Directional Statistics for Polarization Observations of Individual Pulses from Radio Pulsars

TL;DR

This paper develops a three-dimensional statistical model for pulsar radio polarization based on incoherent superposition of orthogonal modes, supported by observational data, and explores the effects of generalized Faraday rotation.

Contribution

It introduces a novel three-dimensional statistical framework for pulsar polarization based on directional statistics and orthogonal mode superposition, aligning with observational data.

Findings

Derived the polarization statistics using Bingham-Mardia and Fisher distributions.

Supported the model with qualitative agreement from pulsar pulse observations.

Linked mode independence to generalized Faraday rotation effects.

Abstract

Radio polarimetry is a three-dimensional statistical problem. The three-dimensional aspect of the problem arises from the Stokes parameters Q, U, and V, which completely describe the polarization of electromagnetic radiation and conceptually define the orientation of a polarization vector in the Poincar'e sphere. The statistical aspect of the problem arises from the random fluctuations in the source-intrinsic polarization and the instrumental noise. A simple model for the polarization of pulsar radio emission has been used to derive the three-dimensional statistics of radio polarimetry. The model is based upon the proposition that the observed polarization is due to the incoherent superposition of two, highly polarized, orthogonal modes. The directional statistics derived from the model follow the Bingham-Mardia and Fisher family of distributions. The model assumptions are supported by the qualitative agreement between the statistics derived from it and those measured with polarization observations of the individual pulses from pulsars. The orthogonal modes are thought to be the natural modes of radio wave propagation in the pulsar magnetosphere. The intensities of the modes become statistically independent when generalized Faraday rotation (GFR) in the magnetosphere causes the difference in their phases to be large. A stochastic version of GFR occurs when fluctuations in the phase difference are also large, and may be responsible for the more complicated polarization patterns observed in pulsar radio emission.