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 sing
le 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 Unpublished supplementary material is appended after the bibliography.
The magneto-ionic structures of the interstellar medium of the Milky Way and the intergalactic medium are still poorly understood, especially at distances larger than a few kiloparsecs from the Sun. The three-dimensional (3D) structure of the Galacti
c magnetic field and electron density distribution may be probed through observations of radio pulsars, primarily owing to their compact nature, high velocities, and highly-polarized short-duration radio pulses. Phase 1 of the SKA, i.e. SKA1, will increase the known pulsar population by an order of magnitude, and the full SKA, i.e. SKA2, will discover pulsars in the most distant regions of our Galaxy. SKA1-VLBI will produce model-independent distances to a large number of pulsars, and wide-band polarization observations by SKA1-LOW and SKA1-MID will yield high precision dispersion measure, scattering measure, and rotation measure estimates along thousands of lines of sight. When combined, these observations will enable detailed tomography of the large-scale magneto-ionic structure of both the Galactic disk and the Galactic halo. Turbulence in the interstellar medium can be studied through the variations of these observables and the dynamic spectra of pulsar flux densities. SKA1-LOW and SKA1-MID will monitor interstellar weather and produce sensitive dynamic and secondary spectra of pulsar scintillation, which can be used to make speckle images of the ISM, study turbulence on scales between ~10^8 and ~10^13 m, and probe pulsar emission regions on scales down to $sim$10 km. In addition, extragalactic pulsars or fast radio bursts to be discovered by SKA1 and SKA2 can be used to probe the electron density distribution and magnetic fields in the intergalactic medium beyond the Milky Way.
We have embarked on a survey for pulsars and fast transients using the 13-beam Multibeam receiver on the Parkes radio telescope. Installation of a digital backend allows us to record 400 MHz of bandwidth for each beam, split into 1024 channels and sa
mpled every 64 us. Limits of the receiver package restrict us to a 340 MHz observing band centred at 1352 MHz. The factor of eight improvement in frequency resolution over previous multibeam surveys allows us to probe deeper into the Galactic plane for short duration signals such as the pulses from millisecond pulsars. We plan to survey the entire southern sky in 42641 pointings, split into low, mid and high Galactic latitude regions, with integration times of 4200, 540 and 270 s respectively. Simulations suggest that we will discover 400 pulsars, of which 75 will be millisecond pulsars. With ~30% of the mid-latitude survey complete, we have re-detected 223 previously known pulsars and discovered 27 pulsars, 5 of which are millisecond pulsars. The newly discovered millisecond pulsars tend to have larger dispersion measures than those discovered in previous surveys, as expected from the improved time and frequency resolution of our instrument.
This paper defines the mathematical convention adopted to describe an electromagnetic wave and its polarisation state, as implemented in the PSRCHIVE software and represented in the PSRFITS definition. Contrast is made between the convention that has
been widely accepted by pulsar astronomers and the IAU/IEEE definitions of the Stokes parameters. The former is adopted as the PSR/IEEE convention, and a set of useful parameters are presented for describing the differences between the PSR/IEEE standard and the conventions (either implicit or explicit) that form part of the design of observatory instrumentation. To aid in the empirical determination of instrumental convention parameters, well-calibrated average polarisation profiles of PSR J0304+1932 and PSR J0742-2822 are presented at radio wavelengths of approximately 10, 20, and 40 cm.
