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Neutrino emission from FRB-emitting magnetars

The detection of a bright radio burst (hereafter FRB 200428) in association with a hard X-ray burst from the Galactic magnetar SGR 1935+2154 suggests that magnetars can make FRBs. We study possible neutrino emission from FRB-emitting magnetars by developing a general theoretical framework. We consider three different sites for proton acceleration and neutrino emission, i.e. within the magnetosphere, in the current sheet region beyond the light cylinder, and in relativistic shocks far away from the magnetosphere. Different cooling processes for protons and pions are considered to calculate the neutrino emission suppression factor within each scenario. We find that the flux of the neutrino emission decreases with increasing radius from the magnetar due to the decrease of the target photon number density. We calculate the neutrino flux from FRB 200428 and its associated X-ray burst. The flux of the most optimistic case invoking magnetospheric proton acceleration is still $\sim4$ orders of magnitude below the IceCube sensitivity. We also estimate the diffuse neutrino background from all FRB-emitting magnetars in the universe. The total neutrino flux of magnetars during their FRB emission phases is a negligible fraction of observed diffuse emission even under the most optimistic magnetospheric scenario for neutrino emission. However, if one assumes that many more X-ray bursts without FRB associations can also produce neutrinos with similar mechanisms, magnetars can contribute up to $10^{-8} \ {\rm GeV \ s^{-1} \ sr^{-1} \ cm^{-2}}$ diffuse neutrino background flux in the GeV to multi-TeV range.