A comprehensive study of neutrino spin-flavour conversion in supernovae and the neutrino mass hierarchy

Resonant spin-flavour (RSF) conversions of supernova neutrinos, which is induced by the interaction between the nonzero neutrino magnetic moment and supernova magnetic fields, are studied for both normal and inverted mass hierarchy. As the case for the pure matter-induced neutrino oscillation (Mikheyev--Smirnov--Wolfenstein (MSW) effect), we find that the RSF transitions are strongly dependent on the neutrino mass hierarchy as well as the value of $\theta_{13}$. Flavour conversions are solved numerically for various neutrino parameter sets, with presupernova profile calculated by Woosley and Weaver. In particular, it is very interesting that the RSF-induced \nu_\rme\to\bar\nu_\rme transition occurs, if the following conditions are all satisfied: the value of $\mu_\nu B$ ($\mu_\nu$ is the neutrino magnetic moment, and $B$ is the magnetic field strength) is sufficiently strong, the neutrino mass hierarchy is inverted, and the value of $\theta_{13}$ is large enough to induce adiabatic MSW resonance. In this case, the strong peak due to original \nu_\rme emitted from neutronization burst would exist in time profile of the neutrino events detected at the Super-Kamiokande detector. If this peak were observed in reality, it would provide fruitful information on the neutrino properties. On the other hand, characters of the neutrino spectra are also different between the neutrino models, but we find that there remains degeneracy among several models. Dependence on presupernova models is also discussed.Comment: 23 pages, 11 figures, corrected minor typos, added references. Final version to appear in Journal of Cosmology and Astroparticle Physic