Neutrino fast flavor pendulum. II. 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 ${\ensuremath{\nu}}_{e}{\overline{\ensuremath{\nu}}}_{e}\ensuremath{\leftrightarrow}{\ensuremath{\nu}}_{x}{\overline{\ensuremath{\nu}}}_{x}$ with $x=\ensuremath{\mu}$, $\ensuremath{\tau}$, 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 $\mathrm{cos}\ensuremath{\vartheta}$ that moves between $+1$ and $\mathrm{cos}{\ensuremath{\vartheta}}_{\mathrm{min}}$, the latter following from a linear mode analysis. As a next step, we include collisional damping of flavor coherence, assuming a common damping rate $\mathrm{\ensuremath{\Gamma}}$ for all modes. Empirically we find that the damped pendular motion reaches an asymptotic level of pair conversion $f=A+(1\ensuremath{-}A)\mathrm{cos}{\ensuremath{\vartheta}}_{\mathrm{min}}$ (numerically $A\ensuremath{\simeq}0.370$) that does not depend on details of the angular distribution (except for fixing $\mathrm{cos}{\ensuremath{\vartheta}}_{\mathrm{min}}$), the initial seed, nor $\mathrm{\ensuremath{\Gamma}}$. 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.

Topics & Concepts