Simple method for determining asymptotic states of fast neutrino-flavor conversion

TL;DR

This paper investigates the asymptotic states of fast neutrino-flavor conversion in dense astrophysical neutrino gases, identifying key properties that determine flavor evolution and providing a simplified scheme for predicting neutrino survival probabilities.

Contribution

It introduces a new understanding of asymptotic states in fast neutrino-flavor conversion based on lepton number conservation and angular crossing disappearance, simplifying the prediction of neutrino flavor outcomes.

Findings

Asymptotic states characterized by lepton number conservation and crossing disappearance.

Flavor equipartition occurs in angular directions with negative or positive ELN-XLN density.

Shallow ELN crossings can still induce significant flavor conversion.

Abstract

Neutrino-neutrino forward scatterings potentially induce collective neutrino oscillation in dense neutrino gases in astrophysical sites such as core-collapse supernovae (CCSN) and binary neutron star mergers (BNSM). In this paper, we present a detailed study of fast neutrino-flavor conversion (FFC), paying special attention to asymptotic states, by linear stability analysis and local simulations with a periodic boundary condition. We find that asymptotic states can be characterized by two key properties of FFC: (1) the conservation of lepton number for each flavor of neutrinos and (2) the disappearance of ELN(electron neutrino-lepton number)-XLN(heavy-leptonic one) angular crossings in the spatial- or time-averaged distributions. The system which initially has the positive (negative) ELN-XLN density reaches a flavor equipartition in the negative (positive) ELN-XLN angular directions, and the other part compensates it to preserve the conservation laws. These properties of FFCs offer an approximate scheme determining the survival probability of neutrinos in asymptotic states without solving quantum kinetic equations. We also demonstrate that the total amount of flavor conversion can vary with species-dependent neutrino distributions for identical ELN-XLN ones. Our results suggest that even shallow or narrow ELN angular crossings have the ability to drive large flavor conversion, exhibiting the need for including the effects of FFCs in the modeling of CCSN and BNSM.