Super-Eddington growth of supermassive black holes and scaling laws for SMBH-host coevolution

Observations suggest a coevolution of supermassive black holes (SMBHs) and host galaxies. In this paper, we consider the mass and energy flow in a near-equilibrium bulge suffused by gases of varying temperatures. By assuming the rate of energy flow independent of the distance from the bulge center and the virial equilibrium for permeated gases, a key parameter $\varepsilon_b$ was identified that quantifies the mass and energy flow in gases and the efficiency of gas cooling and thus regulates the coevolution of both SMBHs and hosts. With the help of Illustris simulations and observations, we determined the redshift variation $\varepsilon_b\propto (1+z)^{5/2}$. A higher $\varepsilon_b$ in the early universe means a more efficient gas cooling that allows rapid evolution of SMBHs and hosts. This simple theory, characterized by a single parameter $\varepsilon_b$, provides the dominant mean cosmic evolution of SMBHs and hosts. All other transient phenomena may only contribute to the dispersion around this mean evolution. Based on this theory and relevant assumptions, scaling laws involving $\varepsilon_b$ were identified for the evolution of SMBHs and hosts. For host galaxies, the mass-size relation $M_b\propto \varepsilon_b^{2/3}r_b^{5/3}G^{-1}$, dispersion-size relation $\sigma_b^2\propto(\varepsilon_b r_b)^{2/3}\propto (1+z)$, or the mass-dispersion relation $M_b\propto \varepsilon_b^{-1}G^{-1}\sigma_b^5$ were identified, where $r_b\propto (1+z)^{-1}$ is the bulge size. For SMBHs, three evolution phases were found involving an initial rapid growth stage with a rising luminosity $L_B\propto (\varepsilon_b M_{BH})^{4/5}$, a transition stage with a declining $L_B\propto \varepsilon_b^2 M_{BH} \propto (1+z)^5$, and a dormant stage with $L_B\propto (\varepsilon_b M_{BH})^{4/3}$. Our results suggest a rapid initial super-Eddington growth in a short period with a new redshift-dependent luminosity limit $L_X\propto\varepsilon_b^{4/5}M_{BH}^{4/5}G^{-1/5}c$, in contrast to the Eddington limit. Analytical solutions were formulated for the BH mass function $\Phi_{BH}$, AGN mass function $\Phi_{AGN}$, and duty cycle $U$ that predict $\Phi_L\propto L^{-1/5}$ for the faint-end luminosity function, $\Phi_{AGN}\propto M^{-1/5}$ for small-mass-end AGN mass function $\Phi_L$, and $U\propto M^{-1/5}$ at high redshift. 

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
2. Cosmic quenching and scaling laws for the evolution of supermassive black holes and host galaxies: 1) arXiv 2) zonodo 3) paper
3. Origin of MOND acceleration & deep-MOND from acceleration fluctuation & energy cascade: 1) arXiv 2) zenodo
4. The baryonic-to-halo mass relation from mass and energy cascade in dark matter flow: 1) arXiv 2) zenodo
5. Universal scaling laws and density slope for dark matter haloes: 1) arXiv 2) zenodo 3) paper
6. Dark matter halo mass functions and density profiles from mass/energy cascade: 1) arXiv 2) zenodo 3) paper
7. Energy cascade for distribution and evolution of supermassive black holes (SMBHs): 2) zenodo

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 is 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 3) 
    paper
11. Evolution of density and velocity distributions and two-thirds law for pairwise velocity: 1) arXiv 2) zenodo slides 3) paper