从漂移集理论得到的晕质量函数。I.光滑尺度上非马尔可夫依赖的高斯涨落
The Halo Mass Function from Excursion Set Theory. I. Gaussian fluctuations with non-markovian dependence on the smoothing scale
摘要：
漂移集理论提供了一种计算暗物质晕质量函数的经典方法，其中密度扰动随平滑尺度随机演化，晕形成概率的计算问题被映射为势垒存在时的首次穿越时间问题.虽然光环形成的完整动力学复杂性只能通过N体模拟来揭示，但偏移集理论为理解这个复杂过程的各个方面提供了一个简单的分析框架。在这一系列的论文中，我们提出了改进的技术和概念方面的偏移集理论，我们探索到这一点的方法可以定量再现数据从N体模拟。在我的一系列文件中，我们展示了如何从路径积分制定的行程集理论。这使我们既可以严格推导出吸收屏障边界条件，在通常的提法只是假设，并处理分析与非马尔可夫性质的随机游走。这种非马尔可夫动力学不可避免地进入时，密度是平滑的过滤器，如在坐标空间中的礼帽过滤器（这是唯一的过滤器相关联的一个定义良好的晕质量）或当一个考虑非高斯波动。在这些情况下，除了“马尔可夫”条款，我们发现“记忆”条款，反映了非马尔可夫的平滑尺度的演变。我们开发了一个一般的形式主义微扰评估这些非马尔可夫修正，在本文中，我们明确地执行高斯波动的晕质量函数的计算，一阶的非马尔可夫修正，由于在坐标空间中使用的礼帽过滤器。
英文摘要：
A classic method for computing the mass function of dark matter halos is provided by excursion set theory, where density perturbations evolve stochastically with the smoothing scale, and the problem of computing the probability of halo formation is mapped into the so-called first-passage time problem in the presence of a barrier. While the full dynamical complexity of halo formation can only be revealed through N-body simulations, excursion set theory provides a simple analytic framework for understanding various aspects of this complex process. In this series of paper we propose improvements of both technical and conceptual aspects of excursion set theory, and we explore up to which point the method can reproduce quantitatively the data from N-body simulations. In paper I of the series we show how to derive excursion set theory from a path integral formulation. This allows us both to derive rigorously the absorbing barrier boundary condition, that in the usual formulation is just postulated, and to deal analytically with the non-markovian nature of the random walk. Such a non-markovian dynamics inevitably enters when either the density is smoothed with filters such as the top-hat filter in coordinate space (which is the only filter associated to a well defined halo mass) or when one considers non-Gaussian fluctuations. In these cases, beside ``markovian'' terms, we find ``memory'' terms that reflect the non-markovianity of the evolution with the smoothing scale. We develop a general formalism for evaluating perturbatively these non-markovian corrections, and in this paper we perform explicitly the computation of the halo mass function for gaussian fluctuations, to first order in the non-markovian corrections due to the use of a tophat filter in coordinate space.
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