correct RM) begins to show up.

The same after subtracting the primary peak near zero. We now clearly see the secondary peak near -45 with a flux of about 0.09 Jy, corresponding to 0.9%.

As a test, I repeated the same exercise using Stokes I (real and imaginary part) instead of Q+iU:

There is only the strong peak near zero (with 10 Jy flux to which the data were calibrated) but no additional peak, as expected.

The polarisation signal is dominated by leakage terms of the order 10%. After subtracting this contribution, a weaker intrinsic polarisation of the pulsar is detected with the correct signature in frequency, corresponding to a rotation measure of about -45 rad/m^2. Note that the sign depends on a number of conventions. It may just be a coincidence that it comes out right.

The polarisation is thus much weaker than found earlier by Ger de Bruyn. This is plausible, because it was found to be variable before. However, my result is not consistent with the recent measurements with MeqTrees using the same data set.

— Olaf Wucknitz 07-Mar-2011 18:48

In the following I show the result for the four good blocks of subbands.

subbands 0-29 (115.0-120.9 MHz):

subbands 61-90 (127.0-132.8 MHz):

subbands 122-151 (138.9-144.7 MHz):

subbands 183-212 (150.8-156.6 MHz):

Note that the Stokes I flux is scaled to 10 Jy for all frequencies. The percentage polarisation has a significant dependence on frequency, but interestingly not monotonical. In the highest bands, the polarised fraction is about 1.7%.

— Olaf Wucknitz 15-Mar-2011 00:23

This is for the highest subband block, but this time calculated for 10min integrations:

The colour scale is about the same as before. The result does not change dramatically, which probably means that the low polarisation is not a result of integrating over the varying ionospheric Faraday rotation.

— Olaf Wucknitz 15-Mar-2011 00:49

Other long baselines show the same behaviour. But note that the only long baselines at the higher frequencies with sufficient S/N are those to FR606.

— Olaf Wucknitz 15-Mar-2011 12:08

These results were presented at the LOFAR Status meeting on 23 March 2011.

— Olaf Wucknitz 23-Mar-2011 12:34