提出宇宙网光谱层级分类法，统一多尺度结构分析。
Spectral Hierarchy of the Cosmic Web
- 用尺度加权核处理密度场，构建多级宇宙网分类框架。
- 高阶导数层级在非线性尺度主导，保留丰富晕分布信息。
- 适合快速生成星系模拟与研究环境依赖的聚类效应。
我们引入一种基于光谱层次的宇宙网分类方法：在标准特征值分类前，对密度场应用简单的尺度加权核。该方法统一并扩展了多种常用定义——大尺度非局域的势/潮汐网、更局部且对峰值和脊线敏感的曲率网，以及更高阶导数层级，逐级强调小尺度结构。由于分类基于滤波场的二阶导数，各级别自然对应重整化偏置和大尺度结构有效描述中的算子族，建立了宇宙网环境与长程与短程非局域偏置成分之间的明确联系。我们通过紧凑统计量量化层次的信息含量：将每个网格单元映射为四种有序的网类型（空洞、片层、丝状、节点），构造对应的‘网对比’场，并在粗网格（ΔL ≈ 5.5 h⁻¹ Mpc）上测量其与AbacusSummit模拟中晕的交叉相关。结果表明，该层次从极大尺度到网格奈奎斯特极限均保持显著的迹线相关信息，其中更局部（曲率/高阶导数）层级在非线性尺度占主导。这使得光谱层次成为快速星系模拟和场级建模的可解释条件基础，也是研究环境依赖聚类与组装偏差的灵活工具。
原文摘要 · Abstract (English)
We introduce a spectral hierarchy of cosmic-web classifications obtained by applying simple scale-weighting kernels to the density field before performing a standard eigenvalue-based web classification. This unifies and extends several widely used web definitions within a single framework: the familiar potential/tidal web (large-scale, nonlocal), a curvature-based web (more local, peak- and ridge-sensitive), and additional higher-derivative levels that progressively emphasize smaller-scale structure. Because the classification is built from second derivatives of the filtered field, successive hierarchy levels align naturally with operator families that appear in renormalised bias and effective descriptions of large-scale structure, providing an explicit bridge between cosmic-web environments and long- and short-range nonlocal bias ingredients. We quantify the information content of the hierarchy with a compact statistic: we map each cell to one of four ordered web types (void, sheet, filament, knot), construct a corresponding ``web contrast'' field, and measure its cross-correlation with halos from the AbacusSummit simulation suite on a coarse mesh with $ΔL\simeq 5.5\,h^{-1}\mathrm{Mpc}$. We find that the hierarchy retains significant tracer-relevant information from very large scales down to the mesh Nyquist limit, with the more local (curvature/higher-derivative) levels dominating toward nonlinear scales. This makes the spectral hierarchy a practical, interpretable conditioning basis for fast mock-galaxy production and field-level modelling, and a flexible tool for studying environment-dependent clustering and assembly bias.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。