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. Applications of cascade and statistical theory for dark matter and bulge-SMBH evolution: Dark matter particle mass ,size, and properties from energy cascade in dark matter flow: 1) arxiv 2) zenodo slides Origin of MOND acceleration & deep-MOND from acceleration fluctuation & energy cascade: 1) arxiv 2) zenodo slides The baryonic-to-halo mass relation from mass and energy cascade in dark matter flow: 1) arxiv 2) zenodo slides Universal scaling laws and density slope for dark matter haloes: 1) arxiv 2) zenodo slides 3) paper Dark matter halo mass functions and density profiles from mass/energy cascade: 1) arxiv 2) zenodo slides 3) paper Energy cascade for distribution and evolution of supermassive black holes (SMBHs): 2) zenodo slides Condensed slides for all applications "Cascade Theory for Turbulence, Dark Matter, and bulge-SMBH evolution " The two relevant datasets and accompanying presentation can be found at: Dark matter flow dataset Part I: Halo-based statistics from cosmological N-body simulation Dark matter flow dataset Part II: Correlation-based statistics from cosmological N-body simulation. 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. Cascade and statistical theory developed by these datasets: Inverse mass cascade in dark matter flow and effects on halo mass functions: 1) arxiv 2) zenodo slides Inverse mass cascade and effects on halo deformation, energy, size, and density profiles: 1) arxiv 2) zenodo slides Inverse energy cascade in dark matter flow and effects of halo shape: 1) arxiv 2) zenodo slides The mean flow, velocity dispersion, energy transfer and evolution of dark matter halos: 1) arxiv 2) zenodo slides Two-body collapse model and generalized stable clustering hypothesis for pairwise velocity 1) arxiv 2) zenodo slides Energy, momentum, spin parameter in dark matter flow and integral constants of motion: 1) arxiv 2) zenodo slides Maximum entropy distributions of dark matter in ΛCDM cosmology: 1) arxiv 2) zenodo slides 3) paper Halo mass functions from maximum entropy distributions in dark matter flow: 1) arxiv 2) zenodo slides On the statistical theory of self-gravitating collisionless dark matter flow: 1) arxiv 2) zenodo slides 3) paper High order kinematic and dynamic relations for velocity correlations in dark matter flow: 1) arxiv 2) zenodo slides Evolution of density and velocity distributions and two-thirds law for pairwise velocity: 1) arxiv 2) zenodo slides