Papers › Evolution of energy, momentum, and spin parameter in dark matter flow and integral...
Evolution of energy, momentum, and spin parameter in dark matter flow and integral constants of motion
Zhijie Xu
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
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 P_y=-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∝a^(3/2) and angular momentum H∝a^(5/2), 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 ∝a^(3/2) 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 $m$th 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.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections