Imprints of magnetic power and helicity spectra on radio polarimetry statistics

Abstract

Statistical properties of turbulent magnetic fields in radio-synchrotron sources should imprint on the statistics of polarimetric observables. In search of these imprints, we calculate correlation and cross-correlation functions from a set of observables containing the total intensity I, the polarized intensity P and the Faraday depth phi. The correlation functions are evaluated for all combinations of observables up to fourth order in the magnetic field B. We derive these as far as possible analytically and from first principles only using some basic assumptions such as Gaussian statistics of the underlying magnetic field in the observed region and statistical homogeneity. We further assume some simplifications to reduce the complexity of the calculations, as for a start we were interested in a proof of concept. Using this statistical approach, we show that it is in principle possible to gain information about the helical part of the magnetic power spectrum, namely via the correlation functions <P(k)phi(k')phi(k")> and <I(k)phi(k')phi(k")>. Using this insight, we construct an easy-to-use test for helicity, called LITMUS (Local Inference Test for Magnetic fields which Uncovers heliceS). For now, all calculations are given in a Faraday-free case, but set up in a way so that Faraday rotational effects could be included later on.