We compute the two-dimensional correlation functions of the binary black hole coalescence detections in LIGO-Virgo’s first and second observation runs. The sky distribution of binary black hole coalescence events is tested for correlations at different angular scales by comparing the observed correlation function to two reference functions that are obtained from mock datasets of localization error regions uniformly distributed in the sky. No excess correlation at any angular scale is found. The power-law slope of the correlation function is estimated to be $\gamma =2.24\pm 0.33$ at the three- $\sigma$ confidence level, a value consistent with the measured distribution of galaxies.

中文翻译：

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二元黑洞合并的二维相关函数

我们在LIGO-Virgo的第一次和第二次观测运行中计算了二进制黑洞合并检测的二维相关函数。通过将观察到的相关函数与从均匀分布在天空中的定位误差区域的模拟数据集获得的两个参考函数进行比较，来测试二进制黑洞合并事件的天空分布在不同角度范围内的相关性。在任何角度范围内都没有发现过多的相关性。相关函数的幂律斜率估计为 $\gamma =2.24\pm 0.33$ 在三个 $\sigma$ 置信水平，该值与测得的星系分布一致。