论文标题
分层旋转流体的局部重力不稳定：气态盘的3D标准
Local gravitational instability of stratified rotating fluids: 3D criteria for gaseous discs
论文作者
论文摘要
人们认为，通过重力不稳定性旋转气体系统的破碎被认为是几种天体物理过程中的至关重要机制，例如在原始碟片中形成行星，银河盘中的分子云以及分子云中的恒星。对于无限薄的椎间盘，引力不稳定是相当理解的。然而，在许多情况下，薄盘近似是没有道理的，并且一般兴趣研究以不同程度的旋转支持和分层的旋转流体的重力不稳定性。我们得出了轴对称扰动的分散关系，可用于在旋转的轴对称气体系统的任何点上研究局部重力稳定性，并具有压缩或斜射线性分布。获得了3D稳定性标准，该标准概括了先前的结果，可用于确定给定的3D结构的旋转系统是否以及何处容易形成结块。对于垂直分层的厚度$ h_z $的气态（定义为包含$ \ $ \ $ 70％的每单位表面质量的70％），局部重力不稳定的足够条件是$ q _ {\ rm 3d} \ equiv \ equiv \ equiv \ left（ h_z^{-1}\right)/{\sqrt{4πGρ}}<1$, where $ρ$ is the gas volume density, $κ$ the epicycle frequency, $c_s$ the sound speed, and $ν^2\equivρ_z p_z/ρ^2$, where $ρ_z$ and $p_z$ are the vertical gradients of, respectively, gas density和压力。旋转（$κ^2 $）和分层（$ν^2 $）的综合稳定效应是显而易见的。在不稳定的光盘中，不稳定的条件通常靠近中平面，在这种情况下，预计会增长的扰动的特征性径向范围为几个$ h_z $。
Fragmentation of rotating gaseous systems via gravitational instability is believed to be a crucial mechanism in several astrophysical processes, such as formation of planets in protostellar discs, of molecular clouds in galactic discs, and of stars in molecular clouds. Gravitational instability is fairly well understood for infinitesimally thin discs. However, the thin-disc approximation is not justified in many cases, and it is of general interest to study the gravitational instability of rotating fluids with different degrees of rotation support and stratification. We derive dispersion relations for axisymmetric perturbations, which can be used to study the local gravitational stability at any point of a rotating axisymmetric gaseous system with either barotropic or baroclinic distribution. 3D stability criteria are obtained, which generalize previous results and can be used to determine whether and where a rotating system of given 3D structure is prone to clump formation. For a vertically stratified gaseous disc of thickness $h_z$ (defined as containing $\approx$70% of the mass per unit surface), a sufficient condition for local gravitational instability is $Q_{\rm 3D}\equiv\left(\sqrt{κ^2+ν^2}+c_s h_z^{-1}\right)/{\sqrt{4πGρ}}<1$, where $ρ$ is the gas volume density, $κ$ the epicycle frequency, $c_s$ the sound speed, and $ν^2\equivρ_z p_z/ρ^2$, where $ρ_z$ and $p_z$ are the vertical gradients of, respectively, gas density and pressure. The combined stabilizing effects of rotation ($κ^2$) and stratification ($ν^2$) are apparent. In unstable discs, the conditions for instability are typically met close to the midplane, where the perturbations that are expected to grow have characteristic radial extent of a few $h_z$.
