Neutrino flavor conversion alters the lepton-emission self-sustained asymmetry in core-collapse supernovae

Abstract

We solve the neutrino equations of motion in a half annulus, accounting for two spatial dimensions. At any location in the annulus, the neutrino momentum is characterized by a polar-angle distribution, two effective azimuthal angles, and an energy distribution. We explore how neutrinos change their flavor while decoupling from matter in the presence of the neutrino-driven hydrodynamical instability LESA (i.e., the Lepton-number Emission Self-sustained Asymmetry) during the stalled-shock phase of a core-collapse supernova. In our setup, LESA is responsible for an excess of ${\nu }_e$'s (${\bar{\nu }}_e$'s) in the Northern (Southern) region of the annulus. Crossings in the ${\nu }_e$-${\bar{\nu }}_e$ angular distributions appear in the ELN-depleted Southern region of the annulus, while crossings in the energy distributions of ${\nu }_e$-${\nu }_x$ and ${\bar{\nu }}_e$-${\bar{\nu }}_x$ are present throughout the annulus. We find that collisional instabilities drive flavor conversion just before neutrino decoupling, fast instabilities are prominent in the Southern region of the annulus, and slow instabilities dominate otherwise. Flavor conversion is most efficient in the Southern region and is responsible for a $5$-$10\%$ enhancement of the LESA dipole, independent of the neutrino-mass ordering. Our findings suggest that direction-dependent flavor conversion can have implications for the development of global neutrino asymmetries and hydrodynamical instabilities in core-collapse supernovae.

26 pages, 22 figures, and 3 appendices