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#### Neutrino Fast Flavor Pendulum. Part 2: Collisional Damping

##### MPS-Authors

Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Tamborra,  Irene
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

Raffelt,  Georg G.
Max Planck Institute for Physics, Max Planck Society and Cooperation Partners;

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##### Citation

Padilla-Gay, I., Tamborra, I., & Raffelt, G. G. (2022). Neutrino Fast Flavor Pendulum. Part 2: Collisional Damping. Physical Review D, 106, 103031. Retrieved from https://publications.mppmu.mpg.de/?action=search&mpi=MPP-2022-126.

Cite as: https://hdl.handle.net/21.11116/0000-000C-B4D1-C
##### 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. Furthermore, we establish a formal connection with a stationary and inhomogeneous neutrino ensemble, showing that our findings also apply to this system.