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

Neutrino-neutrino forward scatterings potentially induce collective neutrino oscillation in dense neutrino gases in astrophysical sites such as core-collapse supernovae (CCSNe) and binary neutron star mergers (BNSMs). In this paper, we present a detailed study of fast neutrino-flavor conversion (FFC), paying special attention to asymptotic states, by means of 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 that 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 shuffle large amount of neutrinos among flavors through FFC in the angular directions where neutrinos are more abundant, indicating the need for including the effects of FFCs in the modeling of CCSN and BNSM.