Xu Zhijie Jay
Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, WA, 99354, USA.
Sci Rep. 2023 Oct 2;13(1):16531. doi: 10.1038/s41598-023-42958-6.
Halo abundance and structure play a central role for modeling structure formation and evolution. Without relying on a spherical or ellipsoidal collapse model, we analytically derive the halo mass function and cuspy halo density (inner slope of -4/3) based on the mass and energy cascade theory in dark matter flow. The hierarchical halo structure formation leads to halo or particle random walk with a position-dependent waiting time [Formula: see text]. First, the inverse mass cascade from small to large scales leads to the halo random walk in mass space with [Formula: see text], where [Formula: see text] is the halo mass and [Formula: see text] is a halo geometry parameter with predicted value of 2/3. The corresponding Fokker-Planck solution for halo random walk in mass space gives rise to the halo mass function with a power-law behavior on small scale and exponential decay on large scale. This can be further improved by considering two different [Formula: see text] for haloes below and above a critical mass scale [Formula: see text], i.e. a double-[Formula: see text] halo mass function. Second, a double-[Formula: see text] density profile can be derived based on the particle random walk in 3D space with a position-dependent waiting time [Formula: see text], where [Formula: see text] is the gravitational potential and r is the particle distance to halo center. Theory predicts [Formula: see text] that leads to a cuspy density profile with an inner slope of -4/3, consistent with the predicted scaling laws from energy cascade. The Press-Schechter mass function and Einasto density profile are just special cases of proposed models. The small scale permanence can be identified due to the scale-independent rate of mass and energy cascade, where density profiles of different halo masses and redshifts converge to the [Formula: see text] scaling law ([Formula: see text]) on small scales. Theory predicts the halo number density scales with halo mass as [Formula: see text], while the halo mass density scales as [Formula: see text]. Results were compared against the Illustris simulations. This new perspective provides a theory for nearly universal halo mass functions and density profiles.
晕轮的丰度和结构在结构形成和演化的建模中起着核心作用。在不依赖于球形或椭球形塌缩模型的情况下，我们基于暗物质流中的质量和能量级联理论，解析推导了晕轮质量函数和尖顶晕轮密度（内斜率为 -4/3）。分层晕轮结构的形成导致晕轮或粒子随机游走，其等待时间与位置有关[公式：见原文]。首先，从小尺度到大尺度的反向质量级联导致晕轮在质量空间中的随机游走，其形式为[公式：见原文]，其中[公式：见原文]是晕轮质量，[公式：见原文]是晕轮几何参数，预测值为2/3。质量空间中晕轮随机游走的相应福克 - 普朗克解产生了在小尺度上具有幂律行为且在大尺度上具有指数衰减的晕轮质量函数。通过考虑临界质量尺度[公式：见原文]以下和以上的晕轮的两种不同的[公式：见原文]，即双[公式：见原文]晕轮质量函数，可以进一步改进这一结果。其次，可以基于在三维空间中具有与位置有关的等待时间[公式：见原文]的粒子随机游走推导出双[公式：见原文]密度分布，其中[公式：见原文]是引力势，r是粒子到晕轮中心的距离。理论预测[公式：见原文]会导致内斜率为 -4/3的尖顶密度分布，这与能量级联预测的标度律一致。普雷斯 - 谢赫特质量函数和艾纳斯托密度分布只是所提出模型的特殊情况。由于质量和能量级联速率与尺度无关，可以确定小尺度上的持久性，不同晕轮质量和红移的密度分布在小尺度上收敛到[公式：见原文]标度律（[公式：见原文]）。理论预测晕轮数密度与晕轮质量的标度关系为[公式：见原文]，而晕轮质量密度的标度关系为[公式：见原文]。将结果与Illustris模拟进行了比较。这一新观点为近乎通用的晕轮质量函数和密度分布提供了一种理论。
