当自相似性与质量谱和各向异性相遇
When self-similarity meets mass spectrum and anisotropy
AI总结：
本文研究了多质量星团中自相似演化的结构稳定性，探讨了质量分层和速度各向异性的作用，通过气体模型近似发展出理论框架，分析了速度分布各向异性对自相似性破坏不稳定性的不同影响。
摘要：
自相似演化的广泛应用于碰撞性恒星动力学理论中，但其在多质量系统中的适用性尚不明确。我们研究了多质量星团中自相似演化的结构稳定性，并评估了质量分层和速度各向异性的作用。通过气体模型近似，我们发展出一个理论框架，以描述自相似背景对质量依赖扰动的响应，其中扰动具有各向同性或各向异性速度分布。我们证明了质量依赖的弛豫导致特征相似尺度的分离，并使单尺度解结构不稳定。在存在速度各向异性的情况下，这种破坏相似性不稳定性分裂成不同的径向和切向模式，其增长速率以方向依赖的方式改变。径向各向异性通过增强径向动能支撑来减少不稳定性，而切向各向异性增加有效增长速率并使中心演化更快。在具有质量谱的系统中，这种不稳定性驱动质量分层和多尺度、近同源演化的出现。这些结果为具有多质量和各向异性速度分布的碰撞性星团提供了自相似演化的理论框架。
英文摘要：
Self-similar evolution is widely used in the theory of collisional stellar dynamics, but its applicability to systems with multiple stellar masses is not well established. We investigate the structural stability of self-similar evolution in multi-mass star clusters and assess the roles of mass segregation and velocity anisotropy. Using a gaseous-model approximation, we develop a theoretical framework to describe the response of a self-similar background to mass-dependent perturbations with isotropic and anisotropic velocity distributions. We show analytically that mass-dependent relaxation leads to a separation of characteristic similarity scales and renders the single-scale solution structurally unstable. In the presence of velocity anisotropy, this similarity-breaking instability splits into distinct radial and tangential modes whose growth rates are modified in a direction-dependent manner. Radial anisotropy reduces the instability through enhanced radial kinetic support, whereas tangential anisotropy increases the effective growth rates and enables faster central evolution. In systems with a mass spectrum, this instability drives mass segregation and the emergence of a multi-scale, near-homologous evolution. Together, these results place self-similar evolution in a consistent theoretical context for collisional star clusters with multiple stellar masses and anisotropic velocity distributions.
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