绝热细丝的引力不稳定性
The Gravitational Instability of Adiabatic Filaments
摘要：
丝状结构，或狭长的物质流，出现在天文学的许多领域。在这里，我们调查的稳定性，这样的细丝进行本征模分析的绝热和多变的流体圆柱体，这是圆柱形模拟的球形多面体。我们表明，这些气缸是重力不稳定的扰动沿轴的圆柱低于临界波数$k_{\rm crit} \simeq few$，其中$k_{\rm crit}$测量相对于圆柱的半径。低于这个临界波数的扰动增长为$\propto e^{σ_{\rm u}τ}$，其中$τ$是相对于穿过圆柱体直径的声音穿越时间的时间，并且我们推导出作为波数的函数的增长率$σ_{\rm u}$。我们发现，有一个最大的增长率$σ_{\rm max} \sim 1$，发生在一个特定的波数$k_{\rm max} \sim 1$，我们推导出的增长率$σ_{\rm max}$和波数$k_{\rm max}$和$k_{\rm crit}$的绝热指数的范围。在某种程度上，纤维状结构可以近似为绝热和流体状，我们的结果意味着这些细丝是不稳定的，而不需要呼吁磁场或外部介质。此外，从这种细丝的不稳定性中凝结出来的物体通过优选的长度尺度分离，在优选的时间尺度上形成，并且具有优选的质量尺度。
英文摘要：
Filamentary structures, or long and narrow streams of material, arise in many areas of astronomy. Here we investigate the stability of such filaments by performing an eigenmode analysis of adiabatic and polytropic fluid cylinders, which are the cylindrical analog of spherical polytropes. We show that these cylinders are gravitationally unstable to perturbations along the axis of the cylinder below a critical wavenumber $k_{\rm crit} \simeq few$, where $k_{\rm crit}$ is measured relative to the radius of the cylinder. Below this critical wavenumber perturbations grow as $\propto e^{σ_{\rm u}τ}$, where $τ$ is time relative to the sound crossing time across the diameter of the cylinder, and we derive the growth rate $σ_{\rm u}$ as a function of wavenumber. We find that there is a maximum growth rate $σ_{\rm max} \sim 1$ that occurs at a specific wavenumber $k_{\rm max} \sim 1$, and we derive the growth rate $σ_{\rm max}$ and the wavenumbers $k_{\rm max}$ and $k_{\rm crit}$ for a range of adiabatic indices. To the extent that filamentary structures can be approximated as adiabatic and fluid-like, our results imply that these filaments are unstable without the need to appeal to magnetic fields or external media. Further, the objects that condense out of the instability of such filaments are separated by a preferred length scale, form over a preferred timescale, and possess a preferred mass scale.
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