标题： 中微子快速风味演化的理论。 第二部分。 不稳定性边缘的解 显示英文标题

标题： Theory of neutrino fast flavor evolution. Part II. Solutions at the edge of instability

摘要： 在密集中微子环境中，如由核心坍缩超新星或中子星合并提供的环境，中微子角分布可能对集体风味转换不稳定，其结果仍未完全理解。 这些转换比流体力学尺度快得多，表明自洽配置可能永远不会强烈不稳定。 鉴于此，我们研究弱不稳定的模式，即那些具有小增长率的模式。 我们表明，我们新开发的色散关系（本系列论文的第一篇）允许对小增长率进行幂级数展开。 对于弱不稳定的分布，我们表明不稳定的模式必须以亚光速相速度移动，或者非常接近光速。 不稳定性来源于与波共振运动的中微子，使我们能够推导出增长率的显式表达式。 对于文献中常假设的轴对称分布，数值例子显示了这些表达式的准确性。 我们还注意到，对于常被研究的一维系统，不应忘记轴对称性破坏模式，并我们提供了显示不稳定的波数范围的显式表达式。 显示英文摘要

摘要： In dense neutrino environments, such as provided by core-collapse supernovae or neutron-star mergers, neutrino angular distributions may be unstable to collective flavor conversions, whose outcome remains to be fully understood. These conversions are much faster than hydrodynamical scales, suggesting that self-consistent configurations may never be strongly unstable. With this motivation in mind, we study weakly unstable modes, i.e., those with small growth rates. We show that our newly developed dispersion relation (Paper~I of this series) allows for an expansion in powers of the small growth rate. For weakly unstable distributions, we show that the unstable modes must either move with subluminal phase velocity, or very close to the speed of light. The instability is fed from neutrinos moving resonantly with the waves, allowing us to derive explicit expressions for the growth rate. For axisymmetric distributions, often assumed in the literature, numerical examples show the accuracy of these expressions. We also note that for the often-studied one-dimensional systems one should not forget the axial-symmetry-breaking modes, and we provide explicit expressions for the range of wavenumbers that exhibit instabilities.