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

Journal Article · 02 October 2023 · Scientific Reports

DOI: https://doi.org/10.1038/s41598-023-42958-6 · OSTI ID:2007234

Xu, Zhijie

Abstract Halo abundance and structure play a central role for modeling structure formation and evolution. 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 $$$$\tau _g$$$$ ${\tau }_g$ . First, the inverse mass cascade from small to large scales leads to the halo random walk in mass space with $$$$\tau _g\propto m_h^{-\lambda }$$$$ ${\tau }_g\propto m_h^{-\lambda }$ , where $$$$m_h$$$$ $m_h$ is the halo mass and $$$$\lambda$$$$ $\lambda$ is a halo geometry parameter with predicted value of 2/3. The corresponding Fokker-Planck solution for halo random walk in mass space gives rise to the halo mass function with a power-law behavior on small scale and exponential decay on large scale. This can be further improved by considering two different $$$$\lambda$$$$ $\lambda$ for haloes below and above a critical mass scale $$$$m_h^*$$$$ $m_h^{\ast }$ , i.e. a double- $$$$\lambda$$$$ $\lambda$ halo mass function. Second, a double- $$$$\gamma$$$$ $\gamma$ density profile can be derived based on the particle random walk in 3D space with a position-dependent waiting time $$$$\tau _g \propto \Phi (r)^{-1} \propto r^{-\gamma }$$$$ ${\tau }_g\propto \Phi {\left(r\right)}^{-1}\propto r^{-\gamma }$ , where $$$$\Phi$$$$ $\Phi$ is the gravitational potential and r is the particle distance to halo center. Theory predicts $$$$\gamma =2/3$$$$ $\gamma =2/3$ that leads to a cuspy density profile with an inner slope of −4/3, consistent with the predicted scaling laws from energy cascade. The Press-Schechter mass function and Einasto density profile are just special cases of proposed models. The small scale permanence can be identified due to the scale-independent rate of mass and energy cascade, where density profiles of different halo masses and redshifts converge to the $$-4/3$$ $-4/3$ scaling law ( $$$$\rho _h \propto r^{-4/3}$$$$ ${\rho }_h\propto r^{-4/3}$ ) on small scales. Theory predicts the halo number density scales with halo mass as $$$$\propto m_h^{-1.9}$$$$ $\propto m_h^{-1.9}$ , while the halo mass density scales as $$$$\propto m_h^{4/9}$$$$ $\propto m_h^{4/9}$ . Results were compared against the Illustris simulations. This new perspective provides a theory for nearly universal halo mass functions and density profiles.

• Sponsoring Organization: USDOE
• Grant/Contract Number: AC05-76RL01830
• OSTI ID: 2007234
• Journal Information: Scientific Reports, Journal Name: Scientific Reports Journal Issue: 1 Vol. 13; ISSN 2045-2322
• Publisher: Nature Publishing GroupCopyright Statement
• Country of Publication: United Kingdom
• Language: English