被自引力气体盘包围的亚秒差距质量黑洞双星的极限偏心率
Limiting eccentricity of sub-parsec massive black hole binaries surrounded by self-gravitating gas discs
摘要：
利用SPH程序Gadget-2研究了嵌入环双星气体盘中的超大质量黑洞双星的动力学行为。亚秒差距双星（总质量为M，质量比q=1/3）已经挖掘出一个间隙，并将其角动量转移到自引力盘（M_disc=0.2 M）。我们通过模拟一系列只有初始偏心率e_0不同的双星模型来探索双星偏心率e的变化。在初始低偏心双星中，偏心率随时间增加，而在高偏心双星中e下降，表明存在一个极限偏心率e_crit，它落在区间[0.6，0.8]内。我们还提出了一个分析解释这个饱和极限。存在e_crit的一个重要结果是，拟议的引力波探测器LISA可以探测到显著的剩余偏心率e_LISA}。发现在进入LISA频域的瞬间，eLISA ~ 10^{-3}-10 ^{-2}是它与大质量环双星盘早期耦合的信号。我们还观察到大的周期性流入的差距，发生在二进制和光盘动力学的时间尺度，而不是粘性的时间。这些吸积率的周期性变化（振幅高达~ 100%，取决于双星的偏心率）可以被认为是在环双星盘内迁移的偏心亚秒差距双星的指纹。
英文摘要：
We study the dynamics of supermassive black hole binaries embedded in circumbinary gaseous discs, with the SPH code Gadget-2. The sub-parsec binary (of total mass M and mass ratio q=1/3) has excavated a gap and transfers its angular momentum to the self--gravitating disc (M_disc=0.2 M). We explore the changes of the binary eccentricity e, by simulating a sequence of binary models that differ in the initial eccentricity e_0, only. In initially low-eccentric binaries, the eccentricity increases with time, while in high-eccentric binaries e declines, indicating the existence of a limiting eccentricity e_crit that is found to fall in the interval [0.6,0.8]. We also present an analytical interpretation for this saturation limit. An important consequence of the existence of e_crit is the detectability of a significant residual eccentricity e_LISA} by the proposed gravitational wave detector LISA. It is found that at the moment of entering the LISA frequency domain e_LISA ~ 10^{-3}-10^{-2}; a signature of its earlier coupling with the massive circumbinary disc. We also observe large periodic inflows across the gap, occurring on the binary and disc dynamical time scales rather than on the viscous time. These periodic changes in the accretion rate (with amplitudes up to ~100%, depending on the binary eccentricity) can be considered a fingerprint of eccentric sub-parsec binaries migrating inside a circumbinary disc.
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