论文标题
关于自我磨碎无碰撞暗物质流的统计理论：高阶运动和动态关系
On the statistical theory of self-gravitating collisionless dark matter flow: high order kinematic and dynamic relations
论文作者
论文摘要
为了更好地了解不同尺度上的无碰撞暗物质流动，必须针对不同类型的流动，例如不可压缩的，恒定的差异和不旋转流动。本文将我们先前关于二阶统计数据（物理流体35，077105）的工作扩展到了高阶统计。在不同尺度上的暗物质流程开发了运动关系和动态关系。结果通过N体模拟验证。在大尺度上，我们发现i）三阶速度相关性可能与密度相关性或成对速度有关； ii）$ p $ th阶速度相关性遵循$ \ propto a^{（p+2）/2} $对于奇数$ $ p $和$ \ propto a^{p/2} $，甚至$ p $，其中$ a $ a $是比例因子; iii）过度密度$δ$与同一尺度上的密度相关性成正比； iv）给定比例$ r $上的速度分散与同一规模的过度密度成正比。在小尺度上，i）通过将光环中的速度分解为运动和光环的运动来开发自相关的速度进化； ii）涡度和肠的演变源自速度的进化； iii）得出动态关系以将二阶和三阶相关性相关联； iv）虽然成对速度的第一时刻遵循$ \langleΔu_l\ rangle = -har $（$ h $是哈勃参数），但第三时刻遵循$ \ langle（ΔU__L）^3 \ rangle \ rangle \ propto \ propto \ varepsilon_uar $，并且可以直接与Simustations相比$ \ VAREPSILON_U \ lot10^{ - 7} $ m $^2 $/s $^3 $是能量级联的常数速率； v）$ p $ th订单速度相关性遵循$ \ propto a^{（3p-5）/4} $对于奇数$ p $和$ \ propto a^{3p/4} $，甚至$ p $。最后，组合的运动学和动态关系导致大小尺度上的指数和四分之一的幂律速度相关性。
To better understand the collisionless dark matter flow on different scales, statistical theory involving kinematic and dynamic relations must be developed for different types of flow, e.g. incompressible, constant divergence, and irrotational flow. This paper extends our previous work on the second-order statistics (Phys. Fluids 35, 077105) to high order statistics. Kinematic and dynamic relations were developed for dark matter flow on different scales. The results were validated by N-body simulations. On large scales, we found i) third-order velocity correlations can be related to density correlation or pairwise velocity; ii) the $p$th-order velocity correlations follow $\propto a^{(p+2)/2}$ for odd $p$ and $\propto a^{p/2}$ for even $p$, where $a$ is the scale factor; iii) the overdensity $δ$ is proportional to density correlation on the same scale; iv) velocity dispersion on a given scale $r$ is proportional to the overdensity on the same scale. On small scales, i) a self-closed velocity evolution is developed by decomposing the velocity into motion in haloes and motion of haloes; ii) the evolution of vorticity and enstrophy are derived from the evolution of velocity; iii) dynamic relations are derived to relate second- and third-order correlations; iv) while the first moment of pairwise velocity follows $\langleΔu_L\rangle=-Har$ ($H$ is the Hubble parameter), the third moment follows $\langle(Δu_L)^3\rangle\propto\varepsilon_uar$ that can be directly compared with simulations and observations, where $\varepsilon_u\approx10^{-7}$m$^2$/s$^3$ is the constant rate for energy cascade; v) the $p$th order velocity correlations follow $\propto a^{(3p-5)/4}$ for odd $p$ and $\propto a^{3p/4}$ for even $p$. Finally, the combined kinematic and dynamic relations lead to exponential and one-fourth power-law velocity correlations on large and small scales, respectively.
