改进红移空间畸变的模拟：I。星系两两速度分布的双变量高斯描述
Improving the modelling of redshift-space distortions: I. A bivariate Gaussian description for the galaxy pairwise velocity distributions
摘要：
作为一个更准确的建模红移空间扭曲的星系调查的一步，我们开发了一个一般性的描述的概率分布函数的星系成对的速度在所谓的流模型的框架内。对于一个给定的星系间距$\vec{r}$，这样的函数可以描述为一个叠加的几乎无限的本地分布。我们的特点，这些方面的时刻，然后考虑的具体情况下，他们是高斯函数，每个都有自己的平均值$μ$和分散$σ$。基于物理上的考虑，我们做出了进一步的关键假设，即这两个参数依次根据二元高斯分布，具有自己的均值和协方差矩阵。使用数值模拟的测试明确表明，这种紧凑的描述可以正确地模拟所有尺度上的红移空间失真，完全捕捉到星系流在不同分离处的整体线性和非线性动力学。特别是，我们自然地获得高斯/指数，偏斜/非偏斜分布函数，这取决于在模拟和数据中观察到的分离。此外，最近提出的单高斯描述的红移空间失真包括在这个模型中作为一个限制的情况下，当双变量高斯崩溃到一个二维狄拉克δ函数。我们还展示了这种描述如何自然地允许$1+ξ_R(r)$周围的$1+ξ_S(\vec{s})$的泰勒展开，从而导致凯泽线性公式时，截断到二阶，明确其连接的时刻的速度分布函数。需要更多的工作，但这些结果表明，一个非常有前途的路径，使我们的计划，以提高RSD估计明确的进展。
英文摘要：
As a step towards a more accurate modelling of redshift-space distortions in galaxy surveys, we develop a general description of the probability distribution function of galaxy pairwise velocities within the framework of the so-called streaming model. For a given galaxy separation $\vec{r}$, such function can be described as a superposition of virtually infinite local distributions. We characterize these in terms of their moments and then consider the specific case in which they are Gaussian functions, each with its own mean $μ$ and dispersion $σ$. Based on physical considerations, we make the further crucial assumption that these two parameters are in turn distributed according to a bivariate Gaussian, with its own mean and covariance matrix. Tests using numerical simulations explicitly show that with this compact description one can correctly model redshift-space distorsions on all scales, fully capturing the overall linear and nonlinear dynamics of the galaxy flow at different separations. In particular, we naturally obtain Gaussian/exponential, skewed/unskewed distribution functions, depending on separation as observed in simulations and data. Also, the recently proposed single-Gaussian description of redshift-space distortions is included in this model as a limiting case, when the bivariate Gaussian is collapsed to a two-dimensional Dirac delta function. We also show how this description naturally allows for the Taylor expansion of $1+ξ_S(\vec{s})$ around $1+ξ_R(r)$, which leads to the Kaiser linear formula when truncated to second order, expliciting its connection with the moments of the velocity distribution functions. More work is needed, but these results indicate a very promising path to make definitive progress in our program to improve RSD estimators.
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