The statistical theory of self-gravitating collisionless dark matter flow for velocity, density, and potential fields 后印本

摘要: N-body simulation is an invaluable tool to understand cosmic velocity field. However, simulation samples velocity only at particle locations that leads to information loss when projecting particle fields onto structured grid. Here we extract two-point statistics without field projection. These statistics, i.e. correlation, structure, dispersion functions in real space and spectrum functions in Fourier space, are modeled on both small and large scales. Kinematic relations between statistical measures are developed for incompressible, constant divergence, and irrotational flow. The nature of dark matter flow is identified by these relations. Much more complex than incompressible flow, peculiar velocity of dark matter flow is of constant divergence on small scale and irrotational on large scale. Incompressible and constant divergence flow share same kinematic relations for even order correlations. The limiting correlation of velocity $\rho_L=1/2$ on the smallest scale ($r=0$) is a unique feature of collisionless flow ($\rho_L=1$ for incompressible flow). Assuming gravity is the only interaction and no radiation produced, this leads to an increase in particle mass converted from kinetic energy upon "annihilation". On large scale, transverse velocity correlation has an exponential form $T_2\propto e^{-r/r_2}$ with a comoving scale $r_2$=21.3Mpc/h that maybe related to the size of sound horizon. All other correlation, structure, dispersion and spectrum functions for velocity, density, and potential are derived analytically from kinematic relations for irrotational flow. On small scale, structure function follows one-fourth law of $S^l_2\propto r^{1/4}$. All other statistical measures can be derived 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 negative density correlation.