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 ${\nu }_e{\bar{\nu }}_e\leftrightarrow {\nu }_x{\bar{\nu }}_x$ 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 $\cos {\vartheta }_{\min }$, 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 $f=A+(1-A)\cos {\vartheta }_{\min }$ (numerically $A\simeq 0.370$) that does not depend on details of the angular distribution (except for fixing $\cos {\vartheta }_{\min }$), 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.

Comments: 9 figures, 14 pages. Matches version published in Phys. Rev. D