Dark matter halo mass functions and density profiles from mass and energy cascade

Abstract

Without relying on a spherical or ellipsoidal collapse model, we analytically derive the halo mass function and cuspy halo density (inner slope of -4/3) based on the mass and energy cascade theory in dark matter flow. The hierarchical halo structure formation leads to halo or particle random walk with a position-dependent waiting time ${\tau }_g$. The inverse mass cascade from small to large scales leads to the halo random walk in mass space with ${\tau }_g\propto m_h^{-\lambda }$, where $m_h$ is the halo mass and $\lambda$ is a halo geometry parameter with predicted value of 2/3. The corresponding Fokker-Planck solution for halo random walk in mass space gives rise to the halo mass function with a power-law behavior on small scale and exponential decay on large scale. This can be further improved by considering two different $\lambda$ for haloes below and above a critical mass scale $m_h^{\ast }$, i.e. a double-$\lambda$ halo mass function. A double-$\gamma$ density profile can be derived based on the particle random walk in 3D space with a position-dependent waiting time ${\tau }_g\propto \Phi (r{)}^{-1}\propto r^{-\gamma }$, where $\Phi$ is the gravitational potential and $r$ is the particle distance to halo center. Theory predicts $\gamma =2/3$ that leads to a cuspy density profile with an inner slope of -4/3, consistent with the predicted scaling laws from energy cascade. The Press-Schechter mass function and Einasto density profile are special cases of proposed models. The small scale permanence can be identified due to the scale-independent rates of mass and energy cascade, where density profiles of different halo masses and redshifts converge to the $-4/3$ scaling law (${\rho }_h\propto r^{-4/3}$) on small scales. Theory predicts halo number density scales with mass as $\propto m_h^{-1.9}$, while halo mass density scales as $\propto m_h^{4/9}$. Results were compared against the Illustris simulations.

14 pages 20 figures

References in corpus (11)

• Too big to fail? The puzzling darkness of massive Milky Way subhaloes
• Dark matter and cosmic structure
• The Halo Mass Function: High-Redshift Evolution and Universality
• Excursion Set Halo Mass Function and Bias in a Stochastic Barrier Model of Ellipsoidal Collapse
• Amplified J-factors in the Galactic Center for velocity-dependent darkmatter annihilation in FIRE simulations
• Universal scaling laws and density slope for dark matter haloes
• Maximum entropy distributions of dark matter in $\Lambda$CDM cosmology
• On the statistical theory of self-gravitating collisionless dark matter flow
• Universal spectrum and scaling laws for halo mass function, structure, and dark matter mass constraints
• Cold freeze out of superheavy dark matter and Hubble tension
• Inverse energy cascade in self-gravitating collisionless dark matter flow and effects of halo shape

Cited by in corpus (6)

• cp3-bench: A tool for benchmarking symbolic regression algorithms tested with cosmology
• On the statistical theory of self-gravitating collisionless dark matter flow: Scale and redshift variation of velocity and density distributions
• On the statistical theory of self-gravitating collisionless dark matter flow: high order kinematic and dynamic relations
• Cosmic quenching and scaling laws for the evolution of supermassive black holes and host galaxies
• Distinguishing thermal histories of dark matter from structure formation
• On a critical acceleration scale of dark matter in Lambda-CDM and dynamical dark energy