Phase-Twist Instability in a Coprecessing Neutrino Plasma

Abstract

Dense neutrino plasmas support collective flavor motion. We derive the first explicit dispersion relation about a flavor-nondiagonal background, focusing on the coprecession solution underlying spectral-split formation during the prompt neutrino burst of an electron-capture supernova. We show that slow phase modulations are unstable Goldstone modes, causing the coprecession plane to wobble with increasing amplitude. The instability emerges in the hydrodynamic limit, governed by conservation laws and without resolving flavor-precession resonances. Coprecessing neutrino plasmas resemble magnetized plasmas: a coherent flavor field drives flavor isospins to precess, and the phase-twist instability is the flavor analog of the firehose instability.