探测双黑洞质量-红移依赖关系及其对 $H_0$ 的启示：基于 GWTC-5.0
Probing the Mass--Redshift Dependence of Binary Black Holes and its Implications for $H_0$ with GWTC-5.0
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中文总结 AI 辅助
本研究利用 copula 函数分析 GWTC-5.0 中 235 个双黑洞事件，探测主质量与红移的依赖关系，发现仅 180°旋转 Clayton copula 模型显示弱相关，且质量-红移依赖对 H0 推断无显著影响，数据仍支持无红移演化。
中文摘要 AI 辅助
并合双黑洞（BBHs）的质量和红移分布携带着其天体物理形成通道的印记。然而，黑洞质量分布是否随红移演化仍是一个悬而未决的问题。本文采用 copula 函数（一种独立于边缘分布描述变量间依赖关系的函数）来探测 BBH 并合的主质量与红移之间的依赖结构。我们通过将主质量和红移的边缘分布与高斯 copula、Clayton copula 或其三种旋转之一耦合，构建了五个种群模型，并利用 GWTC-5.0 中的 235 个 BBH 事件约束其超参数。作为对比，我们还采用了一个假设主质量与红移独立的基线模型。在基于 copula 的模型中，仅采用 $180^\circ$ 旋转 Clayton copula（该模型将较大主质量优先与高红移耦合）的模型显示出非零相关的证据，其 copula 参数偏离独立极限的显著性超过 $1\sigma$。重要的是，从这些模型推导出的哈勃常数（$H_0$）约束在 $68\\%$ 置信水平内相互一致；基线模型给出 $H_0=74.3^{+13.7}_{-19.6}~\mathrm{km\\ s^{-1}\\ Mpc^{-1}}$，表明在当前数据集下，允许质量-红移依赖不会显著偏置 $H_0$ 推断。贝叶斯模型比较倾向于基线模型而非所有基于 copula 的替代模型，对数贝叶斯因子对应于 Jeffreys 尺度上对后者的弱到中等证据。因此，我们的结果表明，当前 GWTC-5.0 样本在所探测的红移范围内，与主质量分布无红移演化的假设保持一致。
英文摘要
The mass and redshift distributions of merging binary black holes (BBHs) bear imprints of their astrophysical formation channels. Whether the BH mass distribution evolves with redshift, however, remains an open question. In this paper, we employ copula functions, which describe the dependence between variables independently of their marginal distributions, to probe the dependence structure between the primary mass and the redshift of BBH mergers. We construct five population models by coupling the marginal distributions of primary mass and redshift with the Gaussian copula, the Clayton copula, or one of its three rotations, and we constrain their hyperparameters using 235 BBH events from GWTC-5.0. For comparison, we also adopt a baseline model in which the primary mass and redshift are assumed independent. Among the copula-based models, only the model with the $180^\circ$ rotated Clayton copula, which couples higher primary masses preferentially with high redshifts, exhibits evidence for a nonzero correlation, with its copula parameter deviating from the independence limit at more than $1σ$ significance. Importantly, the constraints on the Hubble constant ($H_0$) derived from these models are mutually consistent within the $68\%$ confidence level; the baseline model yields $H_0=74.3^{+13.7}_{-19.6}~\mathrm{km\ s^{-1}\ Mpc^{-1}}$, indicating that allowing for a mass--redshift dependence does not significantly bias the $H_0$ inference with the current dataset. Bayesian model comparison favors the baseline model over all copula-based alternatives, with log-Bayes factors corresponding to weak to moderate evidence against the latter on the Jeffreys scale. Our results thus imply that the current GWTC-5.0 sample remains consistent with no redshift evolution of the primary mass distribution over the redshift range probed.
发表机构
- Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台）
- Hunan Normal University（湖南师范大学）
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