AI 中文总结
该研究针对天体物理引力波背景搜寻的互相关估计量，分解其分量并计算累积量，发现LIGO O5下估计量呈高斯性，CE下双黑洞产生的估计量非高斯，验证了高斯似然框架并推动更复杂统计方法发展。
AI 中文摘要
利用地面探测器搜寻随机引力波背景（SGWB）高度依赖互相关估计量$\bar C_f$，其统计特性是构建于其上的推断框架的理论基础。过往分析通常假设$\bar C_f$服从高斯分布，但对于致密双星并合产生的天体物理背景，该假设尚未得到系统检验。本研究将$\bar C_f$分解为三个具有物理意义的分量：（1）平均强度、（2）几何散粒噪声、（3）偏振泄漏，并通过传播并合率的不确定性，计算双黑洞、双中子星及中子星-黑洞并合群体的四阶累积量的90%可信区间。研究发现，对于即将到来的LIGO O5灵敏度，$\bar C_f$对所有三个群体均保持有效高斯性，验证了当前的高斯似然框架。然而，对于宇宙探测器（CE），双黑洞产生的$\bar C_f$呈现非高斯性，在最敏感频带的一年观测期内，其偏度为$0.31^{+0.04}_{-0.03}$，超额峰度为$1.3^{+0.4}_{-0.3}$；对于双中子星和中子星-黑洞并合，即使在CE下，$\bar C_f$仍基本保持高斯性。这些结果表明，埃奇沃思展开式可为下一代观测时代预期的非高斯性提供充分的主导阶描述，同时推动更复杂统计方法的发展以实现更精确的处理。
英文摘要
Searches for the stochastic gravitational-wave background (SGWB) using ground-based detectors rely heavily on the cross-correlation estimator $\bar C_f$, whose statistical properties determine the theoretical foundation for inference frameworks built on it. Past analyses usually assume Gaussianity of $\bar C_f$, but this assumption has not been systematically tested for a background of astrophysical origin like the one produced by compact binary coalescences. In this work, we decompose $\bar C_f$ into three physically motivated components: (1) the mean intensity, (2) the geometrical shot noise, and (3) the polarization leakage, and we compute 90\% credible intervals for its cumulants up to fourth order for the binary black hole, binary neutron star, and neutron star-black hole populations by propagating local merger rate uncertainties. We find that for the upcoming LIGO O5 sensitivity, $\bar C_f$ remains effectively Gaussian for all three populations, validating current Gaussian likelihood frameworks. For Cosmic Explorer (CE), however, the $\bar C_f$ produced by binary black holes becomes non-Gaussian, with skewness and excess kurtosis of $0.31^{+0.04}_{-0.03}$ and $1.3^{+0.4}_{-0.3}$, respectively, in the most sensitive band over a one-year observation period. For binary neutron star and neutron star - black hole mergers, $\bar C_f$ remains largely Gaussian even at CE. These results indicate that the Edgeworth expansion provides an adequate leading-order description of the non-Gaussianity expected in the next-generation era, while also motivating the development of more sophisticated statistical methods for a more accurate treatment.
Comments14 pages, 9 figures
