论文标题
分层聚类的随机理论I.光环质量函数
A Stochastic Theory of the Hierarchical Clustering I. Halo Mass Function
论文作者
论文摘要
我们提出了一种基于随机微分方程的暗物质（DM）光晕的分层聚类（DM）的新理论，该理论构成了有关现有框架的观点的改变（例如，游览设置方法）；这项工作专门针对光晕质量功能。首先，我们提出了一个随机微分方程，该方程描述了DM光晕的质量生长的波动，这是由乘以乘型白色（高斯）噪声驱动的，取决于球形塌陷阈值和DM扰动的功率谱。我们证明，这种噪声会导致光环群的平均漂移向更大的质量，从而定量地呈现标准的分层聚类。然后，我们求解与随机动力学相关的Fokker-Planck方程，并以（固定）解决方案获得压力机和Schechter质量函数。此外，将我们的处理概括为质量依赖性的塌陷阈值，我们获得了一种精确的分析解决方案，能够在质量和红移范围内拟合N体质量功能非常好。总而言之，此处提出的理论提供的新观点可以更好地理解导致跨宇宙时代DM光晕的形成，进化和统计的引力动力学。
We present a new theory for the hierarchical clustering of dark matter (DM) halos based on stochastic differential equations, that constitutes a change of perspective with respect to existing frameworks (e.g., the excursion set approach); this work is specifically focused on the halo mass function. First, we present a stochastic differential equation that describes fluctuations in the mass growth of DM halos, as driven by a multiplicative white (Gaussian) noise dependent on the spherical collapse threshold and on the power spectrum of DM perturbations. We demonstrate that such a noise yields an average drift of the halo population toward larger masses, that quantitatively renders the standard hierarchical clustering. Then, we solve the Fokker-Planck equation associated to the stochastic dynamics, and obtain the Press & Schechter mass function as a (stationary) solution. Moreover, generalizing our treatment to a mass-dependent collapse threshold, we obtain an exact analytic solution capable of fitting remarkably well the N-body mass function over a wide range in mass and redshift. All in all, the new perspective offered by the theory presented here can contribute to better understand the gravitational dynamics leading to the formation, evolution and statistics of DM halos across cosmic times.
