DEFROST: Detecting Excess in Faraday Rotation thrOugh Sophisticated analysis Techniques

Understanding the origin and evolution of cosmological magnetic fields requires a detailed knowledge of the strength of magnetic fields in different extragalactic environments. In this context, a powerful tool is the statistical analysis of the Faraday effect on the linear polarization of a sample of radio sources. This effect carries information about the magnetic fields in our Galaxy, in extragalactic environments between the sources and the observer, and within the emitting radio source itself. An accurate disentangling of all these components is crucial in order to characterize magnetic fields in the large-scale structure of the Universe. The significant amount of data delivered by new radio instruments enables the investigation of increasingly weak magnetic fields. However, a trustworthy characterization is only possible with advanced analysis techniques. In this work, we present a new algorithm capable of simultaneously disentangling the Faraday effect due to our Galaxy from extragalactic contributions, by properly taking into account the observing noise. The algorithm takes as input a catalogue of Faraday depth measurements complemented by auxiliary information, for example as the redshift of the sources. We tested the algorithm with synthetic data to assess its performance and to identify the range of slopes of the Galactic magnetic field power spectrum that allows us to properly disentangle Galactic and extragalactic contributions. Furthermore, we tested the algorithm with synthetic catalogues, based on metre and centimetre data currently available, corresponding to different observing set-ups, noise, and cuts in the absolute value of the Galactic latitude of the radio sources. Considering noise values and density of polarized sources consistent with existing catalogues, we demonstrated that the most robust results are obtained with sources with absolute Galactic latitude greater than 45 degrees, with inference of the extragalactic parameters at most within 5σ, both for dispersion in Faraday rotation of about 1 and 10 rad/m2.