Neutrino Fast Flavor Pendulum. Part 2: Collisional Damping

TL;DR

This paper investigates how collisional damping affects fast neutrino flavor conversions in dense astrophysical environments, revealing that damping leads to a stable asymptotic state but can also induce instabilities under certain asymmetries.

Contribution

It extends the neutrino flavor pendulum model by including collisional damping, showing how damping influences the evolution and stability of flavor conversions.

Findings

Damped flavor oscillations reach a stable asymptotic level independent of initial conditions.

Small asymmetries in damping rates can trigger flavor instabilities in otherwise stable systems.

The asymptotic flavor conversion level depends mainly on the minimum cosine of the pendulum angle.

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 $\nu_e \bar\nu_e \leftrightarrow \nu_x \bar\nu_x$ with $x=\mu,\tau$, 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 $\Gamma$ 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 $\Gamma$. 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.