The effect of core-collapse supernova accretion phase turbulence on neutrino flavor evolution

During the accretion phase of a core-collapse supernovae, large amplitude turbulence is generated by the combination of the standing accretion shock instability and convection driven by neutrino heating. The turbulence directly affects the dynamics of the explosion, but there is also the possibility of an additional, indirect, feedback mechanism due to the effect turbulence can have upon neutrino flavor evolution and thus the neutrino heating. In this paper we consider the effect of turbulence during the accretion phase upon neutrino evolution, both numerically and analytically. Adopting representative supernova profiles taken from the accretion phase of a supernova simulation, we find the numerical calculations exhibit no effect from turbulence. We explain this absence using two analytic descriptions: the stimulated transition model and the distorted phase effect model. In the stimulated transition model turbulence effects depend upon six different lengthscales, and three criteria must be satisfied between them if one is to observe a change in the flavor evolution due to stimulated transition. We further demonstrate that the distorted phase effect depends upon the presence of multiple semi-adiabatic MSW resonances or discontinuities that also can be expressed as a relationship between three of the same lengthscales. When we examine the supernova profiles used in the numerical calculations we find the three stimulated transition criteria cannot be satisfied, independent of the form of the turbulence power spectrum, and that the same supernova profiles lack the multiple semi-adiabatic MSW resonances or discontinuities necessary to produce a distorted phase effect. Thus, we conclude that even though large amplitude turbulence is present in supernova during the accretion phase, it has no effect upon neutrino flavor evolution.