跨波段（X射线×光学）超大质量黑洞双星的周期性搜索：零结果及首个完整性校正约束
A Cross-Band (X-ray $\times$ Optical) Periodicity Search for Supermassive Black Hole Binaries: A Null Result and the First Completeness-Corrected Constraint
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中文总结 AI 辅助
该研究对1194个Swift-BAT和175个4XMM-DR14活动星系核开展跨波段周期性搜索，未发现共周期超大质量黑洞双星，给出首个完整性校正的共周期分数约束，为后续X射线监测做准备。
中文摘要 AI 辅助
我们针对超大质量黑洞双星（SMBHBs）开展了首个样本级搜索，要求其在X射线和光学波段具有共同周期的相干准周期性，研究对象包含1194个Swift-BAT硬X射线活动星系核（第1阶段）和175个4XMM-DR14活动星系核（第2阶段）。未发现任何源为共周期候选体。我们将每个光变曲线建模为阻尼随机游走（DRW），采用Lomb-Scargle周期图并结合经“别处查找”校正的蒙特卡洛显著性进行搜索。由于冕和吸积盘的DRW红噪声在很大程度上相互独立，我们要求两个波段各自具有显著性且周期重合度在5%以内，并用Robnik等人（2024）提出的与模型无关的零信号模板测试对候选体进行筛选。在周期P=100-900天范围内，经完整性校正的共周期分数95%上限与振幅相关：当硬X射线分数调制量≥0.3时，上限≤3%；在0.2时，上限约为15%（受精度限制）；在~0.15以下则无有效约束（ε=1时的下限为0.25%）。灵敏度由硬X射线监测而非光学测光或统计决定，这与通常的假设相反。对最亮活动星系核的每日MAXI和RXTE/ASM监测使X射线完整性提高了5-8倍，搜索仍为零结果。结合BAT黑洞质量函数积分后，全振幅共周期分数的预期值约为3×10⁻² f_bin δ_mod（其中f_bin为亚秒差距双星占比，δ_mod为调制占空比，g为达到可恢复硬X射线振幅的比例，g<1），因此零结果符合预期。我们提供了经验证的跨波段框架及首个共周期分数的完整性校正约束，该框架已为爱因斯坦探针（Einstein Probe）和eROSITA更密集的X射线监测做好准备。
英文摘要
We present the first sample-level search for supermassive black hole binaries (SMBHBs) requiring coherent quasi-periodicity at a common period in the X-ray and optical bands, over 1194 Swift-BAT hard X-ray AGN (Stage 1) and 175 4XMM-DR14 AGN (Stage 2). No source is a co-periodic candidate. Each light curve is modelled as a damped random walk (DRW) and searched with a Lomb-Scargle periodogram and a look-elsewhere-corrected Monte-Carlo significance. Because DRW red noise is largely independent between corona and disc, we require both bands individually significant with periods coincident within 5%, and gate the survivors with the model-independent null-signal-template test of Robnik et al. (2024). Over $P=100$-$900$ d the completeness-corrected 95% upper limit on the co-periodic fraction is amplitude-dependent: $\lesssim 3\%$ for hard-X-ray fractional modulation $\gtrsim 0.3$, $\approx 15\%$ (precision-limited) at 0.2, and uninformative below $\sim 0.15$ (the $ε=1$ floor is 0.25%). The sensitivity is set by the hard X-ray monitoring, not the optical photometry or the statistics, the opposite of the usual assumption. Daily MAXI and RXTE/ASM monitoring of the brightest AGN raises the X-ray completeness 5-8-fold, and the search remains null. Integrated over the BAT black-hole mass function, the expected all-amplitude co-periodic fraction is $\sim 3\times10^{-2}\, f_{\rm bin}\, δ_{\rm mod}$ (modulo a factor $g<1$), with $f_{\rm bin}$ the sub-pc binary fraction, $δ_{\rm mod}$ the modulating duty cycle, and $g$ the fraction reaching recoverable hard-X-ray amplitude, so a null is expected. We deliver a validated cross-band framework and the first completeness-corrected constraint on the co-periodic fraction, ready for the denser X-ray monitoring of Einstein Probe and eROSITA.
