发表机构
Ferdowsi University of Mashhad（马什哈德 Ferdowsi 大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究流体静力分层介质中金斯判据，重新审视其分析，考虑背景物理量梯度并推导修正色散关系，通过线性扰动分析等研究扰动行为，结论是无法得出适用于任意流体静力背景的一般局部引力稳定性判据，但局部短波长极限下标准金斯判据仍有效。
AI 中文摘要
经典的金斯稳定性判据忽略了诸如密度和压力等背景物理量的空间梯度。在此，我们重新审视处于流体静力平衡的非旋转流体的金斯分析，明确考虑这些梯度并推导控制扰动传播的修正色散关系。通过物理论证，我们说明了对于比宿主系统尺寸小的扰动，推导金斯判据为何无需金斯佯谬。我们使用线性扰动分析和平均程序来研究流体静力介质中局部欧拉扰动的行为，表明背景梯度以高度非平凡的方式进入色散关系，排除了适用于任意流体静力系统的一般引力稳定性判据的推导。我们证明，在局部短波长极限下，尽管存在非零背景梯度，标准金斯判据仍然有效，并且流体静力系统中的所有局部扰动对于局部引力坍缩是稳定的。我们得出结论，不可能推导出适用于任意流体静力背景的一般局部引力稳定性判据；然而，在局部短波长极限下，标准金斯判据仍然有效。
英文摘要
The classical Jeans stability criterion neglects spatial gradients in background physical quantities such as density and pressure. Here, we revisit the Jeans analysis for a non-rotating fluid in hydrostatic equilibrium, explicitly accounting for these gradients and deriving a modified dispersion relation governing perturbation propagation. Using physical arguments, we show why the Jeans swindle is not required to derive the Jeans criterion for perturbations that are small compared to the size of the host system. We use linear perturbation analysis alongside an averaging procedure to study the behavior of the local Eulerian perturbations in a hydrostatic medium, showing that background gradients enter the dispersion relation in a highly non-trivial manner, precluding the derivation of a general gravitational stability criterion applicable to an arbitrary hydrostatic system. We demonstrate that, in the local short-wavelength limit, the standard Jeans criterion remains valid despite the presence of nonzero background gradients, and that all local perturbations in a hydrostatic system are stable against local gravitational collapse. We conclude that it is not possible to derive a general local gravitational stability criterion valid for an arbitrary hydrostatic background; however, in the local short-wavelength limit, the standard Jeans criterion remains valid.
Journal refAstronomy & Astrophysics, Volume 713, A15 (2026)
DOI：10.1051/0004-6361/202660817
