Self-induced flavor conversions of supernova (SN) neutrinos can strongly modify the flavor dependent fluxes. We perform a linearized flavor stability analysis with accretion-phase matter profiles of a 15 M spherically symmetric model and corresponding neutrino fluxes. We use realistic energy and angle distributions, the latter deviating strongly from quasi-isotropic emission, thus accounting for both multi-angle and multi-energy effects. For our matter and neutrino density profile we always find stable conditions: flavor conversions are limited to the usual Mikheyev-Smirnov-Wolfenstein effect. In this case one may distinguish the neutrino mass hierarchy in a SN neutrino signal if the mixing angle θ13 is as large as suggested by recent experiments.PACS numbers: 97.60.Bw, 14.60.PqIntroduction.-The huge neutrino fluxes emitted by core-collapse supernovae (SNe) are key to the explosion dynamics and nucleosynthesis [1] and detecting a highstatistics "neutrino light curve" from the next nearby SN is a major goal for neutrino astronomy [2]. Besides probing the core-collapse phenomenon in unprecedented detail, one may detect signatures of flavor oscillations and extract information on neutrino mixing parameters [3,4].The refractive effect caused by matter [5] suppresses flavor oscillations until neutrinos pass through the Mikheyev-Smirnov-Wolfenstein (MSW) region in the collapsing star's envelope [6,7]. However, neutrino-neutrino interactions, through a flavor off-diagonal refractive index [8,9], can trigger self-induced flavor conversions [10][11][12]. This collective effect usually occurs between the neutrino sphere and the MSW region and can strongly modify neutrino spectra [13][14][15], although this would never seem to help explode the star [16]. Actually, in lowmass SNe (not studied here) the density falls off so fast that MSW can occur first, leading to novel effects on the prompt ν e burst [17].Collective oscillations at first seemed unaffected by matter because its influence does not depend on neutrino energies [13]. However, depending on emission angle, neutrinos accrue different matter-induced flavordependent phases until they reach a given radius. This "multi-angle matter effect" can suppress self-induced flavor conversion [18]. Based on schematic flux spectra, this was numerically confirmed for accretion-phase SN models where the density near the core is large [19]. This epoch, before the delayed explosion finally takes off, is when the neutrino luminosity and the difference between theν e andν µ,τ fluxes are largest. If self-induced flavor conversion did not occur and the mixing angle θ 13 was not very small [20], the accretion phase would provide a plausible opportunity to determine the mass hierarchy [3,19].Numerical multi-angle simulations of collective oscillations are very demanding [21], but it is much easier to