Dark matter halo mass functions and density profiles from mass and energy cascade
Abstract
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 $$$$\tau _g$$$$ . First, the inverse mass cascade from small to large scales leads to the halo random walk in mass space with $$$$\tau _g\propto m_h^{-\lambda }$$$$ , where $$$$m_h$$$$ is the halo mass and $$$$\lambda$$$$ is a halo geometry parameter with predicted value of 2/3. The corresponding Fokker-Planck solution for halo random walk in mass space gives rise to the halo mass function with a power-law behavior on small scale and exponential decay on large scale. This can be further improved by considering two different $$$$\lambda$$$$ for haloes below and above a critical mass scale $$$$m_h^*$$$$ , i.e. a double- $$$$\lambda$$$$ halo mass function. Second, a double- $$$$\gamma$$$$ density profile can be derived based on the particle random walk in 3D space with a position-dependent waiting time $$$$\tau _g \propto \Phi (r)^{-1} \propto r^{-\gamma }$$$$ , where $$$$\Phi$$$$ is the gravitational potential and r is the particle distance to halo center. Theory predicts $$$$\gamma =2/3$$$$ that leads to a cuspy density profile with an inner slope of −4/3, consistent with the predicted scaling laws from energy cascade. The Press-Schechter mass function and Einasto density profile are just special cases of proposed models. The small scale permanence can be identified due to the scale-independent rate of mass and energy cascade, where density profiles of different halo masses and redshifts converge to the $$-4/3$$ scaling law ( $$$$\rho _h \propto r^{-4/3}$$$$ ) on small scales. Theory predicts the halo number density scales with halo mass as $$$$\propto m_h^{-1.9}$$$$ , while the halo mass density scales as $$$$\propto m_h^{4/9}$$$$ . Results were compared against the Illustris simulations. This new perspective provides a theory for nearly universal halo mass functions and density profiles.
- Authors:
- Publication Date:
- Research Org.:
- Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program
- OSTI Identifier:
- 2007234
- Alternate Identifier(s):
- OSTI ID: 2280609
- Report Number(s):
- PNNL-SA-187963
Journal ID: ISSN 2045-2322; 16531; PII: 42958
- Grant/Contract Number:
- AC05-76RL01830
- Resource Type:
- Published Article
- Journal Name:
- Scientific Reports
- Additional Journal Information:
- Journal Name: Scientific Reports Journal Volume: 13 Journal Issue: 1; Journal ID: ISSN 2045-2322
- Publisher:
- Nature Publishing Group
- Country of Publication:
- United Kingdom
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; astronomy and astrophysics; dark energy and dark matter
Citation Formats
Xu, Zhijie. Dark matter halo mass functions and density profiles from mass and energy cascade. United Kingdom: N. p., 2023.
Web. doi:10.1038/s41598-023-42958-6.
Xu, Zhijie. Dark matter halo mass functions and density profiles from mass and energy cascade. United Kingdom. https://doi.org/10.1038/s41598-023-42958-6
Xu, Zhijie. Mon .
"Dark matter halo mass functions and density profiles from mass and energy cascade". United Kingdom. https://doi.org/10.1038/s41598-023-42958-6.
@article{osti_2007234,
title = {Dark matter halo mass functions and density profiles from mass and energy cascade},
author = {Xu, Zhijie},
abstractNote = {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$$ τ g . First, the inverse mass cascade from small to large scales leads to the halo random walk in mass space with $$\tau _g\propto m_h^{-\lambda }$$ τ g ∝ m h - λ , where $$m_h$$ m h is the halo mass and $$\lambda$$ λ is a halo geometry parameter with predicted value of 2/3. The corresponding Fokker-Planck solution for halo random walk in mass space gives rise to the halo mass function with a power-law behavior on small scale and exponential decay on large scale. This can be further improved by considering two different $$\lambda$$ λ for haloes below and above a critical mass scale $$m_h^*$$ m h ∗ , i.e. a double- $$\lambda$$ λ halo mass function. Second, a double- $$\gamma$$ γ density profile can be derived based on the particle random walk in 3D space with a position-dependent waiting time $$\tau _g \propto \Phi (r)^{-1} \propto r^{-\gamma }$$ τ g ∝ Φ ( r ) - 1 ∝ r - γ , where $$\Phi$$ Φ is the gravitational potential and r is the particle distance to halo center. Theory predicts $$\gamma =2/3$$ γ = 2 / 3 that leads to a cuspy density profile with an inner slope of −4/3, consistent with the predicted scaling laws from energy cascade. The Press-Schechter mass function and Einasto density profile are just special cases of proposed models. The small scale permanence can be identified due to the scale-independent rate of mass and energy cascade, where density profiles of different halo masses and redshifts converge to the $$-4/3$$ - 4 / 3 scaling law ( $$\rho _h \propto r^{-4/3}$$ ρ h ∝ r - 4 / 3 ) on small scales. Theory predicts the halo number density scales with halo mass as $$\propto m_h^{-1.9}$$ ∝ m h - 1.9 , while the halo mass density scales as $$\propto m_h^{4/9}$$ ∝ 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.},
doi = {10.1038/s41598-023-42958-6},
journal = {Scientific Reports},
number = 1,
volume = 13,
place = {United Kingdom},
year = {Mon Oct 02 00:00:00 EDT 2023},
month = {Mon Oct 02 00:00:00 EDT 2023}
}
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