Statistics of Smoothed Cosmic Fields in Perturbation Theory. I. Formulation and Useful Formulae in Second-Order Perturbation Theory
Statistics of Smoothed Cosmic Fields in Perturbation Theory. I. Formulation and Useful Formulae in Second-Order Perturbation Theory
复制标题
微扰理论中平滑宇宙场的统计。
DOI：
--
复制
发表时间：
2000
期刊：
影响因子：
--
通讯作者：
T. Matsubara
中科院分区：
文献类型：
--
作者：
T. Matsubara
我们给出了光滑宇宙场统计量的微扰估计的一般方法，并为微扰理论在各种统计量中的应用提供了有用的公式。这种形式是对Matsubara所使用的方法的广泛推广，Matsubara推导了三维密度场中属统计量的弱非线性公式。在描述了一般方法之后，我们将形式主义应用于一系列统计，包括属统计、平交统计、闵可夫斯基泛函和密度极值统计，而不考虑每个统计量定义的维度。阐明了闵可夫斯基泛函与其他几何统计量的关系。这些统计数据可以应用于几种宇宙场，包括三维密度场、三维速度场、二维投影密度场等。对二阶形式论的结果作了详细的说明。讨论了偏置的影响。在二阶微扰理论的框架下，讨论了光滑宇宙场作为体积分数重标阈值函数的统计量。在类似cdm的模型中，它们相对于重新标度阈值的线性预测的函数偏差通常比相对于直接阈值的函数偏差要小得多。对于重新标度的阈值，仍然存在轻微的肉丸移位，其特征是属曲线中波谷深度的不对称。提出了一种理论驱动的属曲线不对称因子。
We formulate a general method for perturbative evaluations of statistics of smoothed cosmic fields and provide useful formulae for application of the perturbation theory to various statistics. This formalism is an extensive generalization of the method used by Matsubara, who derived a weakly nonlinear formula of the genus statistic in a three-dimensional density field. After describing the general method, we apply the formalism to a series of statistics, including genus statistics, level-crossing statistics, Minkowski functionals, and a density extrema statistic, regardless of the dimensions in which each statistic is defined. The relation between the Minkowski functionals and other geometrical statistics is clarified. These statistics can be applied to several cosmic fields, including three-dimensional density field, three-dimensional velocity field, two-dimensional projected density field, and so forth. The results are detailed for second-order theory of the formalism. The effect of the bias is discussed. The statistics of smoothed cosmic fields as functions of rescaled threshold by volume fraction are discussed in the framework of second-order perturbation theory. In CDM-like models, their functional deviations from linear predictions plotted against the rescaled threshold are generally much smaller than that plotted against the direct threshold. There is still a slight meatball shift against rescaled threshold, which is characterized by asymmetry in depths of troughs in the genus curve. A theory-motivated asymmetry factor in the genus curve is proposed.