In this paper we present, for the first time, simulated maps of the circularly polarized synchrotron emission from the Crab nebula, using multidimensional state of the art models for the magnetic field geometry. Synchrotron emission is the signature of non-thermal emitting particles, typical of many high-energy astrophysical sources, both Galactic and extra-galactic ones. Its spectral and polarization properties allow us to infer key informations on the particles distribution function and magnetic field geometry. In recent years our understanding of pulsar wind nebulae has improved substantially thanks to a combination of observations and numerical models. A robust detection or non-detection of circular polarization will enable us to discriminate between an electron-proton plasma and a pair plasma, clarifying once for all the origin of the radio emitting particles, setting strong constraints on the pair production in pulsar magnetosphere, and the role of turbulence in the nebula. Previous attempts at measuring the circular polarization have only provided upper limits, but the lack of accurate estimates, based on reliable models, makes their interpretation ambiguous. We show here that those results are above the expected values, and that current polarimetric tecniques are not robust enough for conclusive result, suggesting that improvements in construction and calibration of next generation radio facilities are necessary to achieve the desired sensitivity.
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