弛豫驱动星系核演化的新Fokker-Planck方法
A new Fokker-Planck approach for relaxation-driven evolution of galactic nuclei
摘要：
提出了一种基于一维Fokker-Planck方程的球形各向同性恒星系统碰撞演化的数值模拟方法。一个新颖的方面是，我们使用相体积作为参数的分布函数，而不是传统上使用的能量，这有利于解决方案。公开可用的代码PhaseFlow实现了Fokker-Planck方程的高精度有限元方法，并且可以处理多组分系统，可选地具有中心黑洞并考虑损失锥效应和恒星形成。我们讨论的能量平衡的一般设置，并在应用程序的Bahcall-Wolf尖围绕一个中心黑洞，我们得到一个微扰的解决方案。我们强调，尖点是不是一个稳态结构，而是在振幅的演变，同时保留了约$ρ\propto r^{-7/4}$密度分布。最后，我们将该方法应用于银河系的核星团，并说明了一个可能的演化情景，在该情景中，一个由较轻的主序星和恒星质量黑洞组成的双组分系统在较重的组分中发展出一个Bahcall-Wolf尖点，在较轻的可见组分中发展出一个较弱的$ρ\propto r^{-3/2}$尖点，在几个Gyr的周期内。现今的密度分布与最近发现的中央秒差距内的温和尖点是一致的，并且对初始条件弱敏感。
英文摘要：
We present an approach for simulating the collisional evolution of spherical isotropic stellar systems based on the one-dimensional Fokker-Planck equation. A novel aspect is that we use the phase volume as the argument of the distribution function, instead of the traditionally used energy, which facilitates the solution. The publicly available code, PhaseFlow, implements a high-accuracy finite-element method for the Fokker-Planck equation, and can handle multiple-component systems, optionally with the central black hole and taking into account loss-cone effects and star formation. We discuss the energy balance in the general setting, and in application to the Bahcall-Wolf cusp around a central black hole, for which we derive a perturbative solution. We stress that the cusp is not a steady-state structure, but rather evolves in amplitude while retaining an approximately $ρ\propto r^{-7/4}$ density profile. Finally, we apply the method to the nuclear star cluster of the Milky Way, and illustrate a possible evolutionary scenario in which a two-component system of lighter main-sequence stars and stellar-mass black holes develops a Bahcall-Wolf cusp in the heavier component and a weaker $ρ\propto r^{-3/2}$ cusp in the lighter, visible component, over the period of several Gyr. The present-day density profile is consistent with the recently detected mild cusp inside the central parsec, and is weakly sensitive to initial conditions.
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