准弛豫旋转恒星系统的自洽模型
Self-consistent models of quasi-relaxed rotating stellar systems
摘要：
本文提出了两类新的描述准弛豫旋转恒星系统的自洽轴对称截断平衡模型。第一个扩展的球形国王模型的情况下，固体旋转。第二个特征在于差分旋转，设计为在中心区域是刚性的，并且在外部部分消失，其中能量截断变得有效。该模型是通过求解自洽平均场势的非线性泊松方程而建立的。对于刚性转动构型，通过转动强度参数的渐近展开得到解。差分旋转模型是通过基于密度和势的勒让德级数展开的迭代方法构造的。这两类模型具有互补的性质。刚性旋转的构形向赤道平面变平，偏离球面对称的情况随着离中心的距离增加而增加。对于第二族的模型，偏离球形对称性在中心区域是最强的，而外部部分倾向于准球形。相关的参数空间进行了探索和描述的内在和投影的结构特性。特别注意的是不同的选择截断的分布函数在相空间中的效果。在中等旋转制度的模型最适合应用于球状星团。对于恒星动力学的普遍兴趣，在高值的旋转强度的差分旋转模型表现出嵌入在一个准球形配置的环形核心。物理上简单的分析模型，这里提出的那种动力学机制的见解，并可能是更现实的调查与N体模拟的帮助下的基础。
英文摘要：
Two new families of self-consistent axisymmetric truncated equilibrium models for the description of quasi-relaxed rotating stellar systems are presented. The first extends the spherical King models to the case of solid-body rotation. The second is characterized by differential rotation, designed to be rigid in the central regions and to vanish in the outer parts, where the energy truncation becomes effective. The models are constructed by solving the nonlinear Poisson equation for the self-consistent mean-field potential. For rigidly rotating configurations, the solutions are obtained by an asymptotic expansion on the rotation strength parameter. The differentially rotating models are constructed by means of an iterative approach based on a Legendre series expansion of the density and the potential. The two classes of models exhibit complementary properties. The rigidly rotating configurations are flattened toward the equatorial plane, with deviations from spherical symmetry that increase with the distance from the center. For models of the second family, the deviations from spherical symmetry are strongest in the central region, whereas the outer parts tend to be quasi-spherical. The relevant parameter spaces are explored and the intrinsic and projected structural properties are described. Special attention is given to the effect of different options for the truncation of the distribution function in phase space. Models in the moderate rotation regime are best suited to applications to globular clusters. For general interest in stellar dynamics, at high values of the rotation strength the differentially rotating models exhibit a toroidal core embedded in a quasi-spherical configuration. Physically simple analytical models of the kind presented here provide insights into dynamical mechanisms and may be a basis for more realistic investigations with the help of N-body simulations.
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