On the statistical theory of self-gravitating collisionless dark matter flow

Dark matter, if it exists, accounts for five times as much the ordinary baryonic matter. Compared to hydrodynamic turbulence, flow of dark matter might possess widest presence in our universe. This paper presents a statistical theory that is compared with N-body simulations. By contrast hydrodynamics normal fluids, self-gravitating, long-range, and collisionless scale-dependent behavior. The peculiar velocity field constant divergence nature on small scale irrotational large scale. measures, i.e., correlation, structure, dispersion, spectrum functions, are modeled both scales, respectively. Kinematic relations between measures fully developed incompressible, divergence, flow. Incompressible share same kinematic even order correlations. limiting correlation ρL=1/2 smallest (r = 0) unique feature (ρL=1 incompressible flow). On scale, transverse has an exponential form T2∝e−r/r2 comoving r2=21.3 Mpc/h may be related horizon size at matter–radiation equality. All other functions velocity, density, potential fields derived analytically from longitudinal structure function follows one-fourth law S2l∝r1/4. can obtained Vorticity negatively correlated r 1 7 Mpc/h. Divergence > 30 leads negative density correlation.