Connecting small-scale to large-scale structures of fast neutrino-flavor conversion

We present a systematic study of fast neutrino-flavor conversion (FFC) with both small-scale and large-scale numerical simulations in spherical symmetry. We find that FFCs can, in general, reach a quasi-steady state, and these features in the non-linear phase are not characterized by the growth rate of FFC instability but rather angular structures of electron neutrino lepton number (ELN) and heavy one (XLN). Our result suggests that neutrinos can almost reach a flavor equipartition even in cases with low growth rate of instability (e.g., shallow ELN crossing) and narrow angular regions (in momentum space) where flavor conversions occur vigorously. This exhibits that ELN and XLN angular distributions can not provide a sufficient information to determine total amount of flavor conversion in neutrinos and antineutrinos of all flavors. Based on the results of our numerical simulations, we provide a new approximate scheme of FFC that is designed so that one can easily incorporate effects of FFCs in existing classical neutrino transport codes for the study of core-collapse supernova (CCSN) and binary neutron star merger (BNSM). The scheme has an ability to capture key features of quasi-steady state of FFCs without solving quantum kinetic neutrino transport, which will serve to facilitate access to FFCs for CCSN and BNSM theorists.