arXiv subjects

M. M. McKinnon

Publications and source records attributed to M. M. McKinnon.

12 recordsLinked to original sources

arXiv2026

Polarization Angle Geodesics in PSRs B1133+16 and B2016+28

Recent models of pulsar polarization predict that the position and ellipticity angles of the polarization vector can trace portions of a small or great circle on the Poincare sphere. A great circle can arise from a transition in dominance of orthogonal polarization modes, where the relative intensity of the modes changes with pulse longitude. A small circle may be caused by a rotation of the vector, where the phase difference between the modes changes with pulse longitude or wavelength. Observations of PSRs B1133+16 and B2016+28 are reanalyzed to search for these polarization features within their pulse profiles. The polarization angles observed in part of PSR B1133+16 are shown to follow a great circle on the Poincare sphere. The angles observed across the pulse of PSR B2016+28 follow an arc that resembles a portion of a great circle that has been altered by the pulsar's rotation. The observations are interpreted within the context of three different polarization models. All three models produce similar results for both pulsars and indicate that the observed geodesics are caused by mode transitions. The arc observed in PSR B2016+28 can also be interpreted as a vector rotation, provided the modes are elliptically polarized. The observations and accompanying analysis show that mode transitions are not restricted to the equatorial plane of the Poincare sphere and that arcs and partial circles may be more common than previously recognized.

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arXiv2025

Statistical Properties of a Polarization Vector's Ellipticity Angle

The orientation of a polarization vector on the Poincare sphere is defined by its position angle (PA) and ellipticity angle (EA). The radio emission from pulsars, magnetars, and fast radio bursts can be elliptically polarized, and measurements of the EA have become increasingly important in interpretations and models of their polarization. An in-depth understanding of the statistical properties of the measured polarization angles is a prerequisite to their detailed interpretation. While the statistics of the PA have been understood for some time, the statistics of the EA do not appear to be as well developed as those of the PA. The statistical properties of the EA are derived when the amplitude of the polarization vector is constant, to include its probability density, mean, standard deviation, and confidence limits. Similar to the PA, the standard deviation and confidence limits of the EA vary inversely with the polarization signal-to-noise ratio. However, unlike the PA, the probability density of the EA is generally asymmetric, its standard deviation and confidence limits are dependent upon the intrinsic value of the EA, and the measured EA is biased by the instrumental noise, particularly at low signal-to-noise ratios and large values of the intrinsic EA. General expressions for the joint probability density of the polarization angles and the probability density of the EA are also derived when the amplitude of the polarization vector fluctuates due to the superposition of incoherent modes of orthogonal polarization.

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arXiv2025

Polarization Estimation for Radio Pulsars

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.

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arXiv2024

Behavior of the Position and Ellipticity Angles at Polarization Mode Transitions in Pulsar Radio Emission

Polarization observations of radio pulsars show that abrupt transitions in the polarization vector's position angle can be accompanied by large excursions in the vector's ellipticity angle, suggesting the vector passes near the right or left circular pole of the Poincaré sphere. The behavior of the angles can be explained by a transition in dominance of the orthogonal polarization modes or a vector rotation caused by a change in the phase difference between the modes. Four polarization models are examined to quantify and understand the behavior of the angles at a mode transition: coherent polarization modes, partially coherent modes, incoherent modes with nonorthogonal polarization vectors, and incoherent orthogonal modes with an elliptically polarized emission component. In all four models, the trajectory of the mode transition on the Poincaré sphere follows the geodesic that connects the orientations of the mode polarization vectors. The results from the models can be similar, indicating that the interpretation of an observed transition within the context of a particular model is not necessarily unique. The polarization fraction of the emission and the average ellipticity angle depend upon the statistical character of the mode intensity fluctuations. The polarization fraction increases as the fluctuations increase. The excursion in ellipticity angle can be large when the mode intensities are quasi-stable and is suppressed when the intensity fluctuations are large.

