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Turbulence patterns and neutrino flavor transitions in high-resolution supernova models

During the shock-wave propagation in a core-collapse supernova (SN), matter turbulence may affect neutrino flavor conversion probabilities. Such effects have been usually studied by adding parametrized small-scale random fluctuations (with arbitrary amplitude) on top of coarse, spherically symmetric matter density profiles. Recently, however, two-dimensional (2D) SN models have reached a space resolution high enough to directly trace anisotropic density profiles, down to scales smaller than the typical neutrino oscillation length. In this context, we analyze the statistical properties of a large set of SN matter density profiles obtained in a high-resolution 2D simulation, focusing on a post-bounce time (2 s) suited to study shock-wave effects on neutrino propagation on scales as small as O(100) km and possibly below. We clearly find the imprint of a broken (Kolmogorov-Kraichnan) power-law structure, as generically expected in 2D turbulence spectra. We then compute the flavor evolution of SN neutrinos along representative realizations of the turbulent matter density profiles, and observe no or modest damping of the neutrino crossing probabilities on their way through the shock wave. In order to check the effect of possibly unresolved fluctuations at scales below O(100) km, we also apply a randomization procedure anchored to the power spectrum calculated from the simulation, and find consistent results within \pm 1 sigma fluctuations. These results show the importance of anchoring turbulence effects on SN neutrinos to realistic, fine-grained SN models.