AI 中文总结
该研究利用脉冲星计时阵列通过纳赫兹引力波背景探测超大质量黑洞双星群体物理，构建唯象前向模型，约束三个标准化群体坐标β、有效φ、有效m，量化了脉冲星计时阵列摘要的相对敏感性，且附近群体实现保留大量后验重叠。
AI 中文摘要
脉冲星计时阵列可通过纳赫兹引力波背景探测超大质量黑洞双星的群体物理学。我们构建了一个唯象前向模型，该模型考虑了源丰度、双星停留时间、高质量群体、有限源应变矩和脉冲星计时响应。模拟的可观测量约束了三个标准化的群体坐标：控制停留时间和光谱响应的β；考虑其与β的协方差后描述源归一化的有效φ；主要由高质量截止主导的有效m。在评估集合中，后验均值与模拟值的相关性分别为0.928、0.926和0.884，中心90%的覆盖率分别为0.938±0.015、0.871±0.021和0.898±0.019。频率分辨的可观测量对β最为重要，超出共同过程幂律的应变矩对归一化和高质量坐标具有敏感性；第四应变矩通过罕见的大质量双星识别有效m。这些坐标量化了该群体模型中采用的脉冲星计时阵列摘要的相对敏感性，附近的群体实现保留了大量的后验重叠。
英文摘要
Pulsar timing arrays can probe the population physics of supermassive black-hole binaries through the nanohertz gravitational-wave background. We construct a phenomenological forward model that follows source abundance, binary residence time, the high-mass population, finite-source strain moments, and the pulsar timing response. The simulated observables constrain three standardized population coordinates: $β$, which controls the residence-time and spectral response; $ϕ_{eff}$, which describes source normalization after accounting for its covariance with $β$; and $m_{eff}$, which is dominated by the high-mass cutoff. In the evaluation ensemble, the posterior-mean correlations with the simulated values are $0.928$, $0.926$, and $0.884$, with central 90 per cent coverages of $0.938\pm0.015$, $0.871\pm0.021$, and $0.898\pm0.019$, respectively. Frequency-resolved observables are most important for $β$, and strain moments beyond a common-process power law provide sensitivity to the normalization and high-mass coordinates; the fourth strain moment identifies $m_{eff}$ with rare, massive binaries. These coordinates quantify the relative sensitivity of the adopted PTA summaries within this population model, for which nearby population realizations retain substantial posterior overlap.
