Evolution of collisional neutrino flavor instabilities in spherically symmetric supernova models

We implement a multi-group and discrete-ordinate neutrino transport model in spherical symmetry which allows to simulate collective neutrino oscillations by including realistic collisional rates in a self-consistent way. We utilize this innovative model, based on strategic parameter rescaling, to study a recently proposed collisional flavor instability caused by the asymmetry of emission and absorption rates between $\nu_e$ and $\bar\nu_e$ for four different static backgrounds taken from different stages in a core-collapse supernova simulation. Our results confirm that collisional instabilities generally exist around the neutrinosphere during the SN accretion and post-accretion phase, as suggested by [arXiv:2104.11369]. However, the growth and transport of flavor instabilities can only be fully captured by models with global simulations as done in this work. With minimal ingredient to trigger collisional instabilities, we find that the flavor oscillations and transport mainly affect (anti)neutrinos of heavy lepton flavors around their decoupling sphere, which then leave imprints on their energy spectra in the free-streaming regime. For electron (anti)neutrinos, their properties remain nearly intact. We also explore various effects due to the decoherence from neutrino-nucleon scattering, artificially enhanced decoherence from emission and absorption, neutrino vacuum mixing, and inhomogeneous matter profile, and discuss the implication of our work.