2021/10/19 by Zhijie Xu, Xu, Zhijie
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Astrophysics of Galaxies (astro-ph.GA) #Cosmology and Gravitation Theories #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Galaxies: Formation, Evolution, Phenomena
paper · pdf · doi:10.48550/arxiv.2110.09676
openalex publication_date 2021/10/19 · openalex created_date 2022/07/13 · openalex updated_date 2026/07/28
The halo-mediated inverse mass cascade is a key feature of the intermediate statistically steady state for self-gravitating collisionless dark matter flow (SG-CFD). A broad spectrum of halos and halo groups are necessary to form from inverse mass cascade for long-range interaction system to maximize its entropy. The limiting velocity (\textbf X), speed (\textbf Z), and energy (\textbf E) distributions of collisionless particles can be obtained analytically from a maximum entropy principle. Halo mass function, the distribution of total mass in halos, is a fundamental quantity for structure formation and evolution. Instead of basing mass functions on simplified spherical/elliptical collapse models, it is possible to reformulate mass function as an intrinsic distribution to maximize system entropy during the everlasting statistically steady state. Starting from halo-based description of non-equilibrium dark matter flow, distributions of particle virial dispersion (\textbf H), square of particle velocity (\textbf P), and number of halos (\textbf J) are proposed. Their statistical properties and connections with velocity distribution (\textbf X) are well studied and established. With \textbf H being essentially the halo mass function, two limiting cases of \textbf H distribution are analyzed for large halos (\textbf H_∞) and small halos (\textbf Hs), respectively. For large halos, \textbf H_∞ is shown to also be a maximum entropy distribution. For small halos, \textbf Hs approximates the \textbf P distribution and recovers the Press-Schechter mass function. The full solution of \textbf H distribution is determined by the velocity distribution (\textbf X) that maximizes system entropy and the exact model of halo velocity dispersion.