AI 中文总结
本研究构建框架利用月球激光测距和双卫星测距构型重建旋近大质量双黑洞的啁啾质量与光度距离，发现单基线存在光度距离简并问题，多基线可破解该问题，为低频引力波探测提供了测距方案的参数重建依据。
AI 中文摘要
对地月和地卫距离的精密追踪为探测来自大质量双黑洞旋近的引力波提供了一条新颖的低频途径，可作为天基干涉仪的补充。本文首次开展了从合成距离观测数据中重建双星参数的研究。实验设置：假设地卫双星做理想的无扰动开普勒运动，我们构建了一套框架，可从啁啾源在测距观测量中引发的扰动里，重建其啁啾质量$\u2728M_c$和光度距离$D_L$，并以月球激光测距（LLR）和双卫星测距构型（GUEST）作为具体研究案例。实验结果：我们发现，对于LLR和GUEST两种构型，啁啾质量的恢复精度均严格遵循信噪比的幂律收敛关系（$σ_{M_c}/M_c ∝ \text{SNR}^α$，$α\thickapprox -1$至$-1.8$）。相比之下，在LLR构型中，光度距离与天球取向角存在严重的、与信噪比无关的简并，无论信号强度如何，其相对偏差和不确定度都在百分之几十到百分之百以上。双卫星GUEST构型打破了这一简并，恢复了$D_L$的收敛性且其恢复精度随信噪比的变化规律与啁啾质量相当。这些结果表明，多基线测距架构对于从基于测距的引力波搜索中提取光度距离信息至关重要，而即便仅使用地月系统这类单测距基线，啁啾质量测量仍可可靠实现。
英文摘要
Precision tracking of Earth--Moon and Earth--satellite ranges offers a novel, low-frequency avenue for detecting gravitational waves from inspiralling massive black hole binaries, complementary to space-based interferometers. In this paper, we propose a first study of the reconstruction of the binary parameters from a synthetic set of range observations. \textit{Set-up}: Assuming an ideal unperturbed Keplerian motion for the earth-satellite binary, we develop a framework for reconstructing the chirp mass $\mathcal M_c$ and luminosity distance $D_L$ of chirping sources from the perturbations they induce on ranging observables, using both Lunar Laser Ranging (LLR) and a two-satellite ranging configuration (GUEST) as concrete case studies. \textit{Result}: We find that chirp-mass recovery tightly converges as a power law in SNR ($σ_{M_c}/M_c \propto \mathrm{SNR}^α$, $α\simeq -1$ to $-1.8$) for both LLR and GUEST. In contrast, the luminosity distance suffers from a severe, SNR-independent degeneracy with the sky-orientation angles in the LLR configuration, yielding fractional biases and uncertainties of tens to over a hundred percent regardless of signal strength. The two-satellite GUEST configuration breaks this degeneracy and restores a convergent, SNR-dependent recovery of $D_L$ comparable in scaling to that of the chirp mass. These results demonstrate that multi-baseline ranging architectures are essential for extracting luminosity-distance information from ranging-based gravitational wave searches, while chirp-mass measurements remain reliably accessible even with a single ranging baseline such as the Earth--Moon system.
Comments20 pages, way too many figures, and appendices
