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arXiv 0705.2745astro-ph
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大质量黑洞双星的长期演化。III。碰撞核中的双星演化

Long-Term Evolution of Massive Black Hole Binaries. III. Binary Evolution in Collisional Nuclei

David Merritt, Seppo Mikkola, Andras Szell

摘要:

[摘要]在弛豫时间足够短的星系核中,二元超大质量黑洞可以通过与恒星的持续相互作用而进化到超过其失速半径。我们研究这个“碰撞”的演化制度,使用完全自洽的N体积分和近似的福克-普朗克模型。的N体积分采用粒子数高达0.26 M和直接求和潜在的求解器;密切的相互作用,涉及二进制处理使用一个新的实施的Mikkola-Aarseth链正则化算法。即使在这些大的N值,两体散射发生在足够高的速率在模拟中,他们不能简单地缩放到大N制度的真实星系。Fokker-Planck模型被用来弥补这一差距;它首次包括了双星引起的恒星密度和势能的变化。Fokker-Planck模型精确地再现了N体积分的结果,并将其推广到更大的实际星系N区。解析表达式推导出准确地再现的时间依赖性的二进制半长轴预测的福克-普朗克模型。引力波聚并在速度色散小于80 km/s的原子核中发生在<10 Gyr。核心的形成是由双星的抛射和通过两体散射的耗尽轨道的再补给之间的竞争造成的。在聚并之前产生的质量亏损高达双星质量的约4倍。两个黑洞合并后,在一个弛豫时间内,一个Bahcall-Wolf尖点出现在单个黑洞周围,导致核密度分布由一个扁平的核心和一个内部紧凑的集群组成,类似于在低光度球体中心观察到的情况。

英文摘要:

[Abridged] In galactic nuclei with sufficiently short relaxation times, binary supermassive black holes can evolve beyond their stalling radii via continued interaction with stars. We study this "collisional" evolutionary regime using both fully self-consistent N-body integrations and approximate Fokker-Planck models. The N-body integrations employ particle numbers up to 0.26M and a direct-summation potential solver; close interactions involving the binary are treated using a new implementation of the Mikkola-Aarseth chain regularization algorithm. Even at these large values of N, two-body scattering occurs at high enough rates in the simulations that they can not be simply scaled to the large-N regime of real galaxies. The Fokker-Planck model is used to bridge this gap; it includes, for the first time, binary-induced changes in the stellar density and potential. The Fokker-Planck model is shown to accurately reproduce the results of the N-body integrations, and is then extended to the much larger N regime of real galaxies. Analytic expressions are derived that accurately reproduce the time dependence of the binary semi-major axis as predicted by the Fokker-Planck model. Gravitational wave coalescence is shown to occur in <10 Gyr in nuclei with velocity dispersions below about 80 km/s. Formation of a core results from a competition between ejection of stars by the binary and re-supply of depleted orbits via two-body scattering. Mass deficits as large as ~4 times the binary mass are produced before coalescence. After the two black holes coalesce, a Bahcall-Wolf cusp appears around the single hole in one relaxation time, resulting in a nuclear density profile consisting of a flat core with an inner, compact cluster, similar to what is observed at the centers of low-luminosity spheroids.

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