Dark Matter constraints from Planck observations of the Galactic
  polarized synchrotron emission
  Dark Matter (DM) annihilation in our Galaxy may produce a linearly polarized
synchrotron signal. We use, for the first time, synchrotron polarization to
constrain the DM annihilation cross section by comparing theoretical
predictions with the latest polarization maps obtained by the Planck satellite
collaboration. We find that synchrotron polarization is typically more
constraining than synchrotron intensity by about one order of magnitude,
independently of uncertainties in the modeling of electron and positron
propagation, or of the Galactic magnetic field. Our bounds compete with Cosmic
Microwave Background limits in the case of leptophilic DM.
