The Statistics of Radio Astronomical Polarimetry: Disjoint, Superposed, and Composite Samples

Abstract

A statistical framework is presented for the study of the orthogonally polarized modes of radio pulsar emission via the covariances between the Stokes parameters. To accommodate the typically heavy-tailed distributions of single-pulse radio flux density, the fourth-order joint cumulants of the electric field are used to describe the superposition of modes with arbitrary probability distributions. The framework is used to consider the distinction between superposed and disjoint modes with particular attention to the effects of integration over finite samples. If the interval over which the polarization state is estimated is longer than the timescale for switching between two or more disjoint modes of emission, then the modes are unresolved by the instrument. The resulting composite sample mean exhibits properties that have been attributed to mode superposition, such as depolarization. Because the distinction between disjoint modes and a composite sample of unresolved disjoint modes depends on the temporal resolution of the observing instrumentation, the arguments in favour of superposed modes of pulsar emission are revisited and observational evidence for disjoint modes is described. In principle, the four-dimensional covariance matrix that describes the distribution of sample mean Stokes parameters can be used to distinguish between disjoint modes, superposed modes, and a composite sample of unresolved disjoint modes. More comprehensive and conclusive interpretation of the covariance matrix requires more detailed consideration of various relevant phenomena, including temporally correlated subpulse modulation (e.g. jitter), statistical dependence between modes (e.g. covariant intensities and partial coherence), and multipath propagation effects (e.g. scintillation and scattering). Unpublished supplementary material is appended after the bibliography.

22 pages, 3 figures, includes supplementary material that was not submitted to The Astrophysical Journal and has not been peer reviewed

References in corpus (6)

• The subpulse modulation properties of pulsars at 92 cm and the frequency dependence of subpulse modulation
• Timing, polarimetry and physics of the bright, nearby millisecond pulsar PSR J0437-4715 - a single-pulse perspective
• Single pulse and profile variability study of PSR J1022+1001
• Improving the precision of pulsar timing through polarization statistics
• Revisiting the radio interferometer measurement equation. IV. A generalized tensor formalism
• Orientation Angles of a Pulsar's Polarization Vector

Cited by in corpus (6)

• Polarimetry of 600 pulsars from observations at 1.4 GHz with the Parkes radio telescope
• Artefacts of circumpolar cartography in radio pulsar polarization
• Circular polarization in radio pulsar PSR B1451-68: coherent mode transitions and intrabeam interference
• The polarization of the drifting sub-pulses from PSR B1919+21
• Exponential Fluctuations in the Modes of Orthogonal Polarization in Pulsar Radio Emission
• An Introduction to Single-Antenna Radio Astronomical Polarimetry