Resonant spin-flavor conversion of supernova neutrinos: Dependence on electron mole fraction

Abstract

Detailed dependence of resonant spin-flavor (RSF) conversion of supernova neutrinos on electron mole fraction ${Y}_{e}$ is investigated. Supernova explosion forms a hot-bubble and neutrino-driven wind region of which electron mole fraction exceeds 0.5 in several seconds after the core collapse. When a higher resonance of the RSF conversion is located in the innermost region, flavor change of the neutrinos strongly depends on the sign of $1\ensuremath{-}2{Y}_{e}$. At an adiabatic high RSF resonance the flavor conversion of ${\overline{\ensuremath{\nu}}}_{e}\ensuremath{\leftrightarrow}{\ensuremath{\nu}}_{\ensuremath{\mu},\ensuremath{\tau}}$ occurs in ${Y}_{e}<0.5$ and normal mass hierarchy or in ${Y}_{e}>0.5$ and inverted mass hierarchy. In other cases of ${Y}_{e}$ values and mass hierarchies, the conversion of ${\ensuremath{\nu}}_{e}\ensuremath{\leftrightarrow}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu},\ensuremath{\tau}}$ occurs. The final ${\overline{\ensuremath{\nu}}}_{e}$ spectrum is evaluated in the cases of ${Y}_{e}<0.5$ and ${Y}_{e}>0.5$ taking account of the RSF conversion. Based on the obtained result, time variation of the event number ratios of low ${\overline{\ensuremath{\nu}}}_{e}$ energy to high ${\overline{\ensuremath{\nu}}}_{e}$ energy is discussed. In normal mass hierarchy, an enhancement of the event ratio should be seen in the period when the electron fraction in the innermost region exceeds 0.5. In inverted mass hierarchy, on the other hand, a dip of the event ratio should be observed. Therefore, the time variation of the event number ratio is useful to investigate the effect of the RSF conversion.