2022/02/08 by Zhijie Xu, Xu, Zhijie
Physics and Astronomy · #Astronomy and Astrophysical Research #Astrophysics of Galaxies (astro-ph.GA) #Cosmology and Gravitation Theories #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #Galaxies: Formation, Evolution, Phenomena #Stellar, planetary, and galactic studies
paper · pdf · doi:10.48550/arxiv.2202.04054
openalex publication_date 2022/02/08 · openalex created_date 2022/07/23 · openalex updated_date 2026/08/01
N-body equations of motion in comoving system and expanding background are reformulated in a transformed system with static background and fixed damping. The energy and momentum evolution in dark matter flow are rigorously formulated for both systems. The energy evolution in transformed system has a simple form that is identical to the damped harmonic oscillator. The cosmic energy equation can be easily derived in both systems. For entire N-body system, 1) combined with the two-body collapse model (TBCM), kinetic and potential energy increase linearly with time t such that Kp=εut and Py=-7εut/5, where εu is a constant rate of energy cascade; 2) an effective gravitational potential exponent ne=-10/7≠-1 (ne=-1.38 from simulation) can be identified due to surface energy of fast growing halos; 3) the radial momentum G∝ a3/2 and angular momentum H∝ a5/2, where a is the scale factor. On halo scale, 1) halo kinetic and potential energy can be modelled by two dimensionless constants αs^* and βs^*. Both constants are independent of time and halo mass; 2) both halo radial and angular momentum ∝ a3/2 and can be modeled by two mass-dependent coefficients τs^* and ηs^*; 3) halo spin parameter is determined by αs^* and ηs^* and decreases with halo mass with derived values of 0.09 and 0.031 for small and large halos. Finally, the radial and angular momentum are closely related to the integral constants of motion Im, i.e. the integral of velocity correlation or the mth derivative of energy spectrum at long wavelength limit. On large scale, angular momentum is negligible, I2=0 reflects the conservation of linear momentum, while I4 reflects the fluctuation of radial momentum G. On halo scale, I4 is determined by both momentum that are comparable with each other.