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星际气体层激波的引力不稳定性

Gravitational Instability of Shocked Interstellar Gas Layers

Kazunari Iwasaki, Toru Tsuribe

备注：
12 pages, 21 figures, accepted for publication in PASJ
发表信息：
Publ. Astron. Soc. Japan 60, pp.125-136 (2008)
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摘要：

本文用线性分析方法研究了冲击气体层的引力不稳定性。未扰动状态是一个自引力等温层，它通过云-云碰撞引起的激波前沿的气体吸积而随时间增长。由于未微扰状态不是静态的，并且不能用自相似解描述，因此我们数值求解微扰方程并直接将其随时间积分。我们考虑了物理量沿厚度的分布。线性化的Rankine-Hugoniot关系作为边界条件施加在激波阵面上。非定常线性分析结果表明：扰动初始以振荡模式发展，并在某一时刻开始增长。最快增长模式的波数由$k=2\sqrt{2πGρ_\mathrm{E} {\cal M\mit}}/c_\mathrm{s}$给出，其中$ρ_\mathrm{E}, c_\mathrm{s}$和$\cal M\mit$分别是母云的密度、声速和碰撞速度的马赫数。对于这种模式，从振荡到增长模式的过渡时期由$t_g = 1.2/\sqrt{2πGρ_\mathrm{E} {\cal M\mit}}$给出。最快增长模式变为非线性的时期由$2.4δ_0^{-0.1}/\sqrt{2πG ρ_\mathrm{E}{\cal M\mit}}$给出，其中$δ_0$是柱密度扰动的初始幅度。作为我们的线性分析的应用程序，我们调查的碰撞诱导碎裂的标准。碰撞引发的碎裂只有在母云是冷的或$α_0=5c_\mathrm{s}^2 R/2G M < 1$时才会发生，其中$R$和$M$分别是母云的半径和质量。

英文摘要：

In this paper we investigate gravitational instability of shocked gas layers using linear analysis. An unperturbed state is a self-gravitating isothermal layer which grows with time by the accretion of gas through shock fronts due to a cloud-cloud collision. Since the unperturbed state is not static, and cannot be described by a self-similar solution, we numerically solved the perturbation equations and directly integrated them over time. We took account of the distribution of physical quantities across the thickness. Linearized Rankine-Hugoniot relations were imposed at shock fronts as boundary conditions. The following results are found from our unsteady linear analysis: the perturbation initially evolves in oscillatory mode, and begins to grow at a certain epoch. The wavenumber of the fastest growing mode is given by $k=2\sqrt{2πGρ_\mathrm{E} {\cal M\mit}}/c_\mathrm{s}$, where $ρ_\mathrm{E}, c_\mathrm{s}$ and $\cal M\mit$ are the density of parent clouds, the sound velocity and the Mach number of the collision velocity, respectively. For this mode, the transition epoch from oscillatory to growing mode is given by $t_g = 1.2/\sqrt{2πGρ_\mathrm{E} {\cal M\mit}}$. The epoch at which the fastest growing mode becomes non-linear is given by $2.4δ_0^{-0.1}/\sqrt{2πG ρ_\mathrm{E}{\cal M\mit}}$, where $δ_0$ is the initial amplitude of the perturbation of the column density. As an application of our linear analysis, we investigate criteria for collision-induced fragmentation. Collision-induced fragmentation will occur only when parent clouds are cold, or $α_0=5c_\mathrm{s}^2 R/2G M < 1$, where $R$ and $M$ are the radius and the mass of parent clouds, respectively.

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