The Magnetic Power Spectrum in Faraday Rotation Screens

Abstract

The autocorrelation function and similarly the Fourier-power spectrum of a rotation measure (RM) map of an extended background radio source can be used to measure components of the magnetic autocorrelation and power-spectrum tensor within a foreground Faraday screen. It is possible to reconstruct the full non-helical part of this tensor in the case of an isotropic magnetic field distribution statistics. The helical part is only accessible with additional information; e.g. the knowledge that the fields are force-free. The magnetic field strength, energy spectrum and autocorrelation length l_B can be obtained from the non-helical part alone. We demonstrate that l_B can differ substantially from l_RM, the observationally easily accessible autocorrelation length of an RM map. In typical astrophysical situation l_RM > l_B. Any RM study, which does not take this distinction into account, likely underestimates the magnetic field strength. For power-law magnetic power spectra, and for patchy magnetic field configurations the central RM autocorrelation function is shown to have characteristic asymptotic shapes. Ways to constrain the volume filling factor of a patchy field distribution are discussed. We discuss strategies to analyse observational data, taking into account - with the help of a window function - the limited extent of the polarised radio source, the spatial distribution of the electron density and average magnetic energy density in the screen, and allowing for noise reducing data weighting. We briefly discuss the effects of possible observational artefacts, and strategies to avoid them.