Landau Damping of Collective Neutrino Oscillation Waves

Abstract

Dense neutrino media in core-collapse supernovae and neutron star mergers can experience collective flavor transformations in the form of neutrino oscillation waves. It was recently reported that the stable fast modes of collective oscillations can be damped through a mechanism similar to the Landau damping of plasma waves. In this work, we show that the actual damping rates of fast oscillation waves are usually very small and vanishes in the pure fast limit. This result does not affect the unstable modes that eventually drive collective neutrino flavor conversions in supernovae and neutron star mergers.

Figures (2)

• Figure 1: Left: The contour of the $\omega$-integration of $I(s)$ in Eq. \ref{['eq:I']} is deformed as the pole $\omega^*(s)$ (shown as the solid dot) of the integrand descends across the real axis. Right: The contour of the $s$-integration for the inverse Laplace transform can be deformed from the right half plane to the left half plane except around the poles of $\tilde{\Phi}^\mu(s)$ (shown as the solid dots).
• Figure 2: The monopole moment of the neutrino coherence $|\Phi^0(t)|$ in a homogeneous and isotropic $\nu_e$ gas with a small initial flavor coherence. The solid and dashed lines represent the numerical results for the normal and inverted neutrino mass orderings, respectively. The dotted line represents an exponential decay with the rate predicted by Landau damping for the normal mass ordering.