Imprints of magnetic power and helicity spectra on radio polarimetry statistics

Max-Planck-Institut für Astrophysik, Karl-Schwarzschildstr. 1, 85741 Garching, Germany
e-mail: henrikju@mpa-garching.mpg.de

Received: 6 August 2010
Accepted: 1 February 2011

Abstract

The statistical properties of turbulent magnetic fields in radio-synchrotron sources should be imprinted on the statistics of polarimetric observables. In search of these imprints, i.e. characteristic modifications of the polarimetry statistics caused by magnetic field properties, we calculate correlation and cross-correlation functions from a set of observables that contain total intensity I, polarized intensity P, and Faraday depth φ. The correlation functions are evaluated for all combinations of observables up to fourth order in magnetic field B. We derive these analytically as far as possible and from first principles using only some basic assumptions, such as Gaussian statistics for the underlying magnetic field in the observed region and statistical homogeneity. We further assume some simplifications to reduce the complexity of the calculations, because for a start we were interested in a proof of concept. Using this statistical approach, we show that it is possible to gain information about the helical part of the magnetic power spectrum via the correlation functions $\mathrm{⟨}\mathit{P}\mathrm{\left(}{k}{}_{\mathrm{\perp }}\mathrm{\right)}\mathit{\phi }\mathrm{\left(}{k}\begin{array}{}\mathrm{\prime }\\ \mathrm{\perp }\end{array}\mathrm{\right)}\mathit{\phi }\mathrm{\left(}{k}\begin{array}{}\mathrm{\prime \prime }\\ \mathrm{\perp }\end{array}\mathrm{\right)}{\mathrm{⟩}}_{{B}}$ and $\mathrm{⟨}\mathit{I}\mathrm{\left(}{k}{}_{\mathrm{\perp }}\mathrm{\right)}\mathit{\phi }\mathrm{\left(}{k}\begin{array}{}\mathrm{\prime }\\ \mathrm{\perp }\end{array}\mathrm{\right)}\mathit{\phi }\mathrm{\left(}{k}\begin{array}{}\mathrm{\prime \prime }\\ \mathrm{\perp }\end{array}\mathrm{\right)}{\mathrm{⟩}}_{{B}}$. Using this insight, we construct an easy-to-use test for helicity called LITMUS (Local Inference Test for Magnetic fields which Uncovers heliceS), which gives a spectrally integrated measure of helicity. For now, all calculations are given in a Faraday-free case, but set up so that Faraday rotational effects can be included later.