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arXiv · 1106.5362

Detection Thresholds and Bias Correction in Polarized Intensity

Samuel J. George·Jeroen M. Stil·Ben W. Keller
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Abstract

Detection thresholds in polarized intensity and polarization bias correction are investigated for surveys where the polarization information is obtained from RM synthesis. Considering unresolved sources with a single rotation measure, a detection threshold of $8 \sigma_{QU}$ 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 $5 \sigma_{QU}$, the false detection rate increases to ~4%, depending also on $\lambda^2$ 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 $8 \sigma_{QU}$ similar to Ricean false detection rates at $4.9 \sigma_{QU}$.

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Samuel J. George, Jeroen M. Stil, Ben W. Keller. 2011-06-27. Detection Thresholds and Bias Correction in Polarized Intensity. https://doi.org/10.1071/as11027

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