利用可微强引力透镜模拟器映射未分辨暗物质晕族的信息几何
Mapping the Information Geometry of an Unresolved Dark Matter Population using a Differentiable Strong Lensing Simulator
中文总结 AI 辅助
本文提出基于可微强引力透镜模拟器的框架，利用费舍尔矩阵和费舍尔图拉普拉斯先验量化未分辨暗物质子晕族的信息简并性，为区分暗物质模型提供方法支撑。
中文摘要 AI 辅助
强引力透镜是探测小尺度物质功率谱的独特工具，星系中暗物质子晕的丰度可用于区分标准冷暗物质模型与温暗物质等替代模型。提取该信号面临重大计算挑战，因为子结构诱导的透镜势扰动会与透镜的宏观模型、高灵活性的背景源模型简并。本文引入一种框架，利用可微强引力透镜模拟器量化这些简并性：子结构被表示为局限于透镜像周围环形域的谱基，使NFW子晕族的信号可编码在有限向量空间中；随后利用费舍尔矩阵确定子结构的信息有多少被模型的干扰分量吸收。研究发现，宏观模型简并性主要局限于透镜势的低阶扰动，而随着源模型表达能力提升，与源模型的简并性会在宽尺度范围内强烈抑制灵敏度；最后引入费舍尔图拉普拉斯先验作为诊断工具，研究源模型的内部简并性如何用于调节数据对未分辨暗物质子晕族的灵敏度。
英文摘要
Strong gravitational lensing is a unique probe of the matter power spectrum on small scales, where the abundance of dark matter subhalos in galaxies could be used to distinguish the predictions of the concordance cold dark matter model from alternatives such as warm dark matter. Extracting this signal poses major computational challenges, since perturbations of the lensing potential induced by substructure can be degenerate with both the macro-model of the lens and highly flexible models of the background source. Here, we introduce a framework to quantify these degeneracies using a differentiable strong-lensing simulator. Substructure is represented in a spectral basis confined to an annular domain surrounding the lensed image, allowing signals from a population of NFW subhalos to be encoded in a finite vector space. We then use the Fisher matrix to determine how much information about substructure is absorbed by nuisance components of the model. We find that macro-model degeneracies are largely confined to low-order perturbations of the lensing potential, while degeneracies with the source model can strongly suppress sensitivity across a broad range of scales as the expressivity of the source model is increased. Finally, we introduce the Fisher Graph Laplacian prior as a diagnostic tool to study how the internal degeneracies of the source model can be used to regulate the sensitivity of the data to an unresolved population of dark matter subhalos.
