The statistical theory of self-gravitating collisionless dark matter flow and the correlation, structure, and dispersion functions for velocity, density, and potential fields [CEA]

http://arxiv.org/abs/2202.00910


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 velocity 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 fully developed for incompressible, constant divergence, and irrotational flow. The nature of flow can be 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 feature leads to an increase in particle mass converted from kinetic energy upon “annihilation”. On large scale, transverse velocity correlation has an exponential form with a comoving scale $r_2$=21.3Mpc/h that maybe related to the size of sound horizon. All other correlation/structure/dispersion/spectrum functions for velocity/density/potential 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 are obtained from kinematic relations for constant divergence flow. Vorticity is negatively correlated for $r$ between 1 and 7Mpc/h. Divergence is negatively correlated for $r$>30Mpc/h that leads to negative density correlation.

Read this paper on arXiv…

Z. Xu
Thu, 3 Feb 22
36/56

Comments: 24 figures, 2 tables