论文标题
黑孔星团中的订单disorder相变-III。一个单能群
Order-disorder phase transition in black-hole star clusters -- III. A mono-energetic cluster
论文作者
论文摘要
星系中心的超大质黑洞通常被密集的星形簇包围。对于各种簇特性和轨道半径，这些簇中的共振弛豫时间比哈勃时间短得多。由于谐振弛豫可以保守半轴轴，因此这些簇应处于最大渗透状态，与给定的半轴轴分布一致。我们在简化的模型中确定了这些最大透镜平衡，在该模型中，所有恒星都具有相同的半轴轴。我们发现该簇表现出从无序的球形，高温平衡到有序的低温平衡的相变，使恒星轨道具有优先的方向或猿类线。在这里，“温度”是群集的非忽视或自我灌输能量的量度。在球形状态下，温度是恒星RMS偏心率的函数。我们探索了一个简单的黑洞恒星簇的两参数模型 - 两个参数是半轴轴和黑洞质量-----发现簇在半轴轴的范围内易受偏斜的相变的易感，主要是黑洞质量，大多数是黑洞的质量，大多数是$ 10^{7.5^{7.5^{7.5} $ SOLAR MASSES。
Supermassive black holes at the centres of galaxies are often surrounded by dense star clusters. For a wide range of cluster properties and orbital radii the resonant relaxation times in these clusters are much shorter than the Hubble time. Since resonant relaxation conserves semimajor axes, these clusters should be in the maximum-entropy state consistent with the given semimajor axis distribution. We determine these maximum-entropy equilibria in a simplified model in which all of the stars have the same semimajor axes. We find that the cluster exhibits a phase transition from a disordered, spherical, high-temperature equilibrium to an ordered low-temperature equilibrium in which the stellar orbits have a preferred orientation or line of apsides. Here `temperature' is a measure of the non-Keplerian or self-gravitational energy of the cluster; in the spherical state, temperature is a function of the rms eccentricity of the stars. We explore a simple two-parameter model of black-hole star clusters -- the two parameters are semimajor axis and black-hole mass --- and find that clusters are susceptible to the lopsided phase transition over a range of ~100 in semimajor axis, mostly for black-hole masses less than $10^{7.5}$ solar masses.
