Sufficient and Necessary Conditions for Collective Neutrino Instability: Fast, Slow, and Mixed

Collective neutrino oscillations exhibit instabilities that induce appreciable flavor conversion, with crucial astrophysical implications. While the importance of initial phase-space distributions is well-established, a general instability criterion for distributions dependent on both energy and emission angle has been lacking. We identify and analyze the sufficient (and necessary) conditions for a generic collective neutrino flavor instability.