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arXiv 0709.0480astro-ph
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白矮星的轨道圆化和包含中等质量黑洞的星团中引力辐射源的形成

Orbital circularisation of white dwarfs and the formation of gravitational radiation sources in star clusters containing an intermediate mass black hole

P. B. Ivanov, J. C. B. Papaloizou

摘要:

(略)我们考虑如何在球状星团中形成由质量为$M=10^{3}-10^{4}M_{\odot}$的超大质量黑洞和白矮星组成的紧密双星。我们指出,一个主要部分的白矮星潮汐捕获的黑洞可能会被摧毁的潮汐膨胀过程中正在进行的circularisation,并形成紧密的双星被抑制。然而,有些恒星可能会在高速旋转中幸存下来。由潮汐激发的脉动模引起的引力波发射和非线性效应引起的能量耗散可能与动力潮汐引起的脉动能量增加竞争。这些恒星的半长轴可以降低到一个“临界”值以下,动态潮汐是无效的,因为脉动模式保持连续的近心点通道之间的相位相干性。这种循环星的形成率估计假设它们可以模拟为$n=1.5$多面体和潮汐理论的结果,慢转子可以外推到快速转子。我们估计总捕获率为$\sim \dot N\sim 2.5\cdot 10^{-8}M_{4}^{1.3}r_{0.1}^{-2.1}yr^{-1}$,其中$M_{4}=M/10^4M_{\odot}$和$r_{0.1}$是黑洞的影响半径,单位为$0.1pc$。我们发现,紧对的形成率约为总捕获率的10倍。它被用来估计LISA探测到来自这种紧双星的引力波的概率。我们的结论是,LISA可以检测到这样的双星的球状星团的黑洞的质量范围内的分数是相当大的,并在黑洞的影响半径附近的星团恒星的色散速度超过$\sim 20km/s$。

英文摘要:

(abbreviated) We consider how tight binaries consisting of a super-massive black hole of mass $M=10^{3}-10^{4}M_{\odot}$ and a white dwarf can be formed in a globular cluster. We point out that a major fraction of white dwarfs tidally captured by the black hole may be destroyed by tidal inflation during ongoing circularisation, and the formation of tight binaries is inhibited. However, some stars may survive being spun up to high rotation rates. Then the energy loss through gravitational wave emission induced by tidally excited pulsation modes and dissipation through non linear effects may compete with the increase of pulsation energy due to dynamic tides. The semi-major axes of these stars can be decreased below a 'critical' value where dynamic tides are not effective because pulsation modes retain phase coherence between successive pericentre passages. The rate of formation of such circularising stars is estimated assuming that they can be modelled as $n=1.5$ polytropes and that results of the tidal theory for slow rotators can be extrapolated to fast rotators. We estimate the total capture rate as $\sim \dot N\sim 2.5\cdot 10^{-8}M_{4}^{1.3}r_{0.1}^{-2.1}yr^{-1}$, where $M_{4}=M/10^4M_{\odot}$ and $r_{0.1}$ is the radius of influence of the black hole in units $0.1pc$. We find that the formation rate of tight pairs is approximately 10 times smaller than the total capture rate. It is used to estimate the probability of detection of gravitational waves coming from such tight binaries by LISA. We conclude that LISA may detect such binaries provided that the fraction of globular clusters with black holes in the mass range of interest is substantial and that the dispersion velocity of the cluster stars near the radius of influence of the black hole exceeds $\sim 20km/s$.

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