Dark matter properties from rotation curves and energy cascade: AAS 241st Meeting  2023 Jan Seattle
Creators: name: Xu, Zhijie (Jay)
Publisher: name: Zenodo
Year: 2023
Subjects: cosmology
Galaxy rotation curve
dark matter
astrophysics
energy cascade
scaling laws
dark matter halo

description: After years of null results in the search for dark matter, the biggest mystery of contemporary physics, a different prospective might be required beyond the standard WIMP paradigm. We present a new approach to estimate dark matter particle mass, size, density, and many other properties based on a cascade theory for the flow of dark matter, similar to the cascade in hydrodynamic turbulence. The energy cascade from small to large scales with a constant rate εu≈-4.6x10-7m2/s3 is a fundamental feature of dark matter flow. Energy cascade leads to a two-thirds law for kinetic energy vr2 ≈(εur)2/3 on scale r, as confirmed by N-body simulations. This is equivalent to a four-thirds law for mean halo density ρs enclosed in the halo scale radius rs such that ρs ≈εu2/3G-1rs-4/3, as confirmed by the data from galaxy rotation curves. By identifying key constants on relevant scales, properties of dark matter might be obtained. The smallest length scale in dark matter flow is dependent on the nature of dark matter. For collisionless dark matter, particle mass is estimated to be mX≈(-εuh5G4)1/9≈1012GeV with a size of rη ≈(-εuhG)1/3≈10-13m, where h is the Planck constant. An uncertainty principle for momentum and acceleration fluctuations is also postulated to explain the physical origin of the rate of energy cascade εu. For self-interacting dark matter, the smallest structure has a sale rη ≈εu2G-3(σ/m)3, where σ/m is the cross-section. On halo scale, the energy cascade leads to an asymptotic density slope γ=-4/3 for fully virialized halos with a vanishing radial flow, which might explain the nearly universal halo density. Based on the continuity equation, halo density is analytically shown to be closely dependent on the radial flow and mass accretion such that simulated halos can have different limiting slopes. A modified Einasto density profile is proposed accordingly. Accompanying slides and datasets for this work can be found at https://doi.org/10.5281/zenodo.6569901.


 


Here are some applications of the cascade theory:


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