Detection Thresholds and Bias Correction in Polarized Intensity

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 $4.9{\sigma }_{QU}$.