astro-ph.HE↗

arXiv2023

An Examination of Polarization Mode Transitions in Pulsar Radio Emission

A statistical model is used to determine how stochastic fluctuations in the intensities of orthogonal polarization modes contribute to the modulation and depolarization of pulsar radio emission. General expressions for the distributions of the Stokes parameters, linear polarization, polarization position angle, and fractional polarization are derived when the mode intensities follow the same or different probability distributions. The transition between modes is examined. When the mode intensities follow the same distribution, the fractional linear polarization and modulation index are symmetric about the transition. The symmetry is disrupted when the mode intensities follow different distributions. The fractional linear polarization is minimum and the mode frequency of occurrence changes rapidly at transitions where the mode intensity distributions are the same and the modulation index is small. A lower limit on the fractional linear polarization that can be attained via the simultaneous occurrence of the modes as a function of modulation index is quantified.

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arXiv2022

Exponential Fluctuations in the Modes of Orthogonal Polarization in Pulsar Radio Emission

A statistical model for the polarization of pulsar radio emission is enhanced to account for the heavy modulation of the emission, the possible covariance of the Stokes parameters, and the observed asymmetries in the distributions of total intensity, polarization, and fractional polarization by treating the intensities of the orthogonal polarization modes as exponential random variables. The model is used to derive theoretical distributions to compare with what is observed. The resulting distributions are unimodal and generally asymmetric. The unimodality arises from the model's fundamental assumption that the orthogonal modes are superposed. The asymmetry originates primarily from different fluctuations in mode intensities. The distributions of fractional polarization are truncated at the degree of linear and circular polarization intrinsic to the modes. A number of observable parameters that quantify the statistical properties of the emission and its polarization are derived and are shown to be functions only of the ratio of the modes' mean intensities, M, suggesting their spectra coevolve according to the frequency dependence of M. This particular implementation of the model requires the modes to fluctuate differently in order to replicate the observations. Since a single underlying emission mechanism seems unlikely to selectively modulate the mode intensities, the different fluctuations are attributed either to different emission mechanisms for the modes or to mode-dependent propagation or scattering effects in the pulsar magnetosphere.

astro-ph.HE↗

arXiv2017

An image-based search for pulsars among Fermi unassociated LAT sources

We describe an image-based method that uses two radio criteria, compactness and spectral index, to identify promising pulsar candidates among Fermi Large Area Telescope (LAT) unassociated sources. These criteria are applied to those radio sources from the Giant Metrewave Radio Telescope all-sky survey at 150 MHz (TGSS ADR1) found within the error ellipses of unassociated sources from the 3FGL catalog and a preliminary source list based on 7 years of LAT data. After follow-up interferometric observations to identify extended or variable sources, a list of 16 compact, steep-spectrum candidates is generated. An ongoing search for pulsations in these candidates, in gamma rays and radio, has found six millisecond pulsars and one normal pulsar. A comparison of this method with existing selection criteria based on gamma-ray spectral and variability properties suggests that the pulsar discovery space using Fermi may be larger than previously thought. Radio imaging is a hitherto underutilized source selection method that can be used, as with other multi-wavelength techniques, in the search for Fermi pulsars.

astro-ph.HE↗

arXiv2014

The Analytical Solution to the Temporal Broadening of a Gaussian-Shaped Radio Pulse by Multipath Scattering from a Thin Screen in the Interstellar Medium

The radio pulse from a pulsar can be temporally broadened by multipath scattering in the interstellar medium and by instrumental effects within the radio telescope. The observed pulse shape is a convolution of the intrinsic one with the impulse responses of the scattering medium and instrumentation. Until recently, common methods used to model the observed shape make assumptions regarding the intrinsic pulse shape and impulse responses, compute the convolution numerically, and solve for the pulse width and scattering timescale iteratively. An analytical solution is shown to exist for the specific case of the temporal broadening of a Gaussian-shaped pulse by a thin scattering screen. The solution is applied to multi-frequency observations of PSR B1834-10 to characterize the frequency dependence of its intrinsic pulse width and scattering timescale.

