Neutrino Fast Flavor Pendulum. Part 2: Collisional Damping

Abstract

In compact astrophysical objects, the neutrino density can be so high that neutrino-neutrino refraction can lead to fast flavor conversion of the kind $ν_e \barν_e \leftrightarrow ν_x \barν_x$ with $x=μ,τ$, depending on the neutrino angle distribution. Previously, we have shown that in a homogeneous, axisymmetric two-flavor system, these collective solutions evolve in analogy to a gyroscopic pendulum. In flavor space, its deviation from the weak-interaction direction is quantified by a variable $\cos\vartheta$ that moves between $+1$ and $\cos\vartheta_{\rm min}$, the latter following from a linear mode analysis. As a next step, we include collisional damping of flavor coherence, assuming a common damping rate $Γ$ for all modes. Empirically we find that the damped pendular motion reaches an asymptotic level of pair conversion $f=A+(1-A)\cos\vartheta_{\rm min}$ (numerically $A\simeq 0.370$) that does not depend on details of the angular distribution (except for fixing $\cos\vartheta_{\rm min}$), the initial seed, nor $Γ$. On the other hand, even a small asymmetry between the neutrino and antineutrino damping rates strongly changes this picture and can even enable flavor instabilities in otherwise stable systems.