A four-dimensional statistical description of electromagnetic radiation is developed and applied to the analysis of radio pulsar polarization. The new formalism provides an elementary statistical explanation of the modal broadening phenomenon in sing
le pulse observations. It is also used to argue that the degree of polarization of giant pulses has been poorly defined in past studies. Single and giant pulse polarimetry typically involves sources with large flux densities and observations with high time resolution, factors that necessitate consideration of source-intrinsic noise and small-number statistics. Self noise is shown to fully explain the excess polarization dispersion previously noted in single pulse observations of bright pulsars, obviating the need for additional randomly polarized radiation. Rather, these observations are more simply interpreted as an incoherent sum of covariant, orthogonal, partially polarized modes. Based on this premise, the four-dimensional covariance matrix of the Stokes parameters may be used to derive mode-separated pulse profiles without any assumptions about the intrinsic degrees of mode polarization. Finally, utilizing the small-number statistics of the Stokes parameters, it is established that the degree of polarization of an unresolved pulse is fundamentally undefined; therefore, previous claims of highly polarized giant pulses are unsubstantiated. Unpublished supplementary material is appended after the bibliography.
This paper defines the mathematical convention adopted to describe an electromagnetic wave and its polarisation state, as implemented in the PSRCHIVE software and represented in the PSRFITS definition. Contrast is made between the convention that has
been widely accepted by pulsar astronomers and the IAU/IEEE definitions of the Stokes parameters. The former is adopted as the PSR/IEEE convention, and a set of useful parameters are presented for describing the differences between the PSR/IEEE standard and the conventions (either implicit or explicit) that form part of the design of observatory instrumentation. To aid in the empirical determination of instrumental convention parameters, well-calibrated average polarisation profiles of PSR J0304+1932 and PSR J0742-2822 are presented at radio wavelengths of approximately 10, 20, and 40 cm.
