The origin of MOND acceleration and deep-MOND from acceleration fluctuation and energy cascade in dark matter flow

The origin of MOND acceleration and deep-MOND from acceleration fluctuation and energy cascade in dark matter flow

MOND is an empirically motivated theory using modified gravity to reproduce many astronomical observations without invoking the dark matter hypothesis. Instead of falsifying the existence of dark matter, we propose that MOND is an effective theory naturally emerging from the long-range interaction and collisionless nature of dark matter flow. It describes the dynamics of baryonic mass suspended in fluctuating dark matter fluid. To maximize system entropy, the long-range interaction requires a broad size of halos to be formed. These halos facilitate an inverse mass and energy cascade from small to large mass scales with a constant rate of energy cascade \(\varepsilon _{u} \approx -4.6\times 10^{-7} {m^{2} /s^{3}}\). In addition to velocity fluctuation with a typical scale \(u\), the long-range interaction leads to a fluctuation in acceleration with a typical scale \(a_{0}\). The velocity and acceleration fluctuations in dark matter flow satisfy \(\varepsilon _{u} =-{a_{0}u/(3\pi) ^{2}}\) that determines \(a_0\), where factor \(3\pi\) is from the angle of incidence. With \(u_{0} \equiv u(z=0)\approx 354.61{km/s}\) from N-body simulation, the value of \(a_{0} \left(z=0\right)\approx 1.2\times 10^{-10} {m/s^{2}}\) can be easily obtained and \(a_0 \propto t^{-1/2}\). While Planck constant \(\hbar\), gravitational constant \(G\), and \(\varepsilon_{u}\) are proposed to find the dark matter particle properties on the smallest scale, the velocity scale \(u\), \(G\), and \(\varepsilon_{u}\) determine the halo properties on the largest scale. For a given particle velocity \(v_{p}\), maximum entropy distributions developed for dark matter flow lead to a particle kinetic energy \(\varepsilon _{k} \propto v_{p}\) at small acceleration \(a<a_{0}\) and \(\varepsilon _{k} \propto v_{p}^{2}\) for \(a>a_{0}\). Combining this with the constant rate of energy cascade \(\varepsilon _{u}\), both Newtonian dynamics and "deep-MOND" behavior can be fully recovered. A notable (unexplained) coincidence of cosmological constant \(\Lambda \propto ({a_{0}/c})^{2}\) or a linear relation for light speed \(c=(3\pi)^3u_0\) might point to an entropic origin of dark energy from acceleration fluctuation with its density \(\rho _{vac} \propto {a_{0}^{2}/G}\).

Applications of cascade and statistical theory for dark matter and bulge-SMBH evolution:

1. Dark matter particle mass ,size, and properties from energy cascade in dark matter flow: 1) arxiv 2) zenodo slides
2. Origin of MOND acceleration & deep-MOND from acceleration fluctuation & energy cascade: 1) arxiv 2) zenodo slides
3. The baryonic-to-halo mass relation from mass and energy cascade in dark matter flow: 1) arxiv 2) zenodo slides
4. Universal scaling laws and density slope for dark matter haloes: 1) arxiv 2) zenodo slides 3) paper
5. Dark matter halo mass functions and density profiles from mass/energy cascade: 1) arxiv 2) zenodo slides 3) paper
6. 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: 

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.

Cascade and statistical theory developed by these datasets:

1. Inverse mass cascade in dark matter flow and effects on halo mass functions: 1) arxiv 2) zenodo slides 
2. Inverse mass cascade and effects on halo deformation, energy, size, and density profiles: 1) arxiv 2) zenodo slides
3. Inverse energy cascade in dark matter flow and effects of halo shape: 1) arxiv 2) zenodo slides
4. The mean flow, velocity dispersion, energy transfer and evolution of dark matter halos: 1) arxiv 2) zenodo slides
5. Two-body collapse model and generalized stable clustering hypothesis for pairwise velocity 1) arxiv 2) zenodo slides
6. Energy, momentum, spin parameter in dark matter flow and integral constants of motion: 1) arxiv 2) zenodo slides
7. Maximum entropy distributions of dark matter in ΛCDM cosmology: 1) arxiv 2) zenodo slides 3) paper
8. Halo mass functions from maximum entropy distributions in dark matter flow: 1) arxiv 2) zenodo slides
9. On the statistical theory of self-gravitating collisionless dark matter flow: 1) arxiv 2) zenodo slides 3) paper
10. High order kinematic and dynamic relations for velocity correlations in dark matter flow: 1) arxiv 2) zenodo slides
11. Evolution of density and velocity distributions and two-thirds law for pairwise velocity: 1) arxiv 2) zenodo slides