Estimating extragalactic Faraday rotation^⋆

¹ Max-Planck Institute for Astrophysics, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany
² Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St. George Street, Toronto ON, M5S 3H8, Canada
e-mail: niels@cita.utoronto.ca
³ Argelander-Institut für Astronomie, Auf dem Hügel 71, 52121 Bonn, Germany
⁴ Ludwig-Maximilians-Universität München, Fakultät für Physik, 80799 München, Germany
⁵ Sydney Institute for Astronomy, School of Physics, The University of Sydney, NSW 2006, Australia
⁶ CSIRO Astronomy and Space Science, PO Box 76, Epping, NSW 1700, Australia
⁷ The Oskar Klein Centre, Physics Department, Stockholm University, Albanova University Center, 106 91 Stockholm, Sweden
⁸ School of Chemical & Physical Sciences, Victoria University of Wellington, PO Box 600, Wellington 6014, New Zealand
⁹ Max-Planck Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
¹⁰ Department of Physics and Astronomy, The University of Calgary, 2500 University Drive NW, Calgary AB, T2N 1N4, Canada

Received: 14 April 2014
Accepted: 21 November 2014

Abstract

Observations of Faraday rotation for extragalactic sources probe magnetic fields both inside and outside the Milky Way. Building on our earlier estimate of the Galactic contribution, we set out to estimate the extragalactic contributions. We discuss the problems involved; in particular, we point out that taking the difference between the observed values and the Galactic foreground reconstruction is not a good estimate for the extragalactic contributions. We point out a degeneracy between the contributions to the observed values due to extragalactic magnetic fields and observational noise and comment on the dangers of over-interpreting an estimate without taking into account its uncertainty information. To overcome these difficulties, we develop an extended reconstruction algorithm based on the assumption that the observational uncertainties are accurately described for a subset of the data, which can overcome the degeneracy with the extragalactic contributions. We present a probabilistic derivation of the algorithm and demonstrate its performance using a simulation, yielding a high quality reconstruction of the Galactic Faraday rotation foreground, a precise estimate of the typical extragalactic contribution, and a well-defined probabilistic description of the extragalactic contribution for each data point. We then apply this reconstruction technique to a catalog of Faraday rotation observations for extragalactic sources. The analysis is done for several different scenarios, for which we consider the error bars of different subsets of the data to accurately describe the observational uncertainties. By comparing the results, we argue that a split that singles out only data near the Galactic poles is the most robust approach. We find that the dispersion of extragalactic contributions to observed Faraday depths is most likely lower than 7 rad/m², in agreement with earlier results, and that the extragalactic contribution to an individual data point is poorly constrained by the data in most cases.