Finding a faint polarized signal in wide-band radio data

Abstract

We develop two algorithms, based on maximum likelihood (ML) inference, for estimating the parameters of polarized radio sources which emit at a single rotation measure (RM), e.g., pulsars. These algorithms incorporate the flux density spectrum of the source, either a power law or a scaled version of the Stokes I spectrum, and a variation in sensitivity across the observing band. We quantify the detection significance and measurement uncertainties in the fitted parameters, and we derive weighted versions of the RM synthesis algorithm which, under certain conditions, maximize the likelihood. We use Monte Carlo simulations to compare injected and recovered source parameters for a range of signal-to-noise ratios, investigate the quality of standard methods for estimating measurement uncertainties, and search for statistical biases. These simulations consider one frequency band each for the Australia Telescope Compact Array (ATCA), the Square Kilometre Array (SKA), and the Low Frequency Array (LOFAR). We find that results obtained for one frequency band cannot be easily generalized, and that methods which were developed in the past for correcting bias in individual frequency channels do not apply to wide-band data sets. The standard method for estimating the measurement uncertainty in RM is not accurate for sources with non-zero spectral indices. Furthermore, dividing Stokes Q and U by Stokes I to correct for spectral index effects, in combination with RM synthesis, does not maximize the likelihood.

arXiv commentThis is a resubmission of the original manuscript. The covariance matrix that we calculated in equation (17) was not correct, and several of the η in section 3.1 should be replaced with \hat η. We fixed these mistakes in an Erratum that has been accepted for publication in MNRAS, and in this new version of the manuscript that we uploaded to arXiv

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Cited by in corpus (17)

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• The intra-cluster magnetic field in the double relic galaxy cluster Abell 2345
• CHANG-ES XIII: Transport processes and the magnetic fields of NGC 4666 - indication of a reversing disk magnetic field
• Particle re-acceleration and Faraday-complex structures in the RXC J1314.4-2515 galaxy cluster
• Testing the accuracy of the ionospheric Faraday rotation corrections through LOFAR observations of bright northern pulsars
• S-PASS/ATCA: a window on the magnetic universe in the southern hemisphere
• A Broadband Spectro-polarimetric View of the NVSS Rotation Measure Catalogue I: Breaking the nπ-ambiguity
• A polarization census of bright pulsars using the Ultra-Wideband Receiver on the Parkes radio telescope
• Constraining the Magnetic Field of the Smith High Velocity Cloud using Faraday rotation
• The Complex Large-scale Magnetic Fields in the First Galactic Quadrant as Revealed by the Faraday Depth Profile Disparity
• Reliable detection and characterization of low-frequency polarized sources in the LOFAR M51 field
• Finding a complex polarized signal in wide-band radio data
• Using the polarization properties of double radio relics to probe the turbulent compression scenario
• Rotation measure variations in Galactic Centre pulsars
• Removing non-physical structure in fitted Faraday rotated signals: non-parametric QU-fitting
• The Galactic latitude dependency of Faraday complexity in the S-PASS/ATCA RM catalogue