Title: Topology and geometry of the dark matter web Show Chinese title

Title: 暗物质网的拓扑与几何结构

Abstract: Topological connections in the single-streaming voids and multi-streaming filaments and walls reveal a cosmic web structure different from traditional mass density fields. A single void structure not only percolates the multi-stream field in all the directions, but also occupies over 99 per cent of all the single-streaming regions. Sub-grid analyses on scales smaller than simulation resolution reveal tiny pockets of voids that are isolated by membranes of the structure. For the multi-streaming excursion sets, the percolating structure is much thinner than the filaments in over-density excursion approach. We also introduce, for the first time, a framework to detect dark matter haloes in multi-stream fields. Closed compact regions hosting local maxima of the multi-stream field are detected using local geometrical conditions and properties of the Lagrangian sub-manifold. All the halo particles are guaranteed to be completely outside void regions of the Universe. Majority of the halo candidates are embedded in the largest structure that percolates the entire volume. Show Chinese abstract

Abstract: 宇宙网结构中的拓扑连接在单流空洞和多流丝状结构及墙结构中显示出与传统质量密度场不同的特征。 一个单一的空洞结构不仅在所有方向上渗透多流场，而且占据了所有单流区域的99%以上。 对小于模拟分辨率尺度的网格下分析揭示了由结构膜隔离的微小空洞口袋。 对于多流 excursion 集，渗透结构比过密度 excursion 方法中的丝状结构要薄得多。 我们首次引入了一个框架，在多流场中检测暗物质晕。 使用局部几何条件和拉格朗日子流形的性质，检测到包含多流场局部最大值的封闭紧凑区域。 所有的晕粒子都被保证完全位于宇宙的空洞区域之外。 大多数晕候选体嵌入在渗透整个体积的最大结构中。