Collective Neutrino Flavor Instability Requires a Crossing.

Area of Science:

• * Astrophysics
• * Particle Physics
• * Cosmology

Background:

• * Neutrinos can change flavor collectively and unstably due to neutrino-neutrino interactions.
• * These flavor oscillations are significant in extreme astrophysical environments like supernovae and neutron stars, and in the early Universe.
• * Understanding collective neutrino oscillations is crucial for stellar evolution, nucleosynthesis, and neutrino physics.

Purpose of the Study:

• * To establish a necessary criterion for the occurrence of collective neutrino flavor instability.
• * To unify the understanding of both slow and fast collective neutrino instabilities.
• * To provide a rigorous condition applicable to ultrarelativistic neutrinos in various cosmic scenarios.

Main Methods:

• * Analyzing the Hamiltonian flavor evolution of neutrino occupation matrices.
• * Considering ultrarelativistic standard model neutrinos.
• * Incorporating damping effects from collisions within the relaxation approximation.

Main Results:

• * Proved that a necessary condition for collective instability is a sign change (zero crossing) in the difference of momentum distributions between neutrino flavors.
• * Demonstrated that this criterion unifies previously identified conditions for slow and fast instabilities.
• * Showed the criterion's validity for Hamiltonian flavor evolution, including collisional damping.

Conclusions:

• * A zero crossing in the momentum distribution difference is a fundamental requirement for collective neutrino flavor instability.
• * This unified criterion simplifies the study of neutrino oscillations in astrophysical and cosmological contexts.
• * The findings have implications for understanding supernova dynamics, heavy element formation, and the broader field of neutrino phenomenology.