Dark matter flow dataset Part II: Correlation-based statistics from cosmological N-body simulation

Dark matter (DM), if exists, is believed to be cold, collisionless, dissipationless, non-baryonic, barely interacting with baryonic matter except through gravity, and sufficiently smooth on large scales with a fluid-like behavior. The flow of dark matter can be best described by a self-gravitating collisionless fluid dynamics (SG-CFD). The statistics of dark matter density, velocity, acceleration, energy, momentum, and their redshift evolution play essential roles for structure formation and evolution. These information can be systematically extracted from cosmological N-body simulations by either i) a structural (halo-based) or ii) a statistical (correlation-based) approach. In this correlation-based statistical dataset, i) all particle pairs with any given separation r in a N-body system are identified; ii) statistical measures are calculated over all particle pairs with the same separation r (pairwise average); iii) the redshift (z) and scale (r) dependence of all statistical measures (correlation/moment/structure/dispersion/spectrum functions for density, velocity and potential etc.) are presented.  

The theory developed with this dataset including:

1. Inverse mass cascade in dark matter flow and effects on halo mass functions
2. Inverse mass cascade in dark matter flow and effects on halo deformation, energy, size, and density profiles
3. Inverse energy cascade in self-gravitating collisionless dark matter flow and effects of halo shape
4. The mean flow, velocity dispersion, energy transfer and evolution of rotating and growing dark matter halos
5. Two-body collapse model for gravitational collapse of dark matter and generalized stable clustering hypothesis for pairwise velocity
6. Evolution of energy, momentum, spin parameter in dark matter flow and integral constants of motion
7. The maximum entropy distributions of velocity, speed, and energy from statistical mechanics of dark matter flow
8. Halo mass functions from maximum entropy distributions in self-gravitating collisionless dark matter flow
9. The statistical theory of dark matter flow for velocity, density, and potential fields
10. The statistical theory of dark matter flow and high order kinematic and dynamic relations for velocity correlations
11. The scale and redshift variation of density and velocity distributions in dark matter flow and two-thirds law for pairwise velocity

along with three applications of theory:

1. Dark matter particle mass and properties from two-thirds law and energy cascade in dark matter flow
2. Origin of MOND acceleration and deep-MOND from acceleration fluctuation and energy cascade in dark matter flow
3. The baryonic-to-halo mass relation from mass and energy cascade in dark matter flow

The two relevant datasets and accompanying presentation can be found at: 

1. Dark matter flow dataset Part I: Halo-based statistics from cosmological N-body simulation 
2. Dark matter flow dataset Part II: Correlation-based statistics from cosmological N-body simulation.
3. A comparative study of Dark matter flow & hydrodynamic turbulence and its applications

The same dataset also available on Github at: Github: dark_matter_flow_dataset and zenodo at: Dark matter flow dataset from cosmological N-body simulation.