Steady state of fast-oscillating neutrinos in an inhomogeneous medium

The streaming of neutrinos in an inhomogeneous medium is known to affect the physics of flavor conversion. We employ an ensemble of single-crossed angular distributions and explore the physics of flavor conversion, while neutrinos propagate across a one-dimensional inhomogeneous medium. The advective term in the neutrino equations of motion is responsible for the cascade of flavor waves towards ever smaller spatial and angular scales. However, as the system evolves, perturbations with large wavenumbers are damped, with a resulting smearing of the flavor configuration. We provide a simple recipe that allows to forecast the steady-state flavor configuration achieved by neutrinos without solving their kinetic equations. In particular, we find that flavor equipartition on one side of the angular spectrum and the cancellation of the spectral crossing in the lepton number distributions, proposed in the literature as generic flavor outcome, is a special solution depending on the degree of neutrino-antineutrino asymmetry. This work constitutes a step forward towards the development of semi-analytic schemes to account for flavor conversion physics in hydrodynamic simulations of core-collapse supernovae and neutron-star merger remnants.