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Inverse mass cascade in dark matter flow and effects on halo deformation, energy, size, and density profiles Inverse mass cascade is a key feature of the intermediate statistically steady state for self-gravitating collisionless dark matter flow (SG-CFD). This paper focus on effects of mass cascade on halo energy, momentum, dispersion, size, and density. Halo with fast mass accretion has an expanding core. Mass cascade forms a new layer of mass that deforms the original halo and induces nonzero radial flow (outwards in core and inwards in outer regions). The inward/outward flow leads to an extra length scale (scale radius) that is not present in isothermal profile. Halo concentration c=3.5 can be derived for fast growing halos. For cusp-core controversy, a double-power-law density is proposed as a result of nonzero radial flow. The inner/outer density are controlled by halo deformation rate and halo growth, respectively. The slower deformation at center, the steeper density. For fast growing halos, radial flow at center is simply Hubble flow that leads to the existence of central core. Mass cascade leads to nonzero halo surface energy/tension and radial flow that enhances dispersion in outer region. An effective exponent of gravity ne= -1.3 (not -1) is obtained due to halo surface energy. Evolution of halo size follows a geometric Brownian motion and lognormal distribution. The Brownian motion of particles in evolving halos leads to Fokker-Planck equations for particle distribution that is dependent on the radial and osmotic flow. Complete solutions of particle distribution are presented based on a simple model of osmotic flow. The proposed model agrees with simulation for various halo group sizes. With reference pressure/density defined at center, equation of state can be established for relative pressure/density. Pressure, density, and dispersion at halo center are presented. The core size xcis obtained where Hubble flow is dominant. Simple closures are proposed for self-consistent halo density. Condensed slides for all applications "Cascade Theory for Turbulence, Dark Matter, and Supermassive Black Holes" Applicationsof cascade and statistical theory for dark matter and 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 fromacceleration 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 halos from rotation curves: 1) arxiv 2) zenodo slides A unified theory for dark matter halo mass function and density profile: 1) arxiv 2) zenodo slides Energy cascade for distribution and evolution of supermassive black holes (SMBHs): 2) zenodo slides 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_datasetandzenodo 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)arxiv2)zenodo slides Inverse mass cascade and effects on halo deformation, energy, size, and density profiles: 1) arxiv 2) zenodo slides Inverse energy cascade indark matter flow and effects of halo shape: 1) arxiv 2) zenodo slides The mean flow, velocity dispersion, energy transfer and evolution ofdark matter halos: 1) arxiv 2) zenodo slides Two-body collapse model and generalized stable clustering hypothesis for pairwise velocity1) 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 velocity, speed, and energy indark matter flow: 1) arxiv 2) zenodo slides Halo mass functions from maximum entropy distributions in dark matter flow: 1) arxiv 2) zenodo slides The statistical theory of dark matter flow for velocity, density, and potential fields: 1) arxiv 2) zenodo slides High order kinematic and dynamic relations for velocity correlations in dark matter flow: 1) arxiv 2) zenodo slides Evolution ofdensity andvelocity distributions and two-thirds law for pairwise velocity: 1) arxiv 2) zenodo slides |
