The Arrow of Time in the Collapse of Collisionless Self-gravitating Systems: Non-validity of the Vlasov-Poisson Equation during Violent Relaxation

Autor(es)

Beraldo e Silva, Leandro ; Pedra, Walter de Siqueira ; Sodre, Laerte ; Perico, Eder L. D. ; Lima, Marcos

• Tipo de documento: Artigo Científico
• Fonte: ASTROPHYSICAL JOURNAL; v. 846, n. 2 SEP 10 2017.
• Citações Web of Science: 1

Resumo

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 equation, 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 two-body relaxation timescale 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. (AU)

• Processo FAPESP: 14/23751-4 - Dinâmica e mecânica estatística de halos de matéria escura
• Beneficiário: Leandro José Beraldo e Silva
• Linha de fomento: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 09/54006-4 - Um cluster de computadores para o Departamento de Astronomia do IAG-USP e para o Núcleo de Astrofísica da UNICSUL
• Beneficiário: Elisabete Maria de Gouveia Dal Pino
• Linha de fomento: Auxílio à Pesquisa - Programa Equipamentos Multiusuários
• Processo FAPESP: 16/02503-8 - Comportamento macroscópico de sistemas de férmions não relativísticos interagentes
• Beneficiário: Walter Alberto de Siqueira Pedra
• Linha de fomento: Bolsas no Exterior - Pesquisa
• Processo FAPESP: 12/00800-4 - O universo em 3-D: astrofísica com grandes levantamentos de galáxias
• Beneficiário: Laerte Sodré Junior
• Linha de fomento: Auxílio à Pesquisa - Temático
• Processo FAPESP: 12/16835-1 - A aceleração cósmica e o Dark Energy Survey
• Beneficiário: Marcos Vinicius Borges Teixeira Lima
• Linha de fomento: Auxílio à Pesquisa - Regular