论文标题
关于自我磨碎无碰撞暗物质流的统计理论
On the statistical theory of self-gravitating collisionless dark matter flow
论文作者
论文摘要
暗物质，如果存在，则是普通的重型物质的五倍。与流体动力的湍流相比，暗物质的流动可能具有我们宇宙中最广泛的存在。本文介绍了暗物质流动的统计理论，该理论与N体模拟相比。与正常流体的流体动力学相反，暗物质流动是自我磨损的，远程和无碰撞的依赖性流动行为。特殊的速度场在小规模上具有恒定的差异性质，并且大规模无关。统计度量，即相关性，结构，分散和频谱函数分别在小规模和大尺度上建模。统计措施之间的运动关系是为了不可压缩的，恒定的差异和无旋转流动的全面发展。不可压缩且恒定的差异流共享相同的运动关系，甚至有阶相关。速度$ρ_l= 1/2 $在最小比例尺（$ r = 0 $）的限制相关性是无碰撞流量的独特功能（$ρ_l= 1 $用于不可压缩流）。在大规模上，横向速度相关具有指数形式的$ t_2 \ propto e^{ - r/r_2} $，具有恒定共同量表$ r_2 $ = 21.3mpc/h，这可能与物质 - 拉德相等的地平线大小有关。所有其他相关性，结构，分散和频谱函数的速度，密度和潜在领域都是从运动关系中分析得出的。在小规模上，纵向结构函数遵循$ s^l_2 \ propto r^{1/4} $的四个定律。所有其他统计措施都可以从运动关系中获得恒定发散流。涡度在1至7Mpc/h之间的比例$ r $呈负相关。差异为$> 30mpc/h的差异相关，导致负密度相关性。
Dark matter, if exists, accounts for five times as much as the ordinary baryonic matter. Compared to hydrodynamic turbulence, the flow of dark matter might possess the widest presence in our universe. This paper presents a statistical theory for the flow of dark matter that is compared with N-body simulations. By contrast to hydrodynamics of normal fluids, dark matter flow is self-gravitating, long-range, and collisionless with a scale dependent flow behavior. The peculiar velocity field is of constant divergence nature on small scale and irrotational on large scale. The statistical measures, i.e. correlation, structure, dispersion, and spectrum functions are modeled on both small and large scales, respectively. Kinematic relations between statistical measures are fully developed for incompressible, constant divergence, and irrotational flow. Incompressible and constant divergence flow share same kinematic relations for even order correlations. The limiting correlation of velocity $ρ_L=1/2$ on the smallest scale ($r=0$) is a unique feature of collisionless flow ($ρ_L=1$ for incompressible flow). On large scale, transverse velocity correlation has an exponential form $T_2\propto e^{-r/r_2}$ with a constant comoving scale $r_2$=21.3Mpc/h that maybe related to the horizon size at matter-radiation equality. All other correlation, structure, dispersion, and spectrum functions for velocity, density, and potential fields are derived analytically from kinematic relations for irrotational flow. On small scale, longitudinal structure function follows one-fourth law of $S^l_2\propto r^{1/4}$. All other statistical measures can be obtained from kinematic relations for constant divergence flow. Vorticity is negatively correlated for scale $r$ between 1 and 7Mpc/h. Divergence is negatively correlated for $r$>30Mpc/h that leads to a negative density correlation.
