Statistical Modeling of the Circular Polarization in Pulsar Radio Emission and Detection Statistics of Radio Polarimetry

Abstract

Despite the diverse and seemingly complicated structure of the polarization of individual pulses from radio pulsars, many features of the emission are remarkably similar from pulsar to pulsar. These features include the statistical nature of the fluctuations in the emission's intensity and polarization and the ever-present orthogonal modes of polarization. Another persistent, but often neglected, feature of the emission is the wide, Gaussian-like distribution of fractional circular polarization at most pulse longitudes. This unimodal distribution cannot be explained by an emission model that assumes the orthogonal modes of polarization occur separately. However, the proposition that the modes occur simultaneously is consistent with the observations. Furthermore, a detailed analysis of the statistics of signal detection for radio polarimetry shows that the observed dispersion in the fractional circular polarization is larger than what one would expect from the instrumental noise or from fluctuations in total intensity. Large, pulsar-intrinsic fluctuations in the circular polarization are required to explain the observed distributions. In an attempt to exploit the general features of the emission and extract information regarding the mode polarizations, a statistical model of superposed modes of orthogonal polarization is extended to include circular polarization. The model attributes the large fluctuations in circular polarization required by the observations to a combination of the heavy modulation of the mode intensities and the small, but significant, degree of circular polarization that is intrinsic to the modes. The results of the model indicate that a small degree of mode-intrinsic circular polarization can explain the large fluctuations in fractional circular polarization that are observed. The general statistics of signal detection for linear polarization are also derived.