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arXiv 1209.4594astro-ph.GA
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大质量黑洞周围的恒星能量弛豫

Stellar Energy Relaxation around A Massive Black Hole

Ben Bar-Or, Gábor Kupi, Tal Alexander

摘要:

大质量黑洞(MBH)周围的能量弛豫是建立星系核动力学状态的关键,也是恒星与MBH密切相互作用的本质。作为扩散的弛豫的标准描述在弱两体相互作用极限下提供了微扰的二阶解。我们运行N体模拟,发现这种解决方案未能描述短时间尺度上的非高斯弛豫,这是强烈的极端事件的影响,即使在弱极限,因此难以表征和测量。我们推导出一个非微扰解松弛作为一个异常扩散过程,并开发了一个强大的估计技术来衡量它在模拟。这些使我们能够分析和模拟我们的数值结果,并详细验证,第一次,这个模型的能量弛豫周围的MBH在所有的时间尺度。本文导出了在MBH周围的松弛单质量尖点中,能量扩散时间t_E与小扰动回到稳态的时间t_r之间的关系。我们限制强遭遇的贡献,测量最弱的遭遇,确定库仑对数的值,并提供了一个强大的分析估计t_E在一个有限的核恒星尖。我们发现t_r ~ 10t_E ~(5/32)Q^2P_h/N_h log Q,其中Q=M_bh/M_* 是MBH与恒星的质量比,轨道周期P_h和恒星数N_h是在对应于MBH影响球的能量标度E_h= sigma_inf ^2下计算的,其中sigma_inf是远离MBH的速度色散。利用观测到的宇宙M_bh/sigma相关性,我们得出结论,低质量MBH(M_bh<10^7 Mo)周围的尖点应该是弛豫的,它们在哈勃时间内被动地演化。我们考虑异常能量扩散对银河系MBH附近观测到的恒星轨道摄动的影响。

英文摘要:

[abridged] Energy relaxation around a massive black hole (MBH) is key to establishing the dynamical state of galactic nuclei, and the nature of close stellar interactions with the MBH. The standard description of relaxation as diffusion provides a perturbative 2nd-order solution in the weak two-body interaction limit. We run N-body simulations and find that this solution fails to describe the non-Gaussian relaxation on short timescale, which is strongly influenced by extreme events even in the weak limit, and is thus difficult to characterize and measure. We derive a non-perturbative solution for relaxation as an anomalous diffusion process, and develop a robust estimation technique to measure it in simulations. These enable us to analyze and model our numerical results, and validate in detail, for the first time, this model of energy relaxation around an MBH on all timescales. We derive the relation between the energy diffusion time, t_E, and the time for a small perturbation to return to steady state, t_r, in a relaxed, single mass cusp around a MBH. We constrain the contribution of strong encounters, measure that of the weakest encounters, determine the value of the Coulomb logarithm, and provide a robust analytical estimate for t_E in a finite nuclear stellar cusp. We find that t_r ~ 10t_E ~(5/32)Q^2P_h/N_h log Q, where Q=M_bh/M_* is the MBH to star mass ratio, the orbital period P_h and number of stars N_h are evaluated at the energy scale corresponding to the MBH's sphere of influence, E_h=sigma_inf^2, where sigma_inf is the velocity dispersion far from the MBH. We conclude, using the observed cosmic M_bh/sigma correlation, that cusps around lower-mass MBHs (M_bh<10^7 Mo), which evolved passively over a Hubble time, should be relaxed. We consider the effects of anomalous energy diffusion on orbital perturbations of stars observed near the Galactic MBH.

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