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PSRCHIVE user documentation: pcm
1.0 PurposeThe Polarization Calibration Modeling (pcm) program may be used to estimate the polarimetric response of the observing system, as described in van Straten 2004, ApJS 152:129, and van Straten 2013, ApJS 204:13. There are two different modes of operation:
Measurement Equation Modeling (MEM), described in van Straten (2004), uses uncalibrated observations of
Measurement Equation Template Matching (METM), described in van Straten (2013), uses
2.1 Before running pcmIn order to run pcm in MEM mode, you will need Pulsar::Archive files containing:
This last step produces a total integrated profile from which to choose the best pulse phase bins to be used as model constraints. It is best to choose these from a high S/N profile, but integration in both time and frequency will lead to depolarization (primarily due to the variation of differential phase as a function of frequency, and to the time-varying projection of the receptors onto the sky). The preliminary calibration step minimizes this depolarization.
As described in more detail in Section 4.1, it is possible to either manually choose individual phase bins or ranges of pulse phase that make good model constraints, or allow pcm to automatically choose the best pulse phase bins. When choosing phase bins manually, it is best to choose those with the highest polarized flux density and, if selecting more than one pulse phase bin, to choose states that have orthogonal polarization vectors in the Poincare space.
As more phase bins are used as constraints, more time will be required to converge to a solution. For starters, use only four phase bins; pcm will converge more quickly, providing a first order estimate of the instrumental parameters. More phase bins can then be added to descrease the experimental uncertainty of the results.
2.2 Running pcm
2.2.1 MEM modeIn MEM mode, pcm does the following (not necessarily in this order):
2.2.2 METM modeWhen run with the -S standard.ar option, pcm performs measurement equation template matching, a global fit in which the transformation between the well-calibrated template in standard.ar and the pulsar observations specified on the command is modellded. Calibrator observations are also incorporated as constraints. With the -1 option, an unique fit if performed on each input sub-integration and a separate file is output for each solution (with the extension .mtm).
An example of METM usage. Note that this technique can be used to estimate the differential Faraday rotation between the template and the observation.
2.3 Diagnostic outputs
pcm can optionally produce a number of diagnostic outputs. These are enabled with the -D name command line option, where name is any one of:
2.4 Modeling time variationsIntrinsic variations (including interstellar scintillation)
pcm can compensate for intrinsic variations in the intensity of the pulsar signal by normalizing the Stokes parameters of the pulsar observations by the mean invariant: the square root of the mean of the invariant intervals (I^2 - p^2) of a constant selection of on-pulse phase bins.
This feature is enabled with the -s command line option. The on-pulse phase bins are chosen from either the first archive loaded or the archive specified using the -c command line option, then held fixed for all subsequent archives.
When -s is used, the pulsar is put through a signal path with constant gain set to unity, and the free gain parameter is applied only to the calibrator signal path.
pcm can model the observations with an instrumental backend that varies over time. Each of the absolute gain, differential gain, or differential phase may be independently represented as either
-u PAR model PAR with a step at each CAL -o PAR:N model PAR as N degree polyomialWhere PAR is a single-character code:
3.0 AlgorithmsIn MEM mode, pcm implements the model of reception and the algorithm for solution described in van Straten, W. 2004, Radio Astronomical Polarimetry and Point-Source Calibration, Astrophys. J. Supp. 152, 129-135. arXiv:astro-ph/0401536
In METM mode, pcm implements the frequency-domain algorithm for matrix template matching described in van Straten, W. 2006, Radio Astronomical Polarimetry and High-Precision Pulsar Timing, The Astrophysical Journal 642, 1004-1011 arXiv:astro-ph/0510334
4.0 Testing and examples
5.0 Known bugs and features that require implementation