Detection Thresholds and Bias Correction in Polarized Intensity

TL;DR

This paper investigates detection thresholds and bias correction in polarized intensity measurements using RM synthesis, highlighting the impact of non-Gaussian noise on false detection rates and proposing more accurate thresholds.

Contribution

It provides new insights into detection thresholds and bias correction in polarized intensity, especially considering non-Gaussian noise effects in RM synthesis surveys.

Findings

An 8σ threshold in the Faraday spectrum yields low false detection rates (<10^{-4}).

Non-Gaussian noise significantly increases false detection rates, requiring adjusted thresholds.

Monte Carlo simulations show non-Gaussian noise effects comparable to Ricean bias at lower thresholds.

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 $4.9 \sigma_{QU}$.