The Arrow of Time in the collapse of collisionless self-gravitating systems: non-validity of the Vlasov-Poisson equation during violent relaxation
| Autor: | E. L. D. Perico, Laerte Sodré, Walter de Siqueira Pedra, Leandro Beraldo e Silva, Marcos Lima |
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| Rok vydání: | 2017 |
| Předmět: |
Physics
Logarithm 010308 nuclear & particles physics FOS: Physical sciences Astronomy and Astrophysics GALÁXIAS Astrophysics Astrophysics - Astrophysics of Galaxies 01 natural sciences Distribution function Space and Planetary Science Stellar dynamics Arrow of time Astrophysics of Galaxies (astro-ph.GA) 0103 physical sciences Coulomb Entropy (information theory) Statistical physics Poisson's equation 010303 astronomy & astrophysics Softening |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| DOI: | 10.48550/arxiv.1703.07363 |
| Popis: | The collapse of a collisionless self-gravitating system, with the fast achievement of a quasi-stationary state, is driven by violent relaxation, with a typical particle interacting with the time-changing collective potential. It is traditionally assumed that this evolution is governed by the Vlasov-Poisson equation, in which case entropy must be conserved. We run N-body simulations of isolated self-gravitating systems, using three simulation codes: NBODY-6 (direct summation without softening), NBODY-2 (direct summation with softening) and GADGET-2 (tree code with softening), for different numbers of particles and initial conditions. At each snapshot, we estimate the Shannon entropy of the distribution function with three different techniques: Kernel, Nearest Neighbor and EnBiD. For all simulation codes and estimators, the entropy evolution converges to the same limit as N increases. During violent relaxation, the entropy has a fast increase followed by damping oscillations, indicating that violent relaxation must be described by a kinetic equation other than the Vlasov-Poisson, even for N as large as that of astronomical structures. This indicates that violent relaxation cannot be described by a time-reversible equation, shedding some light on the so-called "fundamental paradox of stellar dynamics". The long-term evolution is well described by the orbit-averaged Fokker-Planck model, with Coulomb logarithm values in the expected range 10-12. By means of NBODY-2, we also study the dependence of the 2-body relaxation time-scale on the softening length. The approach presented in the current work can potentially provide a general method for testing any kinetic equation intended to describe the macroscopic evolution of N-body systems. Comment: 26 pages, 15 figures - Significant changes in the Fokker-Planck description of the long-term evolution - Accepted by ApJ |
| Databáze: | OpenAIRE |
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