Numerical integration of the Fokker-Planck equation and the evolution of star clusters

Journal Article · Sat Dec 15 00:00:00 EST 1979 · Astrophys. J.; (United States)

DOI:https://doi.org/10.1086/157587· OSTI ID:5614730

Cohn, H

A new numerical method for studying the evolution of spherical star clusters is presented. This method employs direct numerical integration of the orbit-averaged Fokker-Planck equation in energy--angular momentum space to advance the stellar distribution in time. The gravitational potential, which is treated self-consistently, is advanced by means of Poisson's equation and adiabatic invariant theory.Detailed numerical results from a study of the evolution of Plummer's model are reported. These results are found to be in generally good agreement with those of the Monte Carlo studies of Henon, and Spitzer and Shull, but show far less statistical noise and extend to a somewhat more advanced state of the evolution.The present numberical results tend to support the homologous core collapse conjecture of Lynden-Bell. The structure of the central regions approaches a self-similar form, and the dependence of central velocity dispersion on central density approaches an asymptotic power law. The late stages of evolution are found to be consistent with the gravothermal instability picture of Lynden-Bell and Wood. In particular the core collapse is observed to change in character at the time the scaled escape energy first exceeds the critical value for the onset of the gravothermal instability.

• Research Organization: Harvard-Smithsonian Center for Astrophysics
• OSTI ID: 5614730
• Journal Information: Astrophys. J.; (United States), Vol. 234:3
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
STAR CLUSTERS
STAR EVOLUTION
ANGULAR MOMENTUM
BINDING ENERGY
DISTRIBUTION FUNCTIONS
FOKKER-PLANCK EQUATION
GRAVITATIONAL COLLAPSE
NUMERICAL SOLUTION
ORBITS
POISSON EQUATION
DIFFERENTIAL EQUATIONS
ENERGY
EQUATIONS
640102* - Astrophysics & Cosmology- Stars & Quasi-Stellar
Radio & X-Ray Sources