Flavor Oscillation Modes In Dense Neutrino Media

We study two-flavor neutrino oscillations in homogeneous neutrino gases in which neutrinos and anti-neutrinos are in nearly pure weak interaction states initially. We find that the monopole and dipole oscillation modes can trigger flavor instabilities in the opposite neutrino mass hierarchies in a nearly isotropic neutrino gas. For a class of simple neutrino systems we are able to identify the normal modes of neutrino oscillations in the linear regime. Our results provide new insights into the recently discovered multi-azimuthal angle (MAA) instability of neutrino oscillations in supernovae.