arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2009.07023astro-ph.COastro-ph.GA
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层次聚类的随机理论I。晕质量函数

A Stochastic Theory of the Hierarchical Clustering I. Halo Mass Function

Andrea Lapi, Luigi Danese

摘要:

我们提出了一个新的理论的层次聚类的暗物质(DM)晕的基础上随机微分方程,这构成了一个变化的角度相对于现有的框架(例如,偏移集方法);这项工作特别关注晕圈质量函数。首先,我们提出了一个随机微分方程,该方程描述了DM晕质量增长的波动,该波动由依赖于球形坍缩阈值和DM扰动功率谱的乘性白(高斯)噪声驱动。我们证明,这样的噪声产生的晕人口向更大的群众,定量呈现标准的层次聚类的平均漂移。然后,我们解决了福克-普朗克方程的随机动力学,并获得压力和Schechter质量函数作为(稳态)的解决方案。此外,推广我们的治疗质量相关的崩溃阈值,我们得到了一个精确的解析解,能够拟合非常好的N-体质量函数在很宽的范围内的质量和红移。总而言之,这里提出的理论提供的新视角可以有助于更好地理解导致DM晕在宇宙时代形成,演化和统计的引力动力学。

英文摘要:

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.

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