Understanding the interaction of massive black hole binaries with their gaseous environment is crucial since at sub-parsec scales the binary is too wide for gravitational wave emission to take over and to drive the two black holes to merge. We here investigate the interaction between a massive black hole binary and a self-gravitating circumbinary disc using 3D smoothed particle hydrodynamics simulations. We find that, when the disc self-gravity regulates the angular momentum transport, the binary semi-major axis decreases regardless the choice of disc masses and temperatures, within the range we explored. In particular, we find that the disc initial temperature (hence the disc aspect ratio) has little effect on the evolution of the binary since discs with the same mass self-regulate towards the same temperature. Initially warmer discs cause the binary to shrink on a slightly shorter timescale until the disc has reached the self-regulated equilibrium temperature. More massive discs drive the binary semi-major axis to decrease at a faster pace compared to less massive discs and result in faster binary eccentricity growth even after the initial-condition-dependent transient evolution. Finally we investigate the effect that the initial cavity size has on the binary-disc interaction and we find that, in the self-gravitating regime, an initially smaller cavity leads to a much faster binary shrinking, as expected. Our results are especially important for very massive black hole binaries such as those in the PTA band, for which gas self gravity cannot be neglected.

中文翻译：

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环绕圆盘自引力控制超大质量黑洞双星合并

了解大质量黑洞双星与其气体环境的相互作用至关重要，因为在亚秒差距尺度上，双星太宽以至于引力波发射无法接管并驱动两个黑洞合并。我们在这里使用 3D 平滑粒子流体动力学模拟来研究大质量黑洞双星和自引力环绕双星盘之间的相互作用。我们发现，当圆盘自重力调节角动量传输时，无论圆盘质量和温度的选择如何，在我们探索的范围内，二元半长轴都会减小。特别是，我们发现圆盘初始温度（因此圆盘纵横比）对双星的演化几乎没有影响，因为具有相同质量的圆盘会自我调节到相同的温度。最初较热的圆盘会导致双星在稍短的时间尺度上收缩，直到圆盘达到自我调节的平衡温度。与质量较小的圆盘相比，更大质量的圆盘驱动双星半长轴以更快的速度减少，并导致更快的双星偏心率增长，即使在初始条件相关的瞬态演化之后也是如此。最后，我们研究了初始腔尺寸对二元盘相互作用的影响，我们发现，在自引力状态下，最初较小的腔会导致更快的二元收缩，正如预期的那样。我们的结果对于非常大质量的黑洞双星（例如 PTA 带中的双星）尤其重要，因为它们的气体自重是不可忽视的。