Detection Thresholds and Bias Correction in Polarized Intensity
Samuel J. George A B , Jeroen M. Stil A and Ben W. Keller AA Institute for Space Imaging Science & Department of Physics and Astronomy, The University of Calgary, 2500 University Drive NW, Calgary AB, T2N 1N4, Canada
B Corresponding author. Email: samuel@ras.ucalgary.ca
Publications of the Astronomical Society of Australia 29(3) 214-220 https://doi.org/10.1071/AS11027
Submitted: 13 June 2011 Accepted: 26 June 2011 Published: 6 October 2011
Abstract
Detection thresholds in polarized intensity and polarization bias correction are investigated for surveys where the polarization information is obtained from rotation measure (RM) synthesis. Considering unresolved sources with a single RM, a detection threshold of 8 σQU applied to the Faraday spectrum will retrieve the RM with a false detection rate less than 10–4, but polarized intensity is more strongly biased than Ricean statistics suggest. For a detection threshold of 5 σQU, the false detection rate increases to ~4%, depending also on λ2 coverage and the extent of the Faraday spectrum. Non-Gaussian noise in Stokes Q and U due to imperfect imaging and calibration can be represented by a distribution that is the sum of a Gaussian and an exponential. The non-Gaussian wings of the noise distribution increase the false detection rate in polarized intensity by orders of magnitude. Monte Carlo simulations assuming non-Gaussian noise in Q and U give false detection rates at 8 σQU similar to Ricean false detection rates at 4.9 σQU.
Keywords: polarization — methods: statistical — methods: data analysis
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