重力热突变：流体模型的动力学稳定性
Gravothermal Catastrophe: the dynamical stability of a fluid model
摘要：
对重力热灾难进行了重新研究。本文用线性微扰分析方法研究了有限体积球形自引力等温流体的动力学稳定性，发现在不同的外界条件下，重力热突变发生的条件与用热力学方法得到的结果一致。这表明，重力热灾难可能减少到金斯不稳定性，重新发现在一个不均匀的框架。我们发现正常的模式和频率的流体系统，并表明不稳定的发展动态的时间尺度。然后我们讨论几个相关的问题。特别是：（1）对于总能量和体积恒定的扰动，我们在能量收支中引入一个简单的启发式项来模拟双星的作用。(2)我们概述了分析的两个组件的情况下，并显示如何线性扰动分析也可以进行在这个更复杂的背景下，在一个相对简单的方式。(3)我们比较了流体模型的行为与无碰撞球体的行为。在无碰撞情况下，不稳定性似乎消失了，这与均匀情况下的线性Jeans稳定性分析不同;我们认为，要理解这种差异，（球形恒星系统预期仅在存在某种碰撞时才经历重力热灾难，这表明不稳定性是耗散的而不是动力学的）在于无碰撞系统中详细角动量的作用。最后，我们简要地评述了玻尔兹曼熵的意义及其在自引力非均匀气体系统动力学研究中的应用。
英文摘要：
A re-investigation of the gravothermal catastrophe is presented. By means of a linear perturbation analysis, we study the dynamical stability of a spherical self-gravitating isothermal fluid of finite volume and find that the conditions for the onset of the gravothermal catastrophe, under different external conditions, coincide with those obtained from thermodynamical arguments. This suggests that the gravothermal catastrophe may reduce to Jeans instability, rediscovered in an inhomogeneous framework. We find normal modes and frequencies for the fluid system and show that instability develops on the dynamical time scale. We then discuss several related issues. In particular: (1) For perturbations at constant total energy and constant volume, we introduce a simple heuristic term in the energy budget to mimic the role of binaries. (2) We outline the analysis of the two-component case and show how linear perturbation analysis can be carried out also in this more complex context in a relatively straightforward way. (3) We compare the behavior of the fluid model with that of the collisionless sphere. In the collisionless case the instability seems to disappear, which is at variance with the linear Jeans stability analysis in the homogeneous case; we argue that a key ingredient to understand the difference (a spherical stellar system is expected to undergo the gravothermal catastrophe only in the presence of some collisionality, which suggests that the instability is dissipative and not dynamical) lies in the role of the detailed angular momentum in a collisionless system. Finally, we briefly comment on the meaning of the Boltzmann entropy and its applicability to the study of the dynamics of self- gravitating inhomogeneous gaseous systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
