Fast Conversion of Neutrinos: Energy Dependence of Flavor Instabilities

Pedro Dedin Neto, Irene Tamborra, Shashank Shalgar

Published 2023-12-11Version 1

In core-collapse supernovae and neutron star mergers, the neutrino density is so large that neutrino-neutrino refraction can lead to flavor conversion, classified as ``fast'' since the neutrino self-interaction strength $\mu=\sqrt{2} G_F n_\nu$ represents the characteristic time-scale of the system. However, it has been empirically realized that the vacuum frequency $\omega=\Delta m^2/2E$ affects the development of flavor conversion even if $\omega \ll \mu$, as is the case in the core of compact astrophysical sources. Focusing on a homogeneous and axially symmetric neutrino gas, we explore the role of $\omega$ in the onset of flavor instabilities. Relying on a perturbative approach, we find that the odd powers of $\omega$ are linked to the angular distribution of the neutrino flavor particle number (FPN). Hence, when $\omega \neq 0$, the flavor conversion dynamics does not depend on the neutrino flavor lepton number only (FLN), like for fast flavor conversion, but also on the FPN. A non-zero vacuum frequency is also responsible for inducing flavor instabilities with a non-negligible growth rate in a neutrino gas that would be otherwise stable for $\omega \rightarrow 0$. Such a neutrino ensemble with $\omega \neq 0$ can be formally mapped into an effective system with $\omega =0$, whose angular distributions have non-zero imaginary components. Our work highlights the overlooked role of vacuum mixing in the development of flavor instabilities in neutrino systems with FLN zero-crossings in the angular distributions.