The Discreteness-driven Relaxation of Collisionless Gravitating Systems: Entropy Evolution in External Potentials, N-dependence, and the Role of Chaos

Autor(es)

Beraldo e Silva, Leandro ^{[1, 2]} ; Pedra, Walter de Siqueira ^[3] ; Valluri, Monica ^[1] ; Sodre, Laerte ^[2] ; Bru, Jean-Bernard ^{[4, 5, 6]}

Afiliação do(s) autor(es)

^[1] Univ Michigan, Dept Astron, Ann Arbor, MI 48109 - USA

^[2] Univ Sao Paulo, Inst Astron Geofis & Ciencias Atmosfer, Dept Astron, BR-05508090 Sao Paulo, SP - Brazil

^[3] Univ Sao Paulo, Inst Fis, Dept Fis Matemat, CP 66318, BR-05314970 Sao Paulo, SP - Brazil

^[4] Univ Basque Country, Fac Ciencia & Tecnol, Dept Matemat, Apartado 644, E-48080 Bilbao - Spain

^[5] BCAM, Mazarredo 14, E-48009 Bilbao - Spain

^[6] Basque Fdn Sci, IKERBASQUE, E-48011 Bilbao - Spain

• Tipo de documento: Artigo Científico
• Fonte: ASTROPHYSICAL JOURNAL; v. 870, n. 2 JAN 10 2019.
• Citações Web of Science: 0

Resumo

We investigate the old problem of the fast relaxation of collisionless N-body systems that are collapsing or perturbed, emphasizing the importance of (noncollisional) discreteness effects. We integrate orbit ensembles in fixed potentials, estimating the entropy to analyze the time evolution of the distribution function. These estimates capture the correct physical behavior expected from the second law of thermodynamics, without any spurious entropy production. For self-consistent (i.e., stationary) samples, the entropy is conserved, while for non-self-consistent samples, it increases within a few dynamical times, stabilizing at a maximum (even in integrable potentials). Our results make transparent that the main ingredient for this fast collisionless relaxation is the discreteness (finite N) of gravitational systems in any potential. Additionally, in nonintegrable potentials, the presence of chaotic orbits accelerates the entropy production. Contrary to the traditional violent relaxation scenario, our results indicate that a time-dependent potential is not necessary for this relaxation. For the first time, in connection with the Nyquist-Shannon theorem, we derive the typical timescale T / tau(cr) approximate to 0.1N(1/6) for this discreteness-driven relaxation, with slightly weaker N-dependencies for nonintegrable potentials with substantial fractions of chaotic orbits. This timescale is much smaller than the collisional relaxation time even for small-N systems such as open clusters and represents an upper limit for the relaxation time of real N-body collisionless systems. Additionally, our results reinforce the conclusion of Beraldo e Silva et al. that the Vlasov equation does not provide an adequate kinetic description of the fast relaxation of collapsing collisionless 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: 17/22340-9 - Métodos construtivos para férmions interagentes com aplicações a teoria microscópica da condutividade e supercondutividade
• Beneficiário: Walter Alberto de Siqueira Pedra
• Linha de fomento: Auxílio à Pesquisa - Pesquisador Visitante - Internacional