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The usual description of self-induced neutrino flavor conversions in core collapse supernovae (SNe) is based on the dominance of the neutrino density n_nu over the net electron density n_e. However, this condition is not met during the post-bounce accretion phase, when the dense matter in a SN is piled up above the neutrinosphere. As recently pointed-out, a dominant matter term in the anisotropic SN environment would dephase the flavor evolution for neutrinos traveling on different trajectories, challenging the occurrence of the collective behavior in the dense neutrino gas. Using the results from recent long term simulations of core-collapse SN explosions, based on three flavor Boltzmann neutrino transport in spherical symmetry, we find that both the situations of complete matter suppression (when n_e >> n_nu) and matter-induced decoherence (when n_e \gtrsim n_nu) of flavor conversions are realized during the accretion phase. The matter suppression at high densities prevents any possible impact of the neutrino oscillations on the neutrino heating and hence on the dynamics of the explosion. Furthermore, it changes the interpretation of the Earth matter effect on the SN neutrino signal during the accretion phase, allowing the possibility of the neutrino mass hierarchy discrimination at not too small values of the leptonic mixing angle \theta_{13} (i.e. \sin^2{\theta}_{13} \gtrsim 10^{-3})., Comment: Revised version (15 pages, 13 eps figures) published on Physical Review D. Discussion enlarged, references updated

The large neutrino fluxes emitted with a distinct flavor hierarchy from core-collapse supernovae (SNe) during the post-bounce accretion phase, offer the best opportunity to detect effects from neutrino flavor oscillations. We perform a dedicated study of the SN neutrino flavor evolution during the accretion phase, using results from recent neutrino radiation hydrodynamics simulations. In contrast to what expected in the presence of only neutrino-neutrino interactions, we find that the multi-angle effects associated with the dense ordinary matter suppress collective oscillations. This is related to the high matter densities during the accretion phase in core-collapse SNe of massive iron-core progenitors. The matter suppression implies that neutrino oscillations will start outside the neutrino transport region and therefore will have a negligible impact on the neutrino heating and the explosion dynamics. Furthermore, the possible detection of the next galactic SN neutrino signal from the accretion phase, based on the usual Mikheyev- Smirnov-Wolfenstein effect in the SN mantle and Earth matter effects, can reveal the neutrino mass hierarchy in the case that the mixing angle $\theta_{13}$ is not very small., Comment: (4 pages, 4 eps figures, v2 revised version. Discussion clarified. Matches the version published on PRL)

The non-isotropic nature of the neutrino emission from a supernova (SN) core might potentially affect the flavor evolution of the neutrino ensemble, via neutrino-neutrino interactions in the deepest SN regions. We investigate the dependence of these "multi-angle effects" on the original SN neutrino fluxes in a three-flavor framework. We show that the pattern of the spectral crossings (energies where F_\nu_e= F_\nu_x, and F_\bar\nu_e= F_\bar\nu_x) is crucial in determining the impact of multi-angle effects on the flavor evolution. For neutrino spectra presenting only a single-crossing, synchronization of different angular modes prevails over multi-angle effects, producing the known "quasi single-angle" evolution. Conversely, in the presence of spectra with multiple crossing energies, synchronization is not stable. In this situation, multi-angle effects would produce a sizable delay in the onset of the flavor conversions, as recently observed. We show that, due to the only partial adiabaticity of the evolution at large radii, the multi-angle suppression can be so strong to dramatically affect the final oscillated neutrino spectra. In particular three-flavor effects, associated with the solar parameters, could be washed-out in multi-angle simulations., Comment: v2(14 pages, 12 eps figures). Matches the version published on PRD. Figures and text clarified. Appendix added. Conclusions unchenged

