2021/09/21 by Zhijie Xu, Xu, Zhijie
Physics and Astronomy · #Galaxies: Formation, Evolution, Phenomena #Cosmology and Gravitation Theories #Advanced Thermodynamics and Statistical Mechanics
paper · pdf · doi:10.48550/arxiv.2109.09985
Between the linear and nonlinear regimes, we identify a universal transition range centered on a characteristic halo mass mh^*∝ 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 mh^* 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 τg∝ mh-λ; A Fokker-Planck equation gives mass function fM∝ mh-λ and λ=2/3 for the gravity-dominant transition range. Locally, a radially directed cascade governs particle migration with waiting time τgr∝ r-γ, yielding density ρr∝ r-2γ and γ=2/3 on scales near mh^*. 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 εu ≈ -10-7m2/s3, a direct potential-energy cascade of -1.4εu, and a net dissipation of -0.4εu via halo mergers and particle migration. The dependence of waiting time and step length on the particle mass suggests new constraints near 1012GeV.