标题： 各向异性质量分选：两组分平均场模型 显示英文标题

标题： Anisotropic mass segregation: two-component mean-field model

摘要： 星系核是宇宙中密度最高的恒星环境，表现出复杂的几何结构。 围绕中心超大质量黑洞运行的恒星在距离中心的径向距离以及轨道平面的倾角上呈现出质量分层分布。 后一种分布可能代表矢量共振松弛（VRR）的平衡状态。 在本文中，我们构建简单的模型以理解之前数值模拟中发现的平衡分布。 通过最大化总熵和四极平均场近似的方法，我们确定了具有两种不同质量、半长轴和偏心率的轴对称双组分引力系统的平衡分布。 我们还研究了当其中一个组分主导总能量和角动量的情况，近似地作为热浴，这可能代表周围的天体物理环境，如来自星系的潮汐扰动、大质量扰动体、气体环或附近的恒星系统。 值得注意的是，在次级组分中，超过临界质量的天体会以普遍的方式凝聚成一个盘。 我们确定了过渡平滑和不连续的系统参数。 后一种情况在这些长程相互作用系统中，无论是经典系综还是微正则系综，都表现出有序盘状态与无序近球形分布之间的相变。 显示英文摘要

摘要： Galactic nuclei, the densest stellar environments in the Universe, exhibit a complex geometrical structure. The stars orbiting the central supermassive black hole follow a mass segregated distribution both in the radial distance from the center and in the inclination angle of the orbital planes. The latter distribution may represent the equilibrium state of vector resonant relaxation (VRR). In this paper, we build simple models to understand the equilibrium distribution found previously in numerical simulations. Using the method of maximising the total entropy and the quadrupole mean-field approximation, we determine the equilibrium distribution of axisymmetric two-component gravitating systems with two distinct masses, semimajor axes, and eccentricities. We also examine the limiting case when one of the components dominates over the total energy and angular momentum, approximately acting as a heat bath, which may represent the surrounding astrophysical environment such as the tidal perturbation from the galaxy, a massive perturber, a gas torus, or a nearby stellar system. Remarkably, the bodies above a critical mass in the subdominant component condense into a disk in a ubiquitous way. We identify the system parameters where the transition is smooth and where it is discontinuous. The latter cases exhibit a phase transition between an ordered disk-like state and a disordered nearly spherical distribution both in the canonical and in the microcanonical ensembles for these long-range interacting systems.