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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Beraldo e Silva, Leandro ; Pedra, Walter de Siqueira ; Sodre, Laerte ; Perico, Eder L. D. ; Lima, Marcos
Total Authors: 5
Document type: Journal article
Source: ASTROPHYSICAL JOURNAL; v. 846, n. 2 SEP 10 2017.
Web of Science Citations: 1

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)

FAPESP's process: 12/00800-4 - The 3-D universe: astrophysics with large galaxy surveys
Grantee:Laerte Sodré Junior
Support type: Research Projects - Thematic Grants
FAPESP's process: 09/54006-4 - A computer cluster for the Astronomy Department of the University of São Paulo Institute of Astronomy, Geophysics and Atmospheric Sciences and for the Cruzeiro do Sul University Astrophysics Center
Grantee:Elisabete Maria de Gouveia Dal Pino
Support type: Multi-user Equipment Program
FAPESP's process: 14/23751-4 - Dynamics and Statistical Mechanics of dark matter halos
Grantee:Leandro José Beraldo e Silva
Support type: Scholarships in Brazil - Post-Doctorate
FAPESP's process: 12/16835-1 - Cosmic acceleration and the dark energy survey
Grantee:Marcos Vinicius Borges Teixeira Lima
Support type: Regular Research Grants
FAPESP's process: 16/02503-8 - Macroscopic behavior of non-relativistic interacting many fermion systems
Grantee:Walter Alberto de Siqueira Pedra
Support type: Scholarships abroad - Research