We study the impact of neutrino magnetic moments on astrophysical neutrinos, in particular supernova neutrinos and ultra-high energy neutrinos from extragalactic sources. We show that magnetic moment-induced conversion of Dirac neutrinos from left-handed states into unobservable right-handed singlet states can substantially change the flux and flavour composition of these neutrinos at Earth. Notably, neutrinos from a supernova's neutronisation burst, whose flux can be predicted with O(10%) accuracy, offer a discovery reach to neutrino magnetic moments ∼ few × 10-13 μB , up to one order of magnitude below current limits. For high-energy neutrinos from distant sources, for which no robust flux prediction exists, we show how the flavour composition at Earth can be used as a handle to establish the presence of non-negligible magnetic moments, potentially down to few× 10-17 μB if the measurement can be performed on neutrinos from a single source. In both cases, the sensitivity strongly depends on the galactic (intergalactic) magnetic field profiles along the line of sight. Therefore, while a discovery is possible down to very small values of the magnetic moment, the absence of a discovery does not imply an equally strong limit. We also comment on the dependence of our results on the right-handed neutrino mass, paying special attention to the transition from coherent deflection by a classical magnetic field to incoherent scattering on individual scattering targets. Finally, we show that a measurement of Standard Model Dirac neutrino magnetic moments, of order 10-19 μB , could be possible under rather optimistic, but not completely outrageous, assumptions using flavour ratios of high-energy astrophysical neutrinos.