It was recently realized that three-flavor effects could peculiarly modify the development of spectral splits induced by collective oscillations, for supernova neutrinos emitted during the cooling phase of a protoneutron star. We systematically explore this case, explaining how the impact of these three-flavor effects depends on the ordering of the neutrino masses. In inverted mass hierarchy, the solar mass splitting gives rise to instabilities in regions of the (anti)neutrino energy spectra that were otherwise stable under the leading two-flavor evolution governed by the atmospheric mass splitting and by the 1-3 mixing angle. As a consequence, the high-energy spectral splits found in the electron (anti)neutrino spectra disappear, and are transferred to other flavors. Imperfect adiabaticity leads to smearing of spectral swap features. In normal mass hierarchy, the three-flavor and the two-flavor instabilities act in the same region of the neutrino energy spectrum, leading to only minor departures from the two-flavor treatment., Comment: v2(11 pages, 9 figures). Matches the version published on PRD. Minor changes in the text and in the Figures. Conclusions unchanged

We give a very brief overview of collective effects in neutrino oscillations in core collapse supernovae where refractive effects of neutrinos on themselves can considerably modify flavor oscillations, with possible repercussions for future supernova neutrino detection. We discuss synchronized and bipolar oscillations, the role of energy and angular neutrino modes, as well as three-flavor effects. We close with a short summary and some open questions., Comment: 6 pages, 2 figures, proceedings for plenary talk by G.Sigl at NOW2008, Conca Specchiulla, Otranto, Italy, September 2008; added reference for the CP-phase

We study two-flavor collective neutrino oscillations in the dense-neutrino region above the neutrino sphere in a supernova (SN). The angular dependence of the neutrino-neutrino interaction potential causes "multi-angle" effects that can lead either to complete kinematical decoherence in flavor space or only to small differences between different trajectories. This nonlinear system switches abruptly between "self-maintained coherence" and "self-induced decoherence" among the angular modes, depending on the strength of the deleptonization flux. For a realistic SN the quasi single-angle behavior is probably typical, simplifying the numerical treatment and probably allowing for the survival of observational features of flavor oscillations., Comment: Contribution to TAUP 07, Sendai, Japan

We study three-flavor collective neutrino transformations in the dense-neutrino region above the neutrino sphere of a supernova core. We find that two-flavor conversions driven by the atmospheric mass difference and the 13-mixing angle capture the full effect if one neglects the second-order difference between the muon and tau neutrino refractive index. Including this "mu-tau matter term" provides a resonance at a density of approximately 3 x 10^7 g cm^-3 that typically causes significant modifications of the overall electron neutrino and antineutrino survival probabilities. This effect is surprisingly sensitive to deviations from maximal 23-mixing, being different for each octant., Comment: 9 pages, 7 figures. New presentation of results, version to be published in PRD

In the dense-neutrino region at 50-400 km above the neutrino sphere in a supernova, neutrino-neutrino interactions cause large flavor transformations. We study when the multi-angle nature of the neutrino trajectories leads to flavor decoherence between different angular modes. We consider a two-flavor mixing scenario between nu_e and another flavor nu_x and assume the usual hierarchy F(nu_e)>F{antinu_e)>F(nu_x)=F(antinu_x) for the number fluxes. We define epsilon=(F(nu_e)-F(antinu_e))/(F(antinu_e)-F(antinu_x)) as a measure for the deleptonization flux which is the one crucial parameter. The transition between the quasi single-angle behavior and multi-angle decoherence is abrupt as a function of epsilon. For typical choices of other parameters, multi-angle decoherence is suppressed for epsilon>0.3, but a much smaller asymmetry suffices if the neutrino mass hierarchy is normal and the mixing angle small. The critical epsilon depends logarithmically on the neutrino luminosity. In a realistic supernova scenario, the deleptonization flux is probably enough to suppress multi-angle decoherence., Comment: 17 pages, 12 figures. Misprint in Eq (14) corrected

We investigate the possibility to use the neutrinos coming from a future galactic supernova explosion to perform neutrino oscillation tomography of the Earth's core. We propose to use existing or planned detectors, resulting in an additional payoff. Provided that all of the discussed uncertainties can be reduced as expected, we find that the average matter densities of the Earth's inner and outer cores could be measured with a precision competitive with geophysics. However, since seismic waves are more sensitive to matter density jumps than average matter densities, neutrino physics would give partly complementary information., Comment: 17 pages, 6 figures, LaTeX. Final version to be published in Astropart. Phys