PSRCHIVE user documentation: pcm

Measurement Equation Modeling (MEM) Degeneracy Under Commutation

It is necessary to make two assumptions to constrain the degeneracy under commutation described in Appendix B of van Straten (2004).
  1. ASSUMPTION 1: To constrain the mixing between Stokes I and V, one of the following four assumptions can be made.
    • 1.A) The noise diode has zero circular polarization; this assumption is selected by specifying the -v command line option.
    • 1.B) While pointing at a standard candle, the baseline flux density has zero circular polarization; this assumption is the default if the calibrator database that is provided to pcm contains FluxCal-On observations.
    • 1.C) Given a set of flux calibration observations, some made while pointing at a standard candle (FluxCal-On) and some made while pointing at "nearby blank sky" (FluxCal-Off), the difference in the off-pulse baseline flux density (FluxCal-On baseline minus FluxCal-Off baseline) is a reasonable approximation to the flux density of the standard candle and is assumed to have zero circular polarization; this assumption is selected by specifying the -Y command line option.
    • 1.D) The mixing between Stokes I and V is zero; that is, the receptors have equal ellipticities. This assumption is selected by specifying the -k command line option.

  2. ASSUMPTION 2: To constrain the mixing between Stokes Q and U (rotation about line of sight), one of the following three assumptions can be made.
    • 2.A) the orientation offset of the first receptor is zero; or
    • 2.B) the orientation offset of the noide diode is zero.

Assumption 1.A is made by default if no Signal::FluxCalOn observations are provided, or if the -v command line option is specified. In this case, Stokes V of the noise diode is fixed at zero.

Assumption 1.B is made by default if a Signal::FluxCalOn observation is included as a constraint. In this case, Stokes V of the noise diode is allowed to vary as a free parameter.

Assumption 1.C is made only if both Signal::FluxCalOn and Signal::FluxCalOff observations are included as constraints and the -Y command line option is specified. In this case, Stokes V of the noise diode is allowed to vary as a free parameter.

Assumption 1.D is made only if the -k command line option is specified. In this case, Stokes V of the noise diode is allowed to vary as a free parameter.

Assumption 2.A is made by default. In this case, Stokes Q of the noise diode is allowed to vary as a free parameter.

Assumption 2.B is made if the -q command line option is specified.

Except for Assumption 1.C, equally valid solutions are derived regardless of the above assumptions; that is, except when Assumption 1.C is adopted, there is no change in the goodness of fit. Assumption 1.C is different because new data (Signal::FluxCalOff observations) are included as constraints.