透过人马座A$^*$的视角：识别并分辨爱因斯坦半径之外的强引力透镜连续引力波
Through the lens of Sgr A$^*$: identifying and resolving strongly lensed Continuous Gravitational Waves beyond the Einstein radius
AI总结：
本文研究经银河系中心Sgr A*引力透镜作用的孤立中子星连续引力波，分析其信号特征与参数估计方法，发现下一代探测器可高精度探测此类系统，提升观测概率，相关方法可推广至更多透镜与源，为天体物理和基础物理研究提供新工具。
摘要：
引力透镜化的引力波将为探测宇宙中的物质分布提供新手段，与电磁信号形成互补。与暂现的致密双星并合引力波相比，引力透镜化的连续引力波带来了新的挑战与机遇。本文研究了孤立中子星发出、经银河系中心超大质量黑洞Sgr A$^*$（人马座A$^*$）引力透镜作用的连续引力波，该系统可被下一代引力波探测器观测到。我们详细分析了该系统的信号特征，开展了参数估计与模型选择研究。得益于观测者-透镜-源系统的相对运动，未来的探测器能够分辨引力透镜化的连续波，对于距离Sgr A$^*$ 2-4个爱因斯坦半径范围内的源，可根据源的距离不同，以约1%-10%的精度测量其参数。由于能够探测到位于数个爱因斯坦半径处的透镜系统，观测到强引力透镜中子星的概率比此前的估计高出一个数量级。多幅像可通过约10毫角秒的角分辨率被分辨，这一精度可与最顶尖的光学望远镜相媲美。通过像的定位，可以探测Sgr A$^*$的轴对称性偏差，以及其在恒星轨道与黑洞成像覆盖范围之外区域的伴天体存在性。我们的方法以及诸多结论可推广至其他透镜（如星系子结构）和源（如长寿命并合双星），使引力透镜化的连续引力波成为天体物理与基础物理领域的多功能探测工具。
英文摘要：
Lensed gravitational waves will offer new means to probe the distribution of matter in the universe, complementary to electromagnetic signals. Lensed continuous gravitational waves provide new challenges and opportunities beyond those of transient compact binary coalescence. Here we consider continuous gravitational waves emitted by isolated neutron stars and lensed by Sgr A$^*$, the supermassive black hole at the center of our galaxy, a system observable by the next generation of gravitational wave detectors. We analyze the signatures of this system in detail, addressing parameter estimation and model selection. Future detectors can distinguish lensed continuous waves and measure their parameters with precision $\sim 1 - 10\%$ for sources within $2-4$ Einstein radii of Sgr A$^*$, depending on the source distance, thanks to the relative motion of the observer-lens-source system. The chances of observing strongly-lensed neutron stars increase by one order of magnitude relative to previous estimates, thanks to the possibility of detecting lensed systems at several Einstein radii. Multiple images can be resolved with an angular accuracy $\sim 10$mas, comparable to the best optical telescopes. Image localization probes deviations from axial symmetry and the existence of companions to Sgr A$^*$ in regions complementary to stellar orbits and black hole imaging. Our methods and many of our results extend to other lenses (e.g. galactic substructure) and sources (e.g. long-lived inspiralling binaries), rendering lensed continuous gravitational waves into versatile probes of astrophysics and fundamental physics.
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