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| - Probing magnetic fields in volume with multifrequency polarized synchrotron emission
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| - We investigate the problem of probing the local spatial structure of the magnetic field of the interstellar medium using multifrequency polarized maps of the synchrotron emission at radio wavelengths. We focus in this paper on the three-dimensional (3D) reconstruction of the largest scales of the magnetic field, relying on the internal depolarization (due to differential Faraday rotation) of the emitting medium as a function of electromagnetic frequency. We argue that multiband spectroscopy in the radio wavelengths, developed in the context of high-redshift extragalactic H i lines, can be a very useful probe of the 3D magnetic field structure of our Galaxy when combined with a maximum a posteriori reconstruction technique. When starting from a fair approximation of the magnetic field, we are able to recover the true one by using a linearized version of the corresponding inverse problem. The spectral analysis of this problem allows us to specify the best sampling strategy in electromagnetic frequency and predicts a spatially anisotropic distribution of posterior errors. The reconstruction method is illustrated for reference fields extracted from realistic magnetohydrodynamical simulations.
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