The Distribution of Fractional Linear Polarization and the Random Component of Polarization Position Angle

Abstract

One of the most fascinating features of the polarization of pulsar radio emission is the occurrence of orthogonal modes of polarization. The origin of the modes is not clear, but, whatever their underlying nature, the modes will affect observables such as the instantaneous linear polarization. We derive an idealized distribution of fractional linear polarization assuming that the modes are superposed and compare our result with observations. We discuss how superposed modes may affect the position angle distributions.Consider a subpulse composed of superposed modes of orthogonal polarization. We assume that each mode is completely linearly-polarized with no dispersion in position angle. If the flux densities of the individual modes are represented by the independent random variablesX1andX2, then the linear polarization of the subpulse is related toX=X1−X2and its total intensity isY=X1+X2. We denote the means of the mode distributions byμ1andμ2and their standard deviations byσ1andσ2. The means are generally not the same because observed distributions of position angle (e.g. Stinebring et al. 1984) show that the modes generally do not occur with equal frequency. If the individual modes are normally-distributed with identical standard deviations,XandYare also normally-distributed, independent random variables. In this ideal case, the distribution of fractional polarization,Z=|X/Y|, is