Predicting dark matter particle mass and properties from two-thirds law and energy cascade in dark matter flow

Predicting dark matter particle mass and properties from two-thirds law and energy cascade in dark matter flow

Dark matter can be characterized by the mass and size of its smallest constituents, which are challenging to be directly probed and detected. After years of null results in the search for thermal WIMPs, a different prospective might be required beyond the standard WIMP paradigm. We present a new approach to estimate the dark matter particle mass, size, density, and many other relevant properties based on the nature of flow of dark matter. A comparison with hydrodynamic turbulence is presented to reveal the unique features of self-gravitating collisionless dark matter flow, i.e. an inverse mass and energy cascade from small to large scales with a scale-independent rate of energy cascade \(\varepsilon_u\approx -4.6\times 10^{-7}m^2/s^3\). For the simplest case with only gravitational interaction involved and in the absence of viscosity in flow, the energy cascade leads to a two-thirds law for pairwise velocity that can be extended down to the smallest scale, where quantum effects become important. Combining the rate of energy cascade \(\varepsilon_u\), the Planck constant \(\hbar\), and the gravitational constant \(G\) on the smallest scale, the mass of dark matter particles is found to be around \(0.9\times10^{12}GeV\) with a size around \(3\times10^{-13}m\). Since the mass scale \(m_X\) is only weakly dependent on \(\varepsilon_u\) as \(m_X \propto (-\varepsilon_u\hbar^5/G^4)^{1/9}\), the estimation of \(m_X\) should be pretty robust for a wide range of possible values of \(\varepsilon_u\). If gravity is the only interaction and dark matter is fully collisionless, mass of around \(10^{12}GeV\) is required to produce the given rate of energy cascade \(\varepsilon_u\). In other words, if mass has a different value, there must be some new interaction beyond gravity. This work strongly suggests a heavy dark matter scenario produced in the early universe (\(\sim 10^{-14}s\)) with a mass much greater than WIMPs. Potential extension to self-interacting dark matter is also presented.

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