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arXiv 1903.02579astro-ph.HEastro-ph.GA
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Milky Way质量星系中吸入黑洞群引力波的可探测性

Detectability of Gravitational Wave from a population of Inspiralling Black Holes in Milky Way Mass Galaxies

Razieh Emami, Abraham Loeb

摘要:

我们估计了银河系质量星系中心超大质量黑洞周围星团中恒星质量BH种群的内旋速率。我们的方法是基于轨道平均的福克-普朗克方法。其次是一个后处理的方法,它结合了角动量扩散和GW耗散系统的演化的影响。我们分别以$f_c(a)/a$和$e$为分布,选取了10000个具有不同初始半主度和偏心率的黑洞样本。其中,$f_c(a)$是指第c种物质的相空间分布函数。角动量扩散导致上述样品中各系统的偏心率增大,从而增加了螺旋上升的速率。我们用信噪比$\rm{SNR} \geq 8$计算每个系统在LISA频带中花费的时间的分数。每一个系统最终都以一个由团簇扩散速率$μ/ \rm{Gyr}^{-1} \lesssim 1 $给出的补充速率接近损失锥。这个小的速率降低了单个MW质量星系的总内旋速率,估计为$R_{obs} \lesssim 10^{-5} yr^{-1}$。然而,预计$N_{gal} \simeq 10^4$ MW质量星系的集合会导致在LISA波段可观测到GW信号。

英文摘要:

We estimate the rate of inspiral for a population of stellar mass BHs in the star cluster around the super massive black hole at the center of Milky Way mass galaxies. Our approach is based on an orbit averaged Fokker Planck approach. This is then followed by a post-processing approach, which incorporates the impact of the angular momentum diffusion and the GW dissipation in the evolution of system. We make a sample of 10000 BHs with different initial semi-major and eccentricities with the distribution of $f_c(a)/a$ and $e$, respectively. Where $f_c(a)$ refers to the phase-space distribution function for cth species. Angular momentum diffusion leads to an enhancement in the eccentricity of every system in the above sample and so increases the rate of inspiral. We compute the fraction of time that every system spends in the LISA band with the signal to noise ratio $\rm{SNR} \geq 8$. Every system eventually approaches the loss-cone with a replenishment rate given by the diffusion rate of the cluster, $μ/ \rm{Gyr}^{-1} \lesssim 1 $. This small rate reduces the total rate of the inspiral for individual MW mass galaxies with an estimate $R_{obs} \lesssim 10^{-5} yr^{-1}$. It is expected though that a collection of $N_{gal} \simeq 10^4$ MW mass galaxies lead to an observable GW signal in the LISA band.

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