圆柱云几何结构和动力学状态方程的自相似坍塌解
Self-Similar Collapse Solutions for Cylindrical Cloud Geometries and Dynamic Equations of State
摘要：
分子气体引力坍缩的自相似理论为探索恒星形成的动力学提供了一个重要的理论框架。在巨大的分子云中观察到的细长和非线性结构的存在下，我们建立在现有的圆柱形自相似坍塌流的工作基础上，包括动态状态方程，不同于产生初始密度分布的有效状态方程。我们主要集中在崩溃的气体是在休息和到处过密从其相应的流体静力平衡配置文件的一个因素$Λ$的初始状态，并将我们的结果对密集，细长的分子核心内的恒星形成的分析。这项工作的一个重要方面是确定质量下落率的范围内的参数定义的整体状态的气体-超密度参数$Λ$，指数$Γ$的静态状态方程，和指数$γ$的动态状态方程。虽然在这项工作中探索的大部分参数空间导致解决方案的基本方程不成为奇异的，我们包括一个讨论如何处理的情况下，解决方案顺利通过奇异表面。此外，我们还提出了一个特殊的情况下，$γ= 1$不同的崩溃的解决方案。
英文摘要：
A self-similar formalism for the study of the gravitational collapse of molecular gas provides an important theoretical framework from which to explore the dynamics of star formation. Motivated by the presence of elongated and filamentary structures observed in giant molecular clouds, we build upon the existing body of work on cylindrical self-similar collapse flows by including dynamic equations of state that are different from the effective equation of state that produces the initial density distribution. We focus primarily on the collapse of initial states for which the gas is at rest and everywhere overdense from its corresponding hydrostatic equilibrium profile by a factor $Λ$, and apply our results toward the analysis of star formation within dense, elongated molecular cores. An important aspect of this work is the determination of the mass infall rates over a range of the parameters which define the overall state of the gas -- the overdensity parameter $Λ$, the index $Γ$ of the static equation of state, and the index $γ$ of the dynamic equation of state. While most of the parameter space explored in this work leads to solutions for which the underlying equations do not become singular, we do include a discussion on how to treat cases for which solutions pass smoothly through the singular surface. In addition, we also present a different class of collapse solutions for the special case $γ= 1$.
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