发表机构
Max Planck Institute for Gravitational Physics (Albert Einstein Institute); Leibniz Universität Hannover（马克斯·普朗克引力物理研究所（爱因斯坦研究所）; 汉诺威莱布尼茨大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出分层贝叶斯框架，将SMBHB并合率密度模型直接嵌入PTA似然，通过泊松点过程推断并合信号，模拟显示可补充SGWB信息并收紧约束。
AI 中文摘要
引力波搜索不仅仅识别单个源——它们还提供了一种推断产生这些源的潜在天体物理种群的方法。目前，脉冲星计时阵列（PTAs）通过随机引力波背景（SGWB）和对单个超大质量黑洞双星（SMBHB）信号的搜索来约束SMBHB并合率密度。后者意味着使用经验估计的探测效率将源上限转换为率上限。我们转而开发了一个分层贝叶斯框架，将SMBHB并合率密度模型直接置于PTA似然中。未知的单个SMBHB并合信号目录被建模为源参数空间上的泊松点过程，因此并合信号的数量是从数据中推断出来的，而不是由探测阈值强加的。我们描述了两种计算途径：一种基于固定数量候选源分析的目录边缘似然，以及一种显式的跨维度采样方法，该方法联合采样种群超参数、潜在并合信号和噪声。我们用一个玩具并合-only种群模型验证了该方法，然后将其应用于一个天体物理SMBHB并合率密度模型，该模型联合预测了SGWB振幅和预期的并合目录大小。在模拟中，单个并合信号为SGWB补充了信息，并可以收紧对并合率种群的约束。
英文摘要
Gravitational-wave searches do more than identify individual sources - they provide a way to infer the underlying astrophysical populations that produce them. Currently, Pulsar Timing Arrays (PTAs) constrain the supermassive black-hole binary (SMBHB) merger-rate density through both the stochastic gravitational-wave background (SGWB) and searches for individual SMBHB signals. The latter implies converting source upper limits into rate upper limits using detection efficiencies estimated empirically. We instead develop a hierarchical Bayesian framework that places the SMBHB merger-rate density model directly inside the PTA likelihood. The unknown catalog of individual SMBHB merger signals is modeled as a Poisson point process on source-parameter space, so that the number of merger signals is inferred from the data rather than imposed by a detection threshold. We describe two computational routes: a catalog-marginal likelihood based on analyses with fixed numbers of candidate sources, and an explicit transdimensional sampling approach that jointly samples population hyperparameters, latent merger signals, and noise. We validate the method with a toy merger-only population model and then apply it to an astrophysical SMBHB merger-rate density model that jointly predicts the SGWB amplitude and the expected merger-catalog size. In simulations, an individual merger signal adds complementary information to the SGWB and can tighten constraints on the merger-rate population.
Comments20 pages, 9 figures
