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Dark Matter (DM) annihilation in our Galaxy may produce a linearly polarizedsynchrotron signal. We use, for the first time, synchrotron polarization toconstrain the DM annihilation cross section by comparing theoreticalpredictions with the latest polarization maps obtained by the Planck satellitecollaboration. We find that synchrotron polarization is typically moreconstraining than synchrotron intensity by about one order of magnitude,independently of uncertainties in the modeling of electron and positronpropagation, or of the Galactic magnetic field. Our bounds compete with CosmicMicrowave Background limits in the case of leptophilic DM.

Dark Matter constraints from Planck observations of the Galactic polarized synchrotron emission