Neutrino fast flavor pendulum. II. Collisional damping

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)(nu) over bar (e) <->nu(x)(nu) over barx 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. that moves between +1 and cosv(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 G for all modes. Empirically we find that the damped pendular motion reaches an asymptotic level of pair conversion f = A + (1 - A) cosv(min) (numerically A similar or equal to 0.370) that does not depend on details of the angular distribution (except for fixing cos.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.