AI 中文总结
利用丽莎引力波研究附近双白矮星方向分布，通过考虑偏振角简并和银道面分布重铸低多极提取为傅里叶分析，对约500个双星样本，该方法对l≤3偶系数不确定性约0.02，可用于丽莎目录。
AI 中文摘要
我们提出了一个利用丽莎研究附近双白矮星双星方向分布的框架，明确考虑了偏振角的四重简并。利用附近样本沿银道面的带状天空分布，我们表明，在基于维格纳-D形式的球谐展开中，低多极提取可以重铸为沿银经的有效一维傅里叶分析。银道面的对称性决定了灵敏度：即使在银道面反射下的模式仍然可以探测到，而奇模式则受到强烈抑制。对于距离小于4千秒差距内约5%的银河系分辨样本中约500个双星的基准样本，该方法对l≤3的偶系数产生约0.02的不确定性，并且很容易应用于即将推出的丽莎目录。
英文摘要
We present a framework to study the orientation distribution of nearby double white dwarf binaries with LISA, explicitly accounting for the fourfold degeneracy in the polarization angle. Exploiting the belt-like sky distribution of the nearby sample along the Galactic plane, we show that the low-multipole extraction can be recast as an effectively one-dimensional Fourier analysis along Galactic longitude, within a spherical-harmonic expansion based on the Wigner-\(D\) formalism. The symmetry with respect to the Galactic plane governs the sensitivity: modes even under reflection across the plane remain accessible, while odd modes are strongly suppressed. For a fiducial sample of about 500 binaries within \(\lesssim 4\) kpc, corresponding to roughly 5\% of the resolved Galactic population, the method yields an uncertainty of order 0.02 for the even coefficients with \(\ell \leq 3\), and is readily applicable to the forthcoming LISA catalog.
Comments9 pages, 2 figures