astro-ph.IM↗

arXiv2010

Directional Statistics for Polarization Observations of Individual Pulses from Radio Pulsars

Radio polarimetry is a three-dimensional statistical problem. The three-dimensional aspect of the problem arises from the Stokes parameters Q, U, and V, which completely describe the polarization of electromagnetic radiation and conceptually define the orientation of a polarization vector in the Poincar'e sphere. The statistical aspect of the problem arises from the random fluctuations in the source-intrinsic polarization and the instrumental noise. A simple model for the polarization of pulsar radio emission has been used to derive the three-dimensional statistics of radio polarimetry. The model is based upon the proposition that the observed polarization is due to the incoherent superposition of two, highly polarized, orthogonal modes. The directional statistics derived from the model follow the Bingham-Mardia and Fisher family of distributions. The model assumptions are supported by the qualitative agreement between the statistics derived from it and those measured with polarization observations of the individual pulses from pulsars. The orthogonal modes are thought to be the natural modes of radio wave propagation in the pulsar magnetosphere. The intensities of the modes become statistically independent when generalized Faraday rotation (GFR) in the magnetosphere causes the difference in their phases to be large. A stochastic version of GFR occurs when fluctuations in the phase difference are also large, and may be responsible for the more complicated polarization patterns observed in pulsar radio emission.

astro-ph.GA↗

arXiv2010

The LEAP of Pulsars in the Milky Way

The location of objects on the celestial sphere is a fundamental measurement in astronomy, and the distribution of these objects within the Milky Way is important for understanding their evolution as well as the large scale structure of the Galaxy. Here, physical concepts in Galactic astronomy are illustrated using straightforward mathematics and simplifying assumptions regarding the geometry of the Galaxy. Specifically, an analytical model for a smooth distribution of particles in an oblate ellipsoid is used to replicate the observed distributions of the Galactic coordinates for pulsars and supernova remnants. The distributions and the Lambert equal area projections (LEAPs) of the coordinates suggest that the dominant factors determining the general shape of the distributions are the heavy concentration of objects in the Galactic plane and the offset of the Galactic center from the coordinate system origin. The LEAPs and the distributions also show that the dispersion of pulsars about and along the plane are much larger than that for their progenitor supernovae. Additionally, the model can be used to derive an analytical expression for the dispersion measure along any line of sight within the Galaxy. The expression is used to create a hypothetical dispersion measure-distance map for pulsars in the Galaxy.

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arXiv2005

Pulsar Astrometry at the Microarcsecond Level

Determination of pulsar parallaxes and proper motions addresses fundamental astrophysical questions. We have recently finished a VLBI astrometry project to determine the proper motions and parallaxes of 27 pulsars, thereby doubling the total number of pulsar parallaxes. Here we summarise our astrometric technique and present the discovery of a pulsar moving in excess of 1000 km/s. As an example of the application of high precision pulsar astrometry we also infer the identification of 2 pulsars originating from a disrupted binary in the Cygnus Superbubble.

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arXiv1993

The Masses of Two Binary Neutron Star Systems

The measurement or constraint of the masses of neutron stars and their binary companions tests theories of neutron star structure and of pulsar formation and evolution. We have measured the rate of the general relativistic advance of the longitude of periastron for the pulsar PSR B1802$-$07: $\dotω=0\fdg060\pm0\fdg009\,\mbox{yr}^{-1}$, which implies a total system mass, pulsar plus companion star, of $M=1.7\pm0.4\,\Msun$. We also present a much improved measurement of the rate of periastron advance for PSR B2303+46: $\dotω= 0\fdg0099\pm0\fdg0002\,\mbox{yr}^{-1}$, implying $M=2.53\pm0.08\,\Msun$ for this system. We discuss the available constraints on distribution of mass between the pulsars and their companions, and we compare the pulsar masses with other determinations of neutron star masses.

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