发表机构
Università degli Studi di Torino; INFN – Istituto Nazionale di Fisica Nucleare, Sezione di Torino; University of Amsterdam; Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo（都灵大学; 意大利国家核物理研究所都灵分部; 阿姆斯特丹大学; 东京大学宇宙物质前沿科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究温暗物质子晕的瞬时尖峰结构是否在波光学强透镜引力波中留下可观测印记，发现LISA频带仅在中间质量范围（20-40 keV）可探测，尖峰对信号调制影响微弱。
AI 中文摘要
暗物质晕预期在其中心形成瞬时的 $\rho \propto r^{-3/2}$ 密度尖峰，而在温暗物质（WDM）宇宙学中，这些尖峰可以主导那些在自由流抑制中幸存下来的低质量子晕的内部结构。我们研究这种内部结构是否能在波光学（WO）区域中被引力透镜的引力波观测到。将强透镜波光学衍射积分框架扩展到WDM，我们使用{\sc sashimi-w}半解析模型生成子晕群体，通过尖峰-晕关系为每个子晕分配一个瞬时尖峰，并在500个独立实现中计算LISA频带内频率相关的放大因子 $F(f)$，对应 $m_\chi \in \{6, 10, 20, 40, 80, 100\}$~keV。信号由WDM抑制的子晕质量函数与LISA频带敏感的 $m_{\rm sub} \sim 10^{4}$ 到 $10^{7}\\,M_\odot$ 范围之间的重叠所主导。对于 $m_\chi \lesssim 10$~keV，调制可忽略不计，到40~keV时达到百分之一水平，然后饱和到类似CDM的平台，因此该可观测信号仅在中间范围 $\sim 20$ 到 40~keV 内可靠地探测 $m_\chi$。在相同的子晕目录上将尖峰振幅设为零并重复40~keV的系综，我们发现瞬时尖峰仅轻微增强振幅调制。在尖峰构成子晕质量大部分的地方，自由流已经耗尽了携带信号的质量范围；而在该范围被填充的地方，尖峰位于菲涅耳半径内部，衍射积分通过投影的封闭质量而非中心密度对其响应。因此，在强透镜的大质量黑洞双星中检测到百分之一的信号将确立菲涅耳尺度上存在子结构，但无法诊断其内部轮廓。
英文摘要
Dark matter halos are expected to form with a prompt $ρ\propto r^{-3/2}$ density cusp at their centres, and in warm dark matter (WDM) cosmologies these cusps can dominate the inner structure of the low-mass subhalos that survive free-streaming suppression. We investigate whether that inner structure is visible to gravitational waves lensed in the wave-optics (WO) regime. Extending the strong lensing WO diffraction-integral framework to WDM, we generate subhalo populations with the {\sc sashimi-w} semi-analytic model, assign each subhalo a prompt cusp through a cusp-halo relation, and compute the frequency-dependent amplification factor $F(f)$ across the LISA band over 500 independent realisations for $m_χ\in \{6, 10, 20, 40, 80, 100\}$~keV. The signal is governed by the overlap between the WDM-suppressed subhalo mass function and the $m_{\rm sub} \sim 10^{4}$ to $10^{7}\,M_\odot$ range to which the LISA band is sensitive. Modulations are negligible for $m_χ\lesssim 10$~keV, reach the percent level by 40~keV, and then saturate to a CDM-like plateau, so the observable reliably probes $m_χ$ only over the intermediate range $\sim 20$ to 40~keV. Repeating the 40~keV ensemble on identical subhalo catalogs with the cusp amplitude set to zero, we find that prompt cusps enhance the amplitude modulation only mildly. Where cusps make up a large fraction of the subhalo mass, free-streaming has already depleted the signal-carrying mass range, and where that range is populated, the cusp lies well inside the Fresnel radius, to which the diffraction integral responds through projected enclosed mass rather than central density. A percent-level detection in a strongly lensed massive black-hole binary would therefore establish the presence of substructure on Fresnel scales without diagnosing its inner profile.
Comments12 pages, 4 figures
