Antonov problem and quasi-equilibrium states in N-body system

Abstract

In this paper, a quantitative characterization for the evolutionary sequence of stellar self-gravitating system is investigated, focusing on the pre-collapse stage of the long-term dynamical evolution. In particular, we consider the quasi-equilibrium behaviors of the N-body systems in the setup of the so-called Antonov problem, i.e., self-gravitating N-body system confined in an adiabatic wall and try to seek a possible connection with thermostatistics of self-gravitating systems. For this purpose, a series of long-term N-body simulations with various initial conditions are performed. We found that a quasi-equilibrium sequence away from the thermal equilibrium can be characterized by the one-parameter family of the stellar models. Especially, the stellar polytropic distribution satisfying the effective equation of state $P\propto {\rho }^{1+1/n}$ provides an excellent approximation to the evolutionary sequence of the N-body system. Based on the numerical results, we discuss a link between the quasi-equilibrium state and the generalized thermostatistics by means of the non-extensive entropy.

arXiv comment26 pages, 26 figures, accepted for publication in MNRAS

References in corpus (17)

• Dynamical evolution of star clusters in tidal fields
• A Family of Models for Spherical Stellar Systems
• GRAPE-6: The massively-parallel special-purpose computer for astrophysical particle simulation
• Statistics of N-body Simulations I. Equal Masess Before Core Collapse
• Tsallis' entropy maximization procedure revisited
• Long-term Evolution of Stellar Self-Gravitating System away from the Thermal Equilibrium: connection with non-extensive statistics
• Gravitational instability of isothermal and polytropic spheres
• The time-scale for core collapse in spherical star clusters
• Post-Collapse evolution of globular clusters
• Gravothermal Catastrophe and Generalized Entropy of Self-Gravitating Systems
• Pre-Collapse Evolution of Galactic Globular Clusters
• On the meaning of Tsallis functional in astrophysics
• Gravothermal Catastrophe and Tsallis' Generalized Entropy of Self-Gravitating Systems III. quasi-equilibrium structure using normalized q-values
• Self-gravitating Stellar Systems and Non-extensive Thermostatistics
• Astrophysics on the GRAPE Family of Special Purpose Computers
• Gravothermal Catastrophe and Tsallis' Generalized Entropy of Self-Gravitating Systems II. Thermodynamic Properties of Stellar Polytrope
• Mass Loss Timescale of Star Clusters in External Tidal Field

Cited by in corpus (11)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Entropic cosmology for a generalized black-hole entropy
• A family of lowered isothermal models
• Test of Nonextensive Statistical Mechanics by Solar Sound Speeds
• Logotropic distributions
• Out-of-equilibrium phase re-entrance(s) in long-range interacting systems
• Stellar polytropes and Navarro-Frenk-White halo models: comparison with observations
• The Chandrasekhar condition of the equilibrium and stability for a star in the nonextensive kinetic theory
• Nonextensivity in the Solar Neighborhood
• $q$-Equilibrium of Gas in Spacetime of Multi-horizon Black Holes
• An approach to the quasi-equilibrium state of a self-gravitating system