The Arrow of Time in the collapse of collisionless self-gravitating systems: non-validity of the Vlasov-Poisson equation during violent relaxation

Abstract

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.

26 pages, 15 figures - Significant changes in the Fokker-Planck description of the long-term evolution - Accepted by ApJ

References in corpus (7)

• An adaptively refined phase-space element method for cosmological simulations and collisionless dynamics
• A new Monte Carlo method for dynamical evolution of non-spherical stellar systems
• The Vlasov-Poisson dynamics as the mean field limit of extended charges
• Phase-space structures I: A comparison of 6D density estimators
• Vlasov versus N-body: the Hénon sphere
• Relaxation in N-body simulations of spherical systems
• Statistical mechanics of self-gravitating systems: mixing as a criterion for indistinguishability

Cited by in corpus (14)

• AGAMA: Action-based galaxy modelling architecture
• Phase-space structure of protohalos: Vlasov versus Particle-Mesh
• Collisionless relaxation of a Lynden-Bell plasma
• Generalized entropy production in collisionless plasma flows and turbulence
• The discreteness-driven relaxation of collisionless gravitating systems: entropy evolution and the Nyquist-Shannon theorem
• Resonant and non-resonant relaxation of globular clusters
• Eccentricity dynamics of wide binaries -- I. The effect of Galactic tides
• The discreteness-driven relaxation of collisionless gravitating systems: entropy evolution in external potentials, N-dependence and the role of chaos
• Phase-space structure analysis of self-gravitating collisionless spherical systems
• Entropy production and Vlasov equation for self-gravitating systems
• A Galactic Transformation -- Understanding the SMC's Structural and Kinematic Disequilibrium
• Dimensional measures of generalized entropy
• Minimum-entropy constraints on galactic potentials
• Chaos in violent relaxation dynamics. Disentangling micro- and macro-chaos in numerical experiments of dissipationless collapse