LCDM宇宙学中演化潮汐场的标度关系
A Scaling Relation of the Evolving Tidal Fields in a LCDM Cosmology
摘要：
我们发现了宇宙网各向异性参数$A$、线性密度均方根涨落σ（r）和线性增长因子D（z）之间的标度关系。利用Millennium模拟得到的512^{3}个网格上z=0、2、5和127的潮汐场，计算了各网格分辨率下局部潮汐张量的最大特征值$λ$，并测量了其距离平均两点关联函数xi_{lambda}，作为局部主轴坐标系中极角cos（θ）余弦的函数。我们发现，xi_{lambda}是相当各向异性的，增加对最小物质压缩的方向，和各向异性的xi_{lambda}增加的红移，z，减少，并作为上距离截止r_{c}减少。将数值结果拟合到解析拟合模型中（\cos θ）\propto（1+A \cos^{n} θ）^{-1}，发现A的最佳拟合值（称为宇宙网各向异性参数）随σ系统地变化（r_{c}）和D（z），使我们能够确定简单的数学标度关系A（r_{c}，z）=0.8，D^{0.76}（z），sigma（r_{c}）$。
英文摘要：
We report the finding of a scaling relation among the cosmic-web anisotropy parameter $A$, the linear density rms fluctuation sigma(r) and the linear growth factor D(z). Using the tidal field derived from the Millennium Simulation on 512^{3} grids at z=0, 2, 5 and 127, we calculate the largest eigenvalues $λ$ of the local tidal tensor at each grid resolution and measure its distance-averaged two-point correlation function, xi_{lambda}, as a function of the cosines of polar angles cos(theta) in the local principal axis frame. We show that xi_{lambda} is quite anisotropic, increasing toward the directions of minimal matter compression, and that the anisotropy of xi_{lambda} increases as the redshift, z, decreases and as the upper distance cutoff r_{c} decreases. Fitting the numerical results to an analytic fitting model ξ_λ(\cosθ)\propto (1+A\cos^{n}θ)^{-1}, it is found that the best fit value of A, dubbed the cosmic-web anisotropy parameter, varies systematically with sigma(r_{c}) and D(z), allowing us to determine the simple empiral scaling relation A(r_{c},z)=0.8, D^{0.76}(z), sigma (r_{c})$.
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