Evaluating approximate asymptotic distributions for fast neutrino flavor conversions in a periodic 1D box

The fast flavor conversions (FFCs) of neutrinos generally exist in core-collapse supernovae and binary neutron-star merger remnants, and can significantly change the flavor composition and affect the dynamics and nucleosynthesis processes. Several analytical prescriptions were proposed recently to approximately explain or predict the asymptotic outcome of FFCs for systems with different initial or boundary conditions, with the aim for providing better understandings of FFCs and for practical implementation of FFCs in hydrodynamic modeling. In this work, we obtain the asymptotic survival probability distributions of FFCs in a survey over thousands of randomly sampled initial angular distributions by means of numerical simulations in one-dimensional boxes with the periodic boundary condition. We also propose improved prescriptions that guarantee the continuity of the angular distributions after FFCs. Detailed comparisons and evaluation of all these prescriptions with our numerical survey results are performed. The survey dataset is made publicly available to inspire the exploration and design for more effective methods applicable to realistic hydrodynamic simulations.