### Abstract

We consider in detail the effects of the 13-mixing (sin^{2} θ_{13}) and of the type of mass hierarchy/ordering (sign[Δm_{13}^{2}]) on neutrino signals from the gravitational collapses of stars. The observables (characteristics of the energy spectra of v_{e} and v̄_{e} events) sensitive to sin ^{2} θ_{13} and sign[Δ_{13}^{2}] have been calculated. They include the ratio of average energies of the spectra, r _{E} ≡ 〈E〉 /〈Ē〉, the ratio of widths of the energy distributions, r_{Γ} ≡ Γ/Γ̄, the ratios of total numbers of v_{e} and v̄_{e} events at low energies, S, and in the high energy tails, R_{tail}. We construct and analyse scatter plots which show the predictions for the observables for different intervals of sin^{2} θ_{13} and signs of Δm_{13}^{2}, taking into account uncertainties in the original neutrino spectra, the star density profile, etc. Regions in the space of observables r_{E}, r_{Γ}, S, R_{tail} exist in which certain mass hierarchy and intervals of sin^{2} θ_{13} can be identified or discriminated. We elaborate on the method of the high energy tails in the spectra of events. The conditions are formulated for which sin^{2} θ_{13} can be (i) measured, (ii) restricted from below, (iii) restricted from above. We comment on the possibility to determine sin^{2} θ_{13} using the time dependence of the signals due to the propagation of the shock wave through the resonance layers of the star. We show that the appearance of the delayed Earth matter effect in one of the channels (v_{e} or v̄_{e}) in combination with the undelayed effect in the other channel will allow us to identify the shock wave appeareance and determine the mass hierarchy.

Original language | English (US) |
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Pages (from-to) | 121-168 |

Number of pages | 48 |

Journal | Journal of Cosmology and Astroparticle Physics |

Issue number | 6 |

DOIs | |

State | Published - Jun 2003 |

Externally published | Yes |

### Keywords

- Neutrino properties
- Supernova neutrinos

### ASJC Scopus subject areas

- Astronomy and Astrophysics

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## Cite this

*Journal of Cosmology and Astroparticle Physics*, (6), 121-168. https://doi.org/10.1088/1475-7516/2003/06/009