The baryonic-to-halo mass relation from mass and energy cascade in self-gravitating collisionless dark matter flow

The baryonic-to-halo mass relation from mass and energy cascade in dark matter flow

The relation between properties of galaxies and dark matter (DM) halos they reside in can be valuable to understand the structure formation and evolution. In particular, the baryonic-to-halo mass ratio (BHMR) and its evolution may provide many important insights. We first review unique properties of self-gravitating collisionless dark matter flow (SG-CFD), followed by their applications in deriving BHMR. 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 scales that involves a constant rate of energy cascade \(\varepsilon_u \approx -4.6\times 10^{-7} m^2/s^3\). The mass and energy cascade represent an intermediate statistically steady state of dark matter flow. In addition, dark matter flow exhibits scale-dependent flow behaviors that is incompressible on small scale and irrotational on large scale. Considering a given halo with a total baryonic mass \(m_b\), halo mass \(m_h\), halo virial size \(r_h\), and flat rotation speed \(v_f\), the baryonic-to-halo mass relation can be analytically derived by combining the baryonic Tully-Fisher relation and the rate of energy cascade \(\varepsilon_u\) in small and large halos. We found a maximum BHMR ratio ~0.076 for halos with a critical mass \(m_{hc}\sim 10^{12}M_{sun}\) at z=0. That ratio is much lower for both smaller and larger halos such that two regimes can be identified: i) for incompressible small halos with mass \(m_h<m_{hc}\), we have \(\varepsilon_u \propto v_f/r_h\), \(v_f \propto r_h\), and \(m_b \propto \left(m_{h} \right)^{{4/3} } \); ii) for large halos with mass \(m_h>m_{hc}\), we have \(\varepsilon_u \propto {v_f^3/r_h}\), \(v_f\propto r_h^{1/3}\), and \(m_b\propto(m_h)^{4/9}\). Combined with double-\(\lambda\) halo mass function, the average BHMR ratio in all halos (~0.024 at z=0) can be analytically derived, along with its redshift evolution. The fraction of total baryons in all galaxies is ~7.6% at z=0 and increases with time \(\propto t^{1/3}\). The SPARC (Spitzer Photometry & Accurate Rotation Curves) data with 175 late-type galaxies were used for derivation and comparison. 

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