Collisional flavor instability in dense neutrino gases

Charged-current neutrino processes such as ${\ensuremath{\nu}}_{e}+n\ensuremath{\rightleftharpoons}p+{e}^{\ensuremath{-}}$ and ${\overline{\ensuremath{\nu}}}_{e}+p\ensuremath{\rightleftharpoons}n+{e}^{+}$ destroy the flavor coherence among the weak-interaction states of a single neutrino and thus damp its flavor oscillation. In a dense neutrino gas such as that inside a core-collapse supernova or the black hole accretion disk formed in a compact binary merger, however, these ``collision'' processes can trigger large flavor conversion in cooperation with the strong neutrino-neutrino refraction. We show that there exist two types of collisional flavor instability in a homogeneous and isotropic neutrino gas which are identified by the dependence of their real frequencies on the neutrino density ${n}_{\ensuremath{\nu}}$. The instability transitions from one type to the other and exhibits a resonancelike behavior in the region where the net electron lepton number of the neutrino gas is negligible. In the transition region, the flavor instability grows exponentially at a rate $\ensuremath{\propto}{n}_{\ensuremath{\nu}}^{1/2}$. We find that the neutrino gas in the black hole accretion disk is susceptible to the collision-induced flavor conversion where the neutrino densities are the highest. Further investigations are needed to confirm if the collisional flavor instability will indeed result in the production of large amounts of heavy-lepton flavor neutrinos in this environment which would have important ramifications in its subsequent evolution.

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