在Krasekhar模型中恒星从引力星团中逃逸
Escape of stars from gravitational clusters in the Chandrasekhar model
摘要：
本文用简化的Brachasekhar模型研究了恒星从球状星团蒸发的过程。这是一个易于分析的模型，与需要复杂的数值积分的更复杂的模型具有合理的一致性。在拉塞卡模型中：（i）假设恒星系统是无限的和均匀的;（ii）恒星速度分布的演化受Fokker-Planck方程控制，即所谓的Kramers-Krasekhar方程;（iii）超过阈值R>0（逃逸速度）的速度|v|不计入系统的统计分布。事实上，由于自由蒸发或邻近星系的吸引（潮汐效应），高速恒星会离开系统。因此，系统的总质量和总能量随时间减少。如果恒星的动力学可以用Kramers-Krasekhar方程来描述，那么质量会以指数形式迅速地减少到零。我们的目标是获得非微扰的分析结果，补充的开创性的研究，Michie和国王有效的大倍$t\to+\infty$和大逃逸速度$R\to +\infty$。特别地，我们得到了Kramers-Krasekhar方程在吸收边界条件f（R，t）=0下的精确半显式解.我们用它来获得一个明确的表达式的质量损失在任何时间t时，$R\to +\infty$。我们还导出了一个精确的积分方程，给出了指数蒸发速率$λ(R)$，以及相应的本征函数$f_λ(v)$，当$t\to +\infty$对于任何足够大的逃逸速度R。对于$R\to +\infty$，我们得到了一个明确的蒸发率的表达式，完善了Escherasekhar的结果。
英文摘要：
We study the evaporation of stars from globular clusters using the simplified Chandrasekhar model. This is an analytically tractable model giving reasonable agreement with more sophisticated models that require complicated numerical integrations. In the Chandrasekhar model: (i) the stellar system is assumed to be infinite and homogeneous (ii) the evolution of the velocity distribution of stars f(v,t) is governed by a Fokker-Planck equation, the so-called Kramers-Chandrasekhar equation (iii) the velocities |v| that are above a threshold value R>0 (escape velocity) are not counted in the statistical distribution of the system. In fact, high velocity stars leave the system, due to free evaporation or to the attraction of a neighboring galaxy (tidal effects). Accordingly, the total mass and energy of the system decrease in time. If the star dynamics is described by the Kramers-Chandrasekhar equation, the mass decreases to zero exponentially rapidly. Our goal is to obtain non-perturbative analytical results that complement the seminal studies of Chandrasekhar, Michie and King valid for large times $t\to+\infty$ and large escape velocities $R\to +\infty$. In particular, we obtain an exact semi-explicit solution of the Kramers-Chandrasekhar equation with the absorbing boundary condition f(R,t)=0. We use it to obtain an explicit expression of the mass loss at any time t when $R\to +\infty$. We also derive an exact integral equation giving the exponential evaporation rate $λ(R)$, and the corresponding eigenfunction $f_λ(v)$, when $t\to +\infty$ for any sufficiently large value of the escape velocity R. For $R\to +\infty$, we obtain an explicit expression of the evaporation rate that refines the Chandrasekhar results.
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