AI 中文总结
本文研究广义纳瓦罗-弗伦克-怀特（gNFW）与艾纳斯托（Einasto）暗物质晕密度轮廓的引力波引力透镜效应，分析其强透镜参数空间、放大因子特性，发现艾纳斯托轮廓透镜效应更强且演化规律独特。
AI 中文摘要
暗物质（DM）晕的密度轮廓承载着暗物质性质的印记，可通过引力波（GW）受晕引力势产生的透镜效应来约束。本文研究两种典型晕密度轮廓的引力波透镜效应，即广义纳瓦罗-弗伦克-怀特（generalized Navarro-Frenk-White，gNFW）密度轮廓与艾纳斯托（Einasto）密度轮廓。利用引力透镜方程，首先在强透镜条件下检验两种轮廓的参数空间分布与成像特征，依据莫尔斯指数将参数空间划分为不同区域；接着对低频区放大因子$F(w,y)$的模$|F|$与相位$\text{Arg}(F)$展开详细分析。结果表明，在固定透镜质量下，增大gNFW斜率$\boldsymbol{\nu}$会使多像区的振幅更大、振荡更迅速、波包形态更显著；与gNFW情况相比，艾纳斯托轮廓（$\boldsymbol{\nu}=0.16$、$y<0.6$且$M_{200}$相同）产生的透镜效应更强，且$F(w,y)$随频率的演化规律与gNFW情况存在差异，表现出独特行为。
英文摘要
The density profiles of Dark matter (DM) halos carry imprints of the DM nature and may be constrained through the lensing effects on gravitational waves (GWs) arising from the halo gravitational potential. In this paper, we investigate GW lensing by two representative types of halo density profiles, i.e., the generalized Navarro-Frenk-White (gNFW) density profile and the Einasto density profile. Using the gravitational lensing equation, we first examine the parameter-space distribution and the imaging characteristics of both profiles under strong lensing, partitioning the parameter space into distinct regions according to the Morse index. We then conduct a detailed analysis of the modulus $\big|F\big|$ and phase $\mathrm{Arg}(F)$ of the amplification factor $F\big(w,y\big)$ at low frequency regime. Our results show that, for a fixed lens mass , increasing the gNFW slope $γ$ leads to a larger amplitude, more rapid oscillation, and more distinct wave-packet morphology in the multiple-image regime. Compared with the gNFW case, the Einasto case (with $α=0.16$, $y<0.6$, and the same $M_{200}$) produces a stronger lensing effect. Notably, the evolution of $F\big(w,y\big)$ with frequency for the Einasto profile differs from that of the gNFW case, making its behavior particularly distinctive.
Comments20 pages, 27 figures, 1 table
