Details

Autor(en) / Beteiligte

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

Titel

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

Ist Teil von

• The Astrophysical journal, 2017-09, Vol.846 (2), p.125

Ort / Verlag

Philadelphia: The American Astronomical Society

Erscheinungsjahr

2017

Link zum Volltext

Quelle

EZB Electronic Journals Library

Beschreibungen/Notizen

• 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.