Evolution of tau-neutrino lepton number in protoneutron stars due to active-sterile neutrino mixing
Anupam Ray, Yong-Zhong Qian
Abstract
We present an approximate treatment of the mixing between ${\ensuremath{\nu}}_{\ensuremath{\tau}}$ (${\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}}$) and a sterile species ${\ensuremath{\nu}}_{s}$ (${\overline{\ensuremath{\nu}}}_{s}$) with a vacuum mass-squared difference of $\ensuremath{\sim}{10}^{2}--{10}^{3}\text{ }\text{ }{\mathrm{keV}}^{2}$ in protoneutron stars created in core-collapse supernovae. Including production of sterile neutrinos through both resonant flavor conversion and collisions, we track the evolution of the ${\ensuremath{\nu}}_{\ensuremath{\tau}}$ lepton number due to both escape of sterile neutrinos and diffusion. Our approach provides a reasonable treatment of the pertinent processes discussed in previous studies and serves a pedagogical purpose to elucidate the relevant physics. We also discuss refinements needed to study more accurately how flavor mixing with sterile neutrinos affects protoneutron star evolution.