论文标题
偏度的演变和宇宙密度场的峰度
Evolution of skewness and kurtosis of cosmic density fields
论文作者
论文摘要
方法。我们为常规LCDM模型执行宇宙Web演变的数值模拟。模拟覆盖了各种盒子尺寸L = 256-4000 mpc/h，质量和力分辨率和时期从很早的矩z = 30到现在z = 0。我们计算了具有各种平滑长度的密度场，以查找密度场对平滑尺度的依赖性。我们计算PDF及其力矩 - 方差，偏度和峰度。结果。我们专注于分布函数的第三个（偏度）和第四（峰度K）矩：它们对平滑尺度的依赖，波动的幅度和红移。在进化过程中，减少的偏度$ s_3 = s/σ$和减少的峰度$ s_4 = k/σ^2 $具有复杂的行为：在固定的红移曲线$ s_3（σ）$和$ s_4（σ）$陡峭地增加，$σ$ at $σ$ 1 $ $ 1 $ $ flatten of flatten $ ge2 $ n of flatten $。如果我们修复了平滑量表$ r_t $，则在达到$σ\ 2 $的最大值后，$σ$的曲线开始逐渐下降。我们为$ s_ {3,4}（σ，z）$的演变提供准确的拟合。偏度和峰度接近早期的恒定水平，具体取决于平滑长度：$ s_3（σ）\大约3 $和$ s_4（σ）\约15 $。结论。暗物质聚类的大多数统计数据（例如，光晕质量函数或浓度质量关系）几乎是通用的：它们主要取决于$σ$，并具有相对适度的校正以明确依赖红移。我们发现偏度和峰度的恰恰相反：矩对进化时期$ z $和平滑长度的依赖性$ r_t $是非常不同的，他们共同决定了$ s_ {3,4}（σ）$的演变。 $ s_3 $和$ s_4 $的演变无法通过当前理论近似来描述。
Methods. We perform numerical simulations of the evolution of the cosmic web for the conventional LCDM model. The simulations cover a wide range of box sizes L = 256 - 4000 Mpc/h, mass and force resolutions and epochs from very early moments z = 30 to the present moment z = 0. We calculate density fields with various smoothing lengths to find the dependence of the density field on smoothing scale. We calculate PDF and its moments - variance, skewness and kurtosis. Results. We focus on the third (skewness S) and fourth (kurtosis K) moments of the distribution functions: their dependence on the smoothing scale, the amplitude of fluctuations and the redshift. During the evolution the reduced skewness $S_3= S/σ$ and reduced kurtosis $S_4=K/σ^2$ present a complex behaviour: at a fixed redshift curves of $S_3(σ)$ and $S_4(σ)$ steeply increase with $σ$ at $σ\le 1$ and then flatten out and become constant at $σ\ge2$. If we fix the smoothing scale $R_t$, then after reaching the maximum at $σ\approx 2$, the curves at large $σ$ start to gradually decline. We provide accurate fits for the evolution of $S_{3,4}(σ,z)$. Skewness and kurtosis approach at early epochs constant levels, depending on smoothing length: $S_3(σ) \approx 3$ and $S_4(σ) \approx 15$. Conclusions. Most of statistics of dark matter clustering (e.g., halo mass function or concentration-mass relation) are nearly universal: they mostly depend on the $σ$ with the relatively modest correction to explicit dependence on the redshift. We find just the opposite for skewness and kurtosis: the dependence of moments on evolutionary epoch $z$ and smoothing length $R_t$ is very different, together they determine the evolution of $S_{3,4}(σ)$ uniquely. The evolution of $S_3$ and $S_4$ cannot be described by current theoretical approximations.
