基于空间引力波探测中时延干涉测量通道的线性重组的定向响应优化
Directional Response Optimization through Linear Recombination of Time-Delay Interferometry Channels in Space-based Gravitational Wave Detection
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- National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）
- School of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）
- The International Center for Theoretical Physics Asia-Pacific (ICTP-AP), University of Chinese Academy of Sciences（中国科学院大学亚太理论物理中心）
- School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院基础科学与数学学院）
- Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
- Taiji Laboratory for Gravitational Wave Universe (Beijing/Hangzhou), University of Chinese Academy of Sciences（中国科学院大学太极引力波宇宙实验室（北京/杭州））
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中文总结 AI 辅助
该研究针对空间引力波探测的TDI通道，通过线性重组构建频域响应矩阵，利用广义特征值问题优化权重以定向增强目标区域响应、抑制其他区域，适用于毫赫兹频段的近单色引力波源搜索。
中文摘要 AI 辅助
空间引力波探测器如LISA、太极（Taiji）、天琴（TianQin）采用时延干涉测量（TDI）来抵消不等臂星座的激光频率噪声。由于不同TDI可观测量呈现出不同的天空响应，候选通道的线性组合可增强某一天空区域的平均响应，同时抑制另一区域的响应。我们为TDI组合构建了频域响应矩阵，对目标和抑制天空区域的响应矩阵取平均，并通过广义特征值问题推导最优权重，该权重可最大化这两个区域响应的比值。在毫赫兹频段，以A、E、T通道，Sagnac组合α、β、γ以及16链路TDI为例，结果表明在选定频率附近可实现天空区域的零点和大的区域对比度，特征值ρ的范围为：小型基组对应O(10)，大型基组对应O(10²)。因此，该方法有望很好地适用于近单色源，如毫赫兹频段中已分辨的银河系双白矮星双星。目标-抑制比（TSR）在设计频率附近达到峰值，远离该频率时迅速下降，故优化后的权重向量本质上是窄带的，适合在选定频率和天空方向附近进行针对性搜索。
英文摘要
Space-based gravitational-wave detectors such as LISA, Taiji, and TianQin employ time-delay interferometry (TDI) to cancel laser-frequency noise for unequal-arm constellations. Since different TDI observables exhibit distinct sky responses, a linear combination of candidate channels can enhance the average response over one sky region while suppressing that of another. We construct a frequency-domain response matrix for TDI combinations, average it across target and suppressed sky regions, and derive the optimal weights via a generalized eigenvalue problem that maximizes the ratio between these two regional responses. At millihertz frequencies, examples with the $A$, $E$, and $T$ channels, the Sagnac combinations $α$, $β$, and $γ$, and 16-links TDI show that a sky-region null and a large regional contrast are possible near the chosen frequency, with eigenvalues $ρ$ ranging from $\mathcal{O}(10)$ for small bases to $\mathcal{O}(10^2)$ for the larger set. The method is therefore expected to be well suited to nearly monochromatic sources such as the resolved Galactic double white dwarf binaries in the millihertz band. The Target-to-Suppression Ratio (TSR) peaks near the design frequency and falls quickly away from it, so the optimized weight vector is inherently narrowband and suited to targeted searches around a chosen frequency and sky direction.
