The Statistics of Radio Astronomical Polarimetry: Bright Sources and High Time Resolution

Abstract

A four-dimensional statistical description of electromagnetic radiation is developed and applied to the analysis of radio pulsar polarization. The new formalism provides an elementary statistical explanation of the modal broadening phenomenon in single pulse observations. It is also used to argue that the degree of polarization of giant pulses has been poorly defined in past studies. Single and giant pulse polarimetry typically involves sources with large flux densities and observations with high time resolution, factors that necessitate consideration of source-intrinsic noise and small-number statistics. Self noise is shown to fully explain the excess polarization dispersion previously noted in single pulse observations of bright pulsars, obviating the need for additional randomly polarized radiation. Rather, these observations are more simply interpreted as an incoherent sum of covariant, orthogonal, partially polarized modes. Based on this premise, the four-dimensional covariance matrix of the Stokes parameters may be used to derive mode-separated pulse profiles without any assumptions about the intrinsic degrees of mode polarization. Finally, utilizing the small-number statistics of the Stokes parameters, it is established that the degree of polarization of an unresolved pulse is fundamentally undefined; therefore, previous claims of highly polarized giant pulses are unsubstantiated. Unpublished supplementary material is appended after the bibliography.

15 pages, 4 figures, published in The Astrophysical Journal, additional supplementary material was not submitted to The Astrophysical Journal and has not been peer reviewed, including ancillary material in the form of Mathematica notebooks and associated PDF documents. Erratum can be found at 10.1088/0004-637X/719/1/985

References in corpus (9)

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• Intrinsic Variability of the Vela Pulsar: Lognormal Statistics and Theoretical Implications
• Pulse-to-pulse intensity modulation and drifting subpulses in recycled pulsars
• Ellipticity and Deviations from Orthogonality in the Polarization Modes of PSR B0329+54
• The Transition between Nonorthogonal Polarization Modes in PSR B2016+28 at 1404 MHz
• On the Excess Dispersion in the Polarization Position Angle of Pulsar Radio Emission
• Three-Dimensional Statistics of Radio Polarimetry
• The intrinsic intensity modulation of PSR B1937+21 at 1410 MHz
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Cited by in corpus (12)

• DSPSR: Digital Signal Processing Software for Pulsar Astronomy
• Giant pulses from the Crab pulsar: A wide-band study
• High signal-to-noise ratio observations and the ultimate limits of precision pulsar timing
• Timing, polarimetry and physics of the bright, nearby millisecond pulsar PSR J0437-4715 - a single-pulse perspective
• A detailed study of giant pulses from PSR B1937+21 using the Large European Array for Pulsars
• A broadband radio study of the average profile and giant pulses from PSR B1821-24A
• Wide-field LOFAR-LBA power-spectra analyses: Impact of calibration, polarization leakage and ionosphere
• Improving the precision of pulsar timing through polarization statistics
• The Statistics of Radio Astronomical Polarimetry: Disjoint, Superposed, and Composite Samples
• The polarization of the drifting sub-pulses from PSR B1919+21
• Ultra-High Resolution Intensity Statistics of a Scintillating Source
• A model for distortions of polarisation-angle curves in radio pulsars