发表机构
INAF – Osservatorio Astrofisico di Torino; University of Torino, Department of Physics; Main Astronomical Observatory of the NAS of Ukraine; Institute of Astronomy of V.N.Karazin Kharkiv National University（意大利国家天体物理研究所都灵天文台; 都灵大学物理系; 乌克兰科学院主天文台; 瓦西里·卡拉津哈尔科夫国立大学天体物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究首次联合分析Gaia类星体自行与脉冲星计时，搜索超低频连续引力波，未发现信号但给出pHz频段最严格上限，并预测未来可突破$h_0<10^{-11}$。
AI 中文摘要
pHz至亚nHz频段的引力波（GW）在很大程度上尚未被探索，但对于描绘超大质量双黑洞（SMBHBs）的早期旋进阶段以及探测早期宇宙物理至关重要。天体测量和脉冲星计时提供了正交且深度互补的长期可观测量，用于研究这一频段。我们旨在展示首次将真实天体测量自行与双星脉冲星计时相结合的联合数据分析，以搜索并约束由SMBHBs在超低频段（$10^{-12} \le f_{GW} \le 10^{-9}$ Hz）产生的连续引力波（CWs）。我们采用贝叶斯模型选择和上限估计框架，将来自Gaia CRF3星表的约$1.5 \times 10^6$颗类星体的视自行位移与11颗高精度双星脉冲星的视线方向轨道周期导数（$\dot{P}_b$）相结合。为防止虚假探测，我们对仪器和天体物理系统效应进行了大量建模：通过蒙特卡洛模拟传播脉冲星的银河势不确定性，并对类星体进行直至八极阶（l=3）的矢量球谐函数（VSH）分解。在联合分析中，我们未发现CWs信号的统计显著证据（$\ln B_{joint} = -0.42 \pm 0.03$）。在无探测的情况下，我们设定了迄今为止对pHz频段CW应变更严格的约束，在参考频率$f_{ref} = 4 \times 10^{-10}$ Hz处给出95%上限$h_0 \le 6.4 \times 10^{-11}$。合并数据集实现了全天覆盖，并将单一数据集的上限改善了20%-30%。结合正交可观测量成功打破了孤立搜索固有的空间简并性。此外，注入-恢复（inj.-rec.）预测表明，随着即将到来的Gaia DR4延长的时间基线和减小的不确定性，这一联合框架有望突破亚nHz CW的$h_0 < 10^{-11}$上限壁垒。
英文摘要
The pHz to sub-nHz GW regime remains largely unexplored but is crucial for mapping the early inspiral stage of SMBHBs and probing early-Universe physics. Astrometry and pulsar timing offer orthogonal and deeply complementary secular observables to investigate this frequency band. We aim to present the first joint data analysis combining real astrometric proper motions with binary pulsar timing, to search for and constrain continuous gravitational waves (CWs) sourced by SMBHBs in the ultra-low-frequency regime ($10^{-12} \le f_{GW} \le10^{-9} Hz$). We employ a Bayesian model selection and upper limit estimation framework to combine apparent proper motion displacements of $\sim 1.5 \times 10^6$ quasars from the Gaia CRF3 catalog with the line-of-sight orbital period derivatives ($\dot{P}_b$) of 11 high-precision binary pulsars. To prevent spurious detections, we heavily model instrumental and astrophysical systematics: we propagate the Galactic potential uncertainty for pulsars via Monte Carlo simulations and perform a Vector Spherical Harmonics (VSH) decomposition up to the octupole order (l=3) for quasars. We find no statistically significant evidence for a CWs signal in the joint analysis ($\ln B_{joint} = -0.42 \pm 0.03$). In the absence of detection, we set the tightest constraints to date on CW strain in the pHz band, yielding a 95% upper limit of $h_0\le6.4x10^{-11}$ at a reference frequency of $f_{ref} = 4 \times 10^{-10}$ Hz. The combined dataset achieves full sky coverage and improves single-dataset upper limits by 20%-30%. Combining orthogonal observables successfully breaks spatial degeneracies intrinsic to isolated searches. Furthermore, forecasts from inj.-rec. indicate that with the extended temporal baseline and reduced uncertainties of the upcoming Gaia DR4, this joint framework is poised to break the $h_0 < 10^{-11}$ upper limit barrier for sub-nHz CWs.
