膨胀壳II的破碎：厚度很重要
The fragmentation of expanding shells II: Thickness matters
摘要：
本文用解析方法研究了有限厚度膨胀壳中引力不稳定性的发展。我们考虑三种模型的径向密度分布的壳：（i）一个解析的均匀密度模型，（ii）一个半解析模型，通过数值解的流体静力平衡方程，和（iii）一个三维流体动力学模拟。我们发现，所有三个配置文件是在密切的协议，这使我们能够使用第一个模型来描述碎片的径向方向的壳。然后，我们使用非线性方程描述的时间演化的一个统一的扁球体，以获得具有不同大小的壳碎片的增长率。这就产生了一个色散关系，它取决于壳体厚度，因此也取决于壳体的压力。我们比较这种色散关系与色散关系，使用标准的薄壳分析，并表明，如果围压低，只有大的碎片是不稳定的。另一方面，如果围压很高，碎片小于薄壳分析预测变得不稳定。最后，我们比较了新的色散关系与三维流体动力学模拟的结果，表明两者是很好的协议。
英文摘要：
We study analytically the development of gravitational instability in an expanding shell having finite thickness. We consider three models for the radial density profile of the shell: (i) an analytic uniform-density model, (ii) a semi-analytic model obtained by numerical solution of the hydrostatic equilibrium equation, and (iii) a 3D hydrodynamic simulation. We show that all three profiles are in close agreement, and this allows us to use the first model to describe fragments in the radial direction of the shell. We then use non-linear equations describing the time-evolution of a uniform oblate spheroid to derive the growth rates of shell fragments having different sizes. This yields a dispersion relation which depends on the shell thickness, and hence on the pressure confining the shell. We compare this dispersion relation with the dispersion relation obtained using the standard thin-shell analysis, and show that, if the confining pressure is low, only large fragments are unstable. On the other hand, if the confining pressure is high, fragments smaller than predicted by the thin-shell analysis become unstable. Finally, we compare the new dispersion relation with the results of 3D hydrodynamic simulations, and show that the two are in good agreement.
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