发表机构
Università degli Studi di Milano-Bicocca; INFN, Sezione di Milano-Bicocca; INAF – Osservatorio Astronomico di Cagliari; INAF – Osservatorio Astronomico di Brera; Vanderbilt University（米兰比可卡大学; 意大利国家核物理研究所米兰比可卡分部; 意大利国家天体物理研究所卡利亚里天文台; 意大利国家天体物理研究所布雷拉天文台; 范德堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出用t过程模型描述纳赫兹引力波背景的功率谱密度，在模拟数据上比较其与幂律和自由谱模型的性能，发现t过程能提供更精确的PSD估计和更高的信噪比，并改进双星定位能力。
AI 中文摘要
脉冲星计时阵列（PTA）合作组织近期报告了在纳赫兹频段存在引力波背景（GWB）信号的证据，该信号最可能源于超大质量黑洞双星（SMBHBs）群体所发射引力波的非相干叠加。由于每个频率仓内发射引力波的双星数量有限，且单个强源可能主导GWB，因此背景的功率谱密度（PSD）预期会显著偏离描述理想化群体的平滑幂律。PTA搜索通常用幂律或自由谱模型描述PSD，后者将每个频率仓的PSD作为自由参数进行拟合。在本文中，我们探索t过程作为第三种模型；它假设底层谱为幂律，但允许每个频率仓自由偏离该幂律。我们在模拟数据集上比较这三种模型的性能，注入100个真实SMBHB群体的实现，以评估每个模型恢复复杂PSD的效果。使用贝叶斯和频率论工具，我们发现t过程模型给出最精确的PSD结果，其不确定性分别比幂律和自由谱模型窄43%和26%，而准确度的提升较小。此外，使用t过程模型，我们计算了各向同性和各向异性的信噪比，在前九个频率仓中，相对于幂律和自由谱，中值增益分别约为46%和65%。t过程还返回较低的各向异性p值，在p<0.01的频率仓中，它能在14.3%的情况下将最响亮的双星定位在天图的角度分辨率内，而幂律和自由谱分别为10%和6.2%。
英文摘要
Pulsar timing array (PTA) collaborations have recently reported evidence for a gravitational wave background (GWB) signal in the nanohertz band, which most likely originates from the incoherent superposition of GWs emitted by a population of supermassive black hole binaries (SMBHBs). Since the number of binaries emitting in each frequency bin is finite, and since individual loud sources can dominate the GWB, the power spectral density (PSD) of the background is expected to deviate significantly from the smooth power law that describes an idealized population. PTA searches usually describe the PSD either with a power law or with a free spectrum model, which fits the PSD in each frequency bin as a free parameter. In this paper, we explore the t-process as a third model; it assumes a power law as the underlying spectrum but leaves each frequency bin free to deviate from it. We compare the performance of these three models on simulated datasets, injecting $100$ realizations of a realistic SMBHB population, to evaluate how well each model recovers a complex PSD. Using Bayesian and frequentist tools, we find that the t-process model gives the most precise PSD results, with uncertainties $43\%$ and $26\%$ narrower than those obtained with the power law and the free spectrum, respectively, while the improvement in accuracy is smaller. Moreover, using the t-process model, we compute isotropic and anisotropic signal-to-noise ratios with median gains of about $46\%$ over the power law and $65\%$ over the free spectrum in the first nine frequency bins. The t-process also returns lower anisotropy p-values and among the frequency bins with $p<0.01$, it allows to localize the loudest binary within the angular resolution of the sky maps in $14.3\%$ of the cases, compared to the $10\%$ for the power law and the $6.2\%$ for the free spectrum.
