近似引力波背景的统计特性
Approximating the statistics of a gravitational wave background
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中文总结 AI 辅助
本文提出基于鞍点近似的工具，用于估计引力波背景的特征应变分布，并证明正确建模高阶矩对推断天体物理模型参数至关重要。
中文摘要 AI 辅助
脉冲星计时阵列（PTA）合作组织报告的引力波背景（GWB）的天体物理起源尚未得到确认。由超大质量黑洞双星（SMBHB）群体产生的单个引力波（GW）之和构成的GWB信号，其频谱特性会显示出离散泊松统计的印记。在本工作中，我们提出了一种基于鞍点近似方法的工具，用于估计任意给定群体模型的特征应变分布。该工具可用于贝叶斯推断，或用于从更真实的半解析模型输出中快速可视化GWB的统计特性。我们引入了方差混合高斯分布的一般族，该分布可模拟非高斯GWB信号所预期的重尾行为分布。我们表明，为高斯自由谱PTA似然设置正确的分层先验，实际上等效于非高斯似然。利用理想模拟，我们比较了鞍点近似与对数正态分布在从GWB统计中推断天体物理模型参数方面的性能，并表明正确建模高阶矩至关重要。未来的PTA分析应在其流程中纳入GWB的统计特性。
英文摘要
The astrophysical origin of the gravitational wave background (GWB) reported by pulsar timing array (PTA) collaborations has yet to be confirmed. A GWB signal made of the sum of individual gravitational wave (GW) from the population of supermassive black hole binaries (SMBHB) would show the imprint of a discrete Poissonian statistics in its spectral properties. In this work, we propose a tool based on the saddlepoint approximation method to estimate the distribution of characteristic strain for any given population model. This tool can be used for Bayesian inference or for a quick visualization of the statistics of the GWB from the output of more realistic semi-analytical models. We introduce the general family of variance mixture Gaussian distributions that models heavy-tailed behavior distributions that is expected for a non-Gaussian GWB signal. We show that setting the correct hierarchical priors to a Gaussian free spectrum PTA likelihood is effectively equivalent to a non-Gaussian likelihood. Using ideal simulations, we compare the performance of the saddlepoint approximation with a log-Normal distribution to infer the parameters of the astrophysical model from the statistics of the GWB and show that correctly modeling higher order moments is essential. Future PTA analyses should include the statistics of the GWB in their pipelines.
发表机构
- Donostia International Physics Center (DIPC)（多诺西亚国际物理中心）
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