Consequences of largeθ13for the turbulence signatures in supernova neutrinos

Abstract

The transition probabilities for a single neutrino emitted from a point proto-neutron source after passage through a turbulent supernova density profile have been found to be random variates drawn from parent distributions whose properties depend upon the stage of the explosion, the neutrino energy and mixing parameters, the observed channel, and the properties of the turbulence such as the amplitude ${C}_{\ensuremath{\star}}$. In this paper we examine the consequences of the recently measured mixing angle ${\ensuremath{\theta}}_{13}$ upon the neutrino flavor transformation in supernova when passing through turbulence, in order to provide some clarity as to what one should expect in the way of turbulence effects in the next supernova neutrino burst signal. We find that the measurements of a relatively large value of ${\ensuremath{\theta}}_{13}$ means the neutrinos are relatively immune to small, ${C}_{\ensuremath{\star}}\ensuremath{\lesssim}1%$, amplitude turbulence but as ${C}_{\ensuremath{\star}}$ increases the turbulence effects grow rapidly and spread to all mixing channels. For ${C}_{\ensuremath{\star}}\ensuremath{\gtrsim}10%$ the turbulence effects in the high density resonance mixing channels are independent of ${\ensuremath{\theta}}_{13}$ but nonresonant mixing channels are more sensitive to turbulence when ${\ensuremath{\theta}}_{13}$ is large.