Universal spectrum and scaling laws for halo mass function, structure, and dark matter mass constraints
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arXiv
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2021
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| _version_ | 1866917114594459648 |
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| author | Xu, Zhijie |
| author_facet | Xu, Zhijie |
| contents | Between the linear and nonlinear regimes, we identify a universal transition range centered on a characteristic halo mass $m_h^*\propto t$, within which gravitational dynamics self-organize the matter field toward an effective spectral index n=-1. In a bottom-up hierarchy, early collapse of low-mass halos preserves imprints of the primordial spectrum, whereas prolonged assembly of halos near $m_h^*$ erases that memory and establishes universality. We formulate a scale-to-scale cascade, the redistribution of mass and energy across scales, that yields universal scaling laws for the halo mass function and internal structure. Globally, the cascade drives a random walk of halos with mass-dependent waiting time $τ_g\propto m_h^{-λ}$; A Fokker-Planck equation gives mass function $f_M\propto m_h^{-λ}$ and $λ=2/3$ for the gravity-dominant transition range. Locally, a radially directed cascade governs particle migration with waiting time $τ_{gr}\propto r^{-γ}$, yielding density $ρ_r\propto r^{-2γ}$ and $γ=2/3$ on scales near $m_h^*$. The cascade drives the system toward a statistically steady state that continuously releases energy and maximizes entropy, characterized by scale-independent rates, preventing mass or energy buildup at intermediate scales. Scale-dependent dominance of the primordial spectrum versus gravity implies two effective exponents, producing double-$λ$ mass functions and double-$γ$ density in excellent agreement with simulations. Using Illustris and Virgo, we measure an inverse kinetic-energy cascade from small to large scales at $\varepsilon_u \approx -10^{-7}$m$^2$/s$^3$, a direct potential-energy cascade of $-1.4\varepsilon_u$, and a net dissipation of -0.4$\varepsilon_u$ via halo mergers and particle migration. The dependence of waiting time and step length on the particle mass suggests new constraints near $10^{12}$GeV. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_09985 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Universal spectrum and scaling laws for halo mass function, structure, and dark matter mass constraints Xu, Zhijie Cosmology and Nongalactic Astrophysics Astrophysics of Galaxies Fluid Dynamics Between the linear and nonlinear regimes, we identify a universal transition range centered on a characteristic halo mass $m_h^*\propto t$, within which gravitational dynamics self-organize the matter field toward an effective spectral index n=-1. In a bottom-up hierarchy, early collapse of low-mass halos preserves imprints of the primordial spectrum, whereas prolonged assembly of halos near $m_h^*$ erases that memory and establishes universality. We formulate a scale-to-scale cascade, the redistribution of mass and energy across scales, that yields universal scaling laws for the halo mass function and internal structure. Globally, the cascade drives a random walk of halos with mass-dependent waiting time $τ_g\propto m_h^{-λ}$; A Fokker-Planck equation gives mass function $f_M\propto m_h^{-λ}$ and $λ=2/3$ for the gravity-dominant transition range. Locally, a radially directed cascade governs particle migration with waiting time $τ_{gr}\propto r^{-γ}$, yielding density $ρ_r\propto r^{-2γ}$ and $γ=2/3$ on scales near $m_h^*$. The cascade drives the system toward a statistically steady state that continuously releases energy and maximizes entropy, characterized by scale-independent rates, preventing mass or energy buildup at intermediate scales. Scale-dependent dominance of the primordial spectrum versus gravity implies two effective exponents, producing double-$λ$ mass functions and double-$γ$ density in excellent agreement with simulations. Using Illustris and Virgo, we measure an inverse kinetic-energy cascade from small to large scales at $\varepsilon_u \approx -10^{-7}$m$^2$/s$^3$, a direct potential-energy cascade of $-1.4\varepsilon_u$, and a net dissipation of -0.4$\varepsilon_u$ via halo mergers and particle migration. The dependence of waiting time and step length on the particle mass suggests new constraints near $10^{12}$GeV. |
| title | Universal spectrum and scaling laws for halo mass function, structure, and dark matter mass constraints |
| topic | Cosmology and Nongalactic Astrophysics Astrophysics of Galaxies Fluid Dynamics |
| url | https://arxiv.org/abs/2109.09985 |