Prospects for Neutrino Spin Coherence in Supernovae

We present neutrino bulb model simulations of Majorana neutrino coherent spin transformation (i.e., neutrino-antineutrino transformation), coupled to neutrino flavor evolution, for conditions corresponding to the neutronization burst epoch of an Oxygen-Neon-Magnesium (O-Ne-Mg) core collapse supernova. Significant neutrino spin transformation in, for example, the neutronization burst, could alter the fluences of neutrinos and antineutrinos in a way which is potentially detectable for a Galactic core collapse supernova. Our calculations for the first time incorporate geometric dilution in the spin evolution of the neutrinos and combine two-flavor and three-flavor evolution with spin mixing physics. We find that significant spin transformations can occur, but only with a large neutrino luminosity and an electron fraction ($Y_e$) profile which facilitates adiabatic conditions for the spin-channel resonance. Using our adopted parameters of neutrino energy spectra, luminosity, density and $Y_e$ profiles, our calculations require an unrealistically large neutrino rest mass to sustain the spin transformation. It is an open question whether examining different density profiles or incorporating other sources of nonlinear feedback, such as $Y_e$ feedback, could mitigate this need. We find that spin transformations are not sensitive to the flavor structure of neutrinos, i.e., the spin transformations occur regardless of whether we simulate two- or three-flavor transformations. In the two-flavor case, spin transformations were insensitive to the choice of solar or atmospheric mass-squared splitting as well as the choice of the Majorana phase. Importantly, our three-flavor simulations, as well as our two-flavor simulations done with the atmospheric mass-squared splitting, show that the inclusion of spin degrees of freedom can significantly and qualitatively alter neutrino flavor evolution.