论文标题
关于自我磨碎无碰撞暗物质流的统计理论：速度和密度分布的尺度和红移变化
On the statistical theory of self-gravitating collisionless dark matter flow: Scale and redshift variation of velocity and density distributions
论文作者
论文摘要
本文通过一种基于光晕的非投影方法研究了自我磨碎无碰撞暗物质流动中密度和速度分布的规模和红移变化。将所有颗粒分为光环和北极颗粒，以进行红移的分布变化。如果不将粒子场投影到结构化的网格上，则通过在不同尺度上$ r $识别所有粒子对来分析比例变化。我们证明：i）Delaunay Tessellation可用于重建密度场。获得了密度相关性，光谱和分散功能，并与N体模拟进行了建模。 ii）速度分布在小规模和大尺度上都是对称的，由于逆级别级联反向级数，以恒定速率$ \ varepsilon_u $在中间尺度上具有负偏度； iii）在小尺度上，成对速度的偶数时刻$ΔU_l$遵循三分之二的法律$ \ propto {（ - \ varepsilon_ur）}^{2/3} $，而奇数订单遵循线性缩放量表$ \ langle（Δu_l）^{2n+1} \ rangle =（2n+1）\ langle（ΔU_L）^{2n} \ rangle \langleΔU_L\ rangle \ rangle \ rangle \ rangle \ prop propto {rangle propto {r} $; iv）研究了针对纵向速度$ u_l $或$ u_l $或$ u_l^{'} $的速度分布的比例变化，成对速度（速度差）$ΔU_L$ = $ = $ = $ u_l^{'}'} $ - $ u_l $ and $ u_l $ and velocity和velocity和$ u__ $ $ u__l $ u__l $ = $ = u = u = u =完全发达的速度场在任何规模上从来都不是高斯，尽管它们最初可以是高斯。 v）在小尺度上，$ u_l $和$σu_l$可以通过$ x $分布来建模，以最大化系统熵； vi）在大尺度上，$Δu_l$和$σu_l$可以通过逻辑或$ x $分布来建模； vii）速度分布的红移变化遵循$ x $分布的演变，该分布涉及形状参数$α（z）$随时间减少。
This paper studies the scale and redshift variation of density and velocity distributions in self-gravitating collisionless dark matter flow by a halo-based non-projection approach. All particles are divided into halo and out-of-halo particles for redshift variation of distributions. Without projecting particle fields onto a structured grid, the scale variation is analyzed by identifying all particle pairs on different scales $r$. We demonstrate that: i) Delaunay tessellation can be used to reconstruct the density field. The density correlation, spectrum, and dispersion functions were obtained, modeled, and compared with the N-body simulation; ii) the velocity distributions are symmetric on both small and large scales and are non-symmetric with a negative skewness on intermediate scales due to the inverse energy cascade at a constant rate $\varepsilon_u$; iii) On small scales, the even order moments of pairwise velocity $Δu_L$ follow a two-thirds law $\propto{(-\varepsilon_ur)}^{2/3}$, while the odd order moments follow a linear scaling $\langle(Δu_L)^{2n+1}\rangle=(2n+1)\langle(Δu_L)^{2n}\rangle\langleΔu_L\rangle\propto{r}$; iv) The scale variation of the velocity distributions was studied for longitudinal velocities $u_L$ or $u_L^{'}$, pairwise velocity (velocity difference) $Δu_L$=$u_L^{'}$-$u_L$ and velocity sum $Σu_L$=$u^{'}_L$+$u_L$. Fully developed velocity fields are never Gaussian on any scale, despite that they can initially be Gaussian; v) On small scales, $u_L$ and $Σu_L$ can be modeled by a $X$ distribution to maximize the system entropy; vi) On large scales, $Δu_L$ and $Σu_L$ can be modeled by a logistic or a $X$ distribution; vii) the redshift variation of the velocity distributions follows the evolution of the $X$ distribution involving a shape parameter $α(z)$ decreasing with time.
