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 Unpublished supplementary material is appended after the bibliography.

arXiv comment22 pages, 3 figures, includes supplementary material that was not submitted to The Astrophysical Journal and has not been peer reviewed

References in corpus (26)

• Fourier Techniques for Very Long Astrophysical Time Series Analysis
• The subpulse modulation properties of pulsars at 21 cm
• Faint Scattering Around Pulsars: Probing the Interstellar Medium on Solar System Size Scales
• The Brightest Pulses in the Universe: Multifrequency Observations of the Crab Pulsar's Giant Pulses
• Interpretation of parabolic arcs in pulsar secondary spectra
• Theory of Parabolic Arcs in Interstellar Scintillation Spectra
• The subpulse modulation properties of pulsars at 92 cm and the frequency dependence of subpulse modulation
• Drifting Sub-Pulse Analysis Using the Two-Dimensional Fourier Transform
• Pulse-to-pulse intensity modulation and drifting subpulses in recycled pulsars
• Radio Astronomical Polarimetry and the Lorentz Group
• Ellipticity and Deviations from Orthogonality in the Polarization Modes of PSR B0329+54
• Simultaneous single-pulse observations of radio pulsars III. The behaviour of circular polarization
• A transient component in the pulse profile of PSR J0738-4042
• 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
• Intrinsic Variability and Field Statistics for the Vela Pulsar: 2. Systematics and Single-Component Fits
• The Polarization of Drifting Subpulses
• Improving the precision of pulsar timing through polarization statistics
• Revisiting the radio interferometer measurement equation. IV. A generalized tensor formalism
• The Transition between Nonorthogonal Polarization Modes in PSR B2016+28 at 1404 MHz
• Stochastic Faraday Rotation
• On the Excess Dispersion in the Polarization Position Angle of Pulsar Radio Emission
• Using the Intensity Modulation Index to Test Pulsar Radio Emission Models
• Three-Dimensional Statistics of Radio Polarimetry
• The Statistics of Radio Astronomical Polarimetry: Bright Sources and High Time Resolution
• Orientation Angles of a Pulsar's Polarization Vector

Cited by in corpus (9)

• Polarimetry of 600 pulsars from observations at 1.4 GHz with the Parkes radio telescope
• Evidence for magnetospheric effects on the radiation of radio pulsars
• MWA Tied-Array Processing II: Polarimetric Verification and Analysis of two Bright Southern Pulsars
• 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
• Multifrequency behaviour of the anomalous events of PSR J0922+0638
• Exponential Fluctuations in the Modes of Orthogonal Polarization in Pulsar Radio Emission
• An Introduction to Single-Antenna Radio Astronomical Polarimetry