2012A&A...543A.113B

Modern radio telescopes allow us to record a large number of spectral channels. The application of a Fourier transform to spectropolarimetric data in radio continuum, Faraday rotation measure (RM) synthesis, yields the ``Faraday spectrum'', which hosts valuable information about the magneto-ionic medium along the line of sight. We investigate whether the method of wavelet-based RM synthesis can help us to identify structures of regular and turbulent magnetic fields in extended magnetized objects, such as galaxies and galaxy clusters. The analysis of spectropolarimetric radio observations of multi-scale targets calls for a corresponding mathematical technique. Wavelets allow us to reformulate the RM synthesis method in a scale-dependent way and to visualize the data as a function of Faraday depth and scale. We present observational tests to recognize magnetic field structures. A region with a regular magnetic field generates a broad ``disk'' in Faraday space, with two ``horns'' when the distribution of cosmic-ray electrons is broader than that of the thermal electrons. Each field reversal generates one asymmetric ``horn'' on top of the ``disk''. A region with a turbulent field can be recognized as a ``Faraday forest'' of many components. These tests are applied to the spectral ranges of various synthesis radio telescopes. We argue that the ratio of maximum to minimum wavelengths determines the range of scales that can be identified in Faraday space. A reliable recognition of magnetic field structures in spiral galaxies or galaxy clusters requires the analysis of data cubes in position-position-Faraday depth space (``PPF cubes''), observed over a wide and continuous frequency range, allowing the recognition of a wide range of scales as well as high resolution in Faraday space. The planned Square Kilometre Array (SKA) will fulfill this condition and will be close to representing a perfect ``Faraday telescope''. The combination of data from the Low Frequency Array (LOFAR, at low frequencies) and the Expanded Very Large Array (EVLA, at high frequencies) appears to be a promising approach for the recognition of magnetic structures on all scales. The addition of data at intermediate frequencies from the Westerbork Synthesis Radio Telescope (WSRT) or the Giant Meterwave Radio Telescope (GMRT) would fill the gap between the LOFAR and EVLA frequency ranges. The Global Magneto-Ionic Medium Survey (GMIMS), planned with several single-dish telescopes at low angular resolution, will also provide good scale recognition and high resolution in Faraday space.