AI 中文总结
本研究针对类太极任务，结合时域模拟与频域似然，建立SGWB的全协方差贝叶斯推断框架，经模拟验证其能准确恢复天体物理背景，且可纳入一阶相变声波谱。
AI 中文摘要
针对类太极任务，我们实现了一种贝叶斯谱推断框架，将第二代时延干涉测量（TDI）的时域（TD）模拟与用于随机引力波背景（SGWB）分析的频域（FD）谱似然相结合。使用Triangle-Simulator生成的X、Y、Z迈克尔逊流被划分为有限段，进行傅里叶变换，并采用依赖于段的复3×3协方差矩阵建模。对于每个段，我们评估依赖于轨道的响应函数和噪声传递函数，使不等臂和随时间演化的效应通过完整的XYZ协方差进入分析。使用Triangle-Simulator进行的受控模拟显示，在保留的频带内（远离TDI零点），计算出的函数以百分之几的水平再现了实现平均谱。随后，我们比较了静态等臂FD、等臂TD和不等臂TD构型的参数估计结果，每种情况下使用与对应探测器构型匹配的完整XYZ协方差似然。在对仪器噪声和有效的银道面双白矮前景进行边缘化后，三者均给出了天体物理背景恢复的一致不确定性趋势和贝叶斯证据诊断。最后，我们加入了来自一阶相变的声波谱。
英文摘要
For Taiji-like missions, we implement a Bayesian spectral inference framework that combines second-generation time-domain (TD) simulations of time-delay interferometry (TDI) with a frequency-domain (FD) spectral likelihood for stochastic gravitational-wave background (SGWB) analyses. The \(X,Y,Z\) Michelson streams generated with \trianglesim{} are divided into finite segments, Fourier transformed, and modeled with a segment-dependent complex \(3\times3\) covariance matrix. For each segment we evaluate the orbit-dependent response functions and noise transfer functions, allowing unequal-arm and time-evolving effects to enter through the full \(XYZ\) covariance. Controlled simulations performed with \trianglesim{} show that the calculated functions reproduce the realization-averaged spectra at the few-percent level over the retained frequency band away from TDI nulls. We then compare parameter-estimation results for static equal-arm FD, equal-arm TD, and unequal-arm TD configurations, using in each case a full \(XYZ\)-covariance likelihood matched to the corresponding detector configuration. All three yield consistent uncertainty trends and Bayesian-evidence diagnostics for astrophysical-background recovery after marginalizing over instrumental noise and an effective Galactic double-white-dwarf foreground. Finally, in a ten-parameter model containing instrumental noise, an effective Galactic double-white-dwarf foreground, a stochastic astrophysical background, and a sound-wave spectrum from a cosmological first-order phase transition, we recover its peak amplitude and frequency and find Bayesian evidence favoring its inclusion in all three matched configurations.
Comments46 pages, 15 figures, 5 tables
