arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1206.6548astro-ph.CO
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暗物质晕与自相似性

Dark matter halo's and self similarity

C. Alard

摘要:

本文探讨了Vlasov-Poisson系统的自相似解及其与动力冷系统的引力坍缩的关系。导出了一维幂律势的解析解,并提出了三维幂律势解析解的推广。其次,数值研究了冷动力系统坍缩的自相似性。相空间中的折叠系统与解析的自相似解是一致的,这些解呈现出所有的自相似标度。另外一点是,在幂律指数大于$-(1/2)$的初始条件下,系统中心出现$x^{-(1/2)}$定律。它被发现,第一次出现的$x^{-(1/2)}$法律对应于一个奇点的形成非常接近的中心。最后研究了自相似多维解在平衡点附近的一般性质。光滑和连续的自相似解在平衡态下具有幂律行为。然而,冷的初始条件会导致相空间解的不连续,并且平滑后的相空间密度失去了自相似性。通过观察相空间密度$P$的概率分布除了缩放参数之外与平滑的相空间密度$P_S$的概率分布相同,该问题容易解决。因此,$P_S$继承了$P$的自相似特性。这个特殊的属性是在$ρ/{σ^3}$的数值模拟中观察到的普遍幂律的起源。$P_S$的自相似性质意味着其他量也应该具有可预测指数的普适幂律行为。利用冷暗物质晕相空间密度的数值模型对这一假设进行了检验,得到了很好的一致性。

英文摘要:

This papers explores the self similar solutions of the Vlasov-Poisson system and their relation to the gravitational collapse of dynamically cold systems. Analytic solutions are derived for power law potential in one dimension, and extensions of these solutions in three dimensions are proposed. Next the self similarity of the collapse of cold dynamical systems is investigated numerically. The fold system in phase space is consistent with analytic self similar solutions, the solutions present all the proper self-similar scalings. An additional point is the appearance of an $x^{-(1/2)}$ law at the center of the system for initial conditions with power law index larger than $-(1/2)$. It is found that the first appearance of the $x^{-(1/2)}$ law corresponds to the formation of a singularity very close to the center. Finally the general properties of self similar multi dimensional solutions near equilibrium are investigated. Smooth and continuous self similar solutions have power law behavior at equilibrium. However cold initial conditions result in discontinuous phase space solutions, and the smoothed phase space density looses its auto similar properties. This problem is easily solved by observing that the probability distribution of the phase space density $P$ is identical except for scaling parameters to the probability distribution of the smoothed phase space density $P_S$. As a consequence $P_S$ inherit the self similar properties of $P$. This particular property is at the origin of the universal power law observed in numerical simulation for $ρ/{σ^3}$. The self similar properties of $P_S$ implies that other quantities should have also an universal power law behavior with predictable exponents. This hypothesis is tested using a numerical model of the phase space density of cold dark matter halo's, an excellent agreement is obtained.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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