On the reliability of polarization estimation using Rotation Measure Synthesis

We benchmark the reliability of the Rotation Measure (RM) synthesis algorithm using the 1005 Centaurus A field sources of Feain et al. (2009). The RM synthesis solutions are compared with estimates of the polarization parameters using traditional methods. This analysis provides verification of the reliability of RM synthesis estimates. We show that estimates of the polarization parameters can be made at lower S/N if the range of RMs is bounded, but reliable estimates of individual sources with unusual RMs require unconstrainted solutions and higher S/N. We derive from first principles the statistical properties of the polarization amplitude associated with RM synthesis in the presence of noise. The amplitude distribution depends explicitly on the amplitude of the underlying (intrinsic) polarization signal. Hence it is necessary to model the underlying polarization signal distribution in order to estimate the reliability and errors in polarization parameter estimates. We introduce a Bayesian method to derive the distribution of intrinsic amplitudes based on the distribution of measured amplitudes. The theoretically-derived distribution is compared with the empirical data to provide quantitative estimates of the probability that an RM synthesis solution is correct as a function of S/N. We provide quantitative estimates of the probability that any given RM synthesis solution is correct as a function of measured polarized amplitude and the intrinsic polarization amplitude compared to the noise.