2025ApJ...982..136M

A number of polarization estimators have been developed for a variety of astrophysical applications to compensate measurements of linear polarization for a bias contributed by the instrumental noise. Most derivations of the estimators assume that the amplitude and orientation of the polarization vector are constant. This assumption generally is not valid for the radio emission from pulsars that fluctuates from pulse to pulse. The radio emission from pulsars, fast radio bursts, and magnetars can be elliptically polarized, and estimators of the total polarization and absolute value of the circular polarization are used in their observations. However, these estimators have not been formally developed to a level that is commensurate with those of linear polarization. Estimators are derived for circular, linear, and total polarization when the amplitude of the polarization vector is a constant or a random variable. Hybrid estimators are proposed for general application to pulsar polarization observations. They are shown to be more effective at removing instrumental noise than their commonly used counterparts.