发表机构
Institute of Science Tokyo（东京科学大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究引力透镜放大因子的低频行为，推导玻恩近似下的系统展开，揭示密度轮廓矩与频率依赖的普适联系，并给出玻恩近似有效性的判据。
AI 中文摘要
我们研究了引力透镜中放大因子的低频行为，并探讨了它如何编码透镜天体的密度轮廓信息。在玻恩近似下，我们推导了一类广泛的投影密度轮廓的放大因子低频展开式。对于在大距离处比任何幂律衰减更快的球对称轮廓，我们推导了放大因子按频率幂次的系统展开，其中对数依赖仅出现在首项中，并表明每个展开系数由密度轮廓的有限阶矩确定。然后，我们将分析扩展到具有幂律尾部的轮廓，并证明此类轮廓会引入额外的非解析频率依赖，包括分数幂和对数项，这些直接反映了密度分布的渐近行为。此外，我们研究了非球对称性的影响，并表明在低频区域，四极矩的贡献仅作为相对于球对称分量的高阶修正出现。最后，我们研究了低频展开中玻恩近似的有效性。我们推导了一个判据，用于确定在玻恩近似相对于后玻恩修正保持主导的情况下，低频展开的最大阶数。
英文摘要
We investigate the low-frequency behavior of the amplification factor in gravitational lensing and explore how it encodes information about the density profile of the lensing object. We derive the low-frequency expansion of the amplification factor under the Born approximation for a broad class of projected density profiles. For spherically symmetric profiles that decay faster than any power law at large distances, we derive a systematic expansion of the amplification factor in powers of frequency, with the logarithmic dependence appearing only in the leading term, and show that each expansion coefficient is determined by a finite set of moments of the density profile. We then extend the analysis to profiles with power-law tails and demonstrate that such profiles induce additional non-analytic frequency dependences, including fractional powers and logarithmic terms, which directly reflect the asymptotic behavior of the density distribution. Furthermore, we investigate the effects of non-sphericity and show that contributions from the quadrupole moment appear only as higher-order corrections relative to the spherically symmetric component in the low-frequency regime. Finally, we investigate the validity of the Born approximation in the low-frequency expansion. We derive a criterion for the maximum order of the low-frequency expansion up to which the Born approximation remains dominant over the post-Born corrections.
Comments27 pages, 3 figures
