Rotation measure (RM) synthesis

WSClean provides several options that facilitate rotation measure synthesis. The options -squared-channel-joining and -fit-rm are specifically intended for RM synthesis when combined with -join-channels and -join-polarizations. This is explained below.

Before reading this chapter, it is useful to understand the following concepts:

Basic RM synthesis imaging

RM synthesis requires imaging the Stokes Q and U parameters across many frequency channels. After that, this QU-frequency cube can be Fourier transformed with an external tool to produce an RM cube.

Generating these QU images with WSClean can be done similarly to imaging stokes I, but several additional options are particularly useful for RM synthesis. The general procedure for creating image cubes is explained in Making image cubes, including the use of -channels-out option to partition the bandwidth. The -pol option can be added to do this for Q and U:

wsclean -pol QU -channels-out 100 \
  -scale 1amin -size 1024 1024 observation.ms

This produces an uncleaned image cube for the Q and U polarizations. Standard deconvolution parameters can be added to clean each polarization and frequency channel independently. However, the results will be limited by the noise in a single channel. This can be improved by using -join-polarizations to perform peak finding in QU or IQUV space. It is however beneficial to use the full bandwidth for cleaning. This is described below.

Note

RM synthesis often involves deconvolving a large number of channels. During deconvolution, all channels need to be loaded into memory, and it is therefore quite easy to run out of memory. It may help to start with small images and keep an eye on memory usage. Deconvolving big images with a large number of channels might only be possible on systems with large amounts of memory.

Using the full bandwidth for cleaning QU cubes

WSClean has multi-frequency deconvolution options as described in the multi-frequency deconvolution chapter. Multi-frequency deconvolution makes it possible to use all images together during peak finding, while still subtracting the corresponding model components from the individual images. When joining channels, the default is to do the peak finding in the sum over the channels. For example, if 100 channels of Stokes Q are imaged and -join-channels is used, peak finding is performed on the integrated bandwidth in Stokes Q. This is undesirable when expecting signals with non-zero RM values, because these signals will average out over the bandwidth. Therefore, the option -squared-channel-joining was added. When used, WSClean will perform peak finding in the sum of squares of the images. Components with large RM values will thus not average out. This option can be combined with -join-polarizations to take the sum over \(Q^2 + U^2\).

Additionally, each CLEAN component can be fitted with a rotation measure. This will model each component by a sinusoidal signal (combining the values from Stokes \(Q\) and \(U\) in the fit) in squared wavelength space, effectively performing RM synthesis during deconvolution. Because only one Faraday depth is deconvolved in each iteration, it may take more iterations compared to not using -fit-rm, but the benefit is that the spectra of components are more constrained, and therefore less noisy. This method is described in Offringa & Smirnov (2017).

Putting everything together, this is an example of how to perform RM synthesis:

wsclean -pol QU -fit-rm -join-polarizations \
  -join-channels -squared-channel-joining -channels-out <nr> \
  [-niter/-mgain/-scale/-multiscale/... etc.] observation.ms

This mode often enables deeper and more accurate cleaning than per-channel QU imaging.

When using -squared-channel-joining, an MFS image will be stored in addition to the channel images, as is normal in multi-channel imaging, and the MFS image will still have the normal average value (not the sum of squares).

A cleaning threshold can be specified as normal, and cleaning stops when the square root of the average of squares is below that value. The statistical properties of this quantity therefore differ from the standard case, and deconvolution will generally begin cleaning noise sooner. Some experimentation with the threshold might be required.

These options work together with auto-masking, which can be effective in removing all components up to the noise.

Polarimetric multiscale deconvolution

The multi-scale mode works together with squared channel joining and RM fitting. This did not work well before version 3.8 of WSClean, where it could regularly become stuck by repeatedly selecting the same structure [1], but WSClean 3.8 introduced a new algorithm. Be aware though that this algorithm is considerably slower than the normal multi-scale algorithm: some of the optimizations that are possible when adding channels linearly are not possible in squared-channel mode. With this algorithm, the scale is determined by correlating the individual images with the scale kernel before taking the sum of the squared images.

Effect of different option combinations

Here are a few examples, along with a description of how peak finding is performed with the given settings:

wsclean -pol QU -channels-out 100 ...

Cleaning is performed independently for each polarization, peaks are found in each individual image.

wsclean -pol QU -join-polarizations -channels-out 100 ...

Peak finding is performed in \(Q^2 + U^2\), but independently for each channel.

wsclean -pol Q -join-channels -channels-out 100

Peak finding is performed in the sum over channels of one polarization, \(\sum\limits_{ch} Q_{ch}\). Pixels with non-zero RM values will average out and will not be cleaned (adding -squared-channel-joining would remedy this).

wsclean -pol QU -join-channels -channels-out 100

Peak finding is performed independently for Stokes Q and Stokes U, using the summed image over frequency: \(\sum\limits_{ch} Q_{ch}\) and similarly for U. Again, pixels with non-zero RM values will average out and will not be cleaned (adding -squared-channel-joining would remedy this).

wsclean -pol QU -join-polarizations -join-channels -squared-channel-joining -channels-out 100 ...

Peak finding is performed in the \(Q\) and \(U\) squared sum over channels: \(\sum\limits_{ch} Q_{ch}^2 + U_{ch}^2\). Each component spectrum is unconstrained.

wsclean -pol QU -join-polarizations -join-channels -channels-out 100 ...

Peak finding is performed in \(\sum\limits_{ch} \sqrt{Q_{ch}^2 + U_{ch}^2}\). Note that in this mode, emission with non-zero RM values also does not get averaged out, hence squaring is not strictly necessary. One difference between this example and the above example including -squared-channel-joining is the noise properties during peak finding: taking the square root results in slightly less favourable noise statistics, hence squaring is preferred (although the difference is likely to be small). Another difference is that this example will not trigger the polarimetric multiscale algorithm, whereas the example before this one would use it.

wsclean -pol QU -fit-rm -join-polarizations -join-channels -squared-channel-joining -channels-out 100 ...

This is the most advanced method, where peak finding is performed on the sum over channels of \(Q_{ch}^2 + U_{ch}^2\), and each component is modelled by the signal from a single Faraday depth. When doing RM synthesis, this is often the most sensible option. The -multiscale option can be added for cleaning diffuse emission.

Note that these examples differ only in how deconvolution is performed; they do not otherwise affect the output images.

Availability