A new powerful method for solving the orbit-averaged Fokker-Planck equation regarding stellar dynamics

Details A new powerful method for solving the orbit-averaged Fokker-Planck equation regarding stellar dynamics A new powerful method for solving the orbit-averaged Fokker-Planck equation regarding stellar dynamics

Apr 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993pasj...45..233t&link_type=abstract

PASJ: Publications of the Astronomical Society of Japan (ISSN 0004-6264), vol. 45, no. 2, p. 233-242.

Astronomy and Astrophysics

Astronomy

11

Fokker-Planck Equation, Globular Clusters, Gravitational Collapse, Stellar Motions, Stellar Evolution, Variational Principles

Scientific paper

A new numerical method for solving the orbit-averaged Fokker-Planck equation used in collisional stellar dynamics is presented. The method is an alternative to a direct integration method (Cohn, 1980) for the 1D energy-space Fokker-Planck equation. Our method is based on a variational method, while Cohn's method is based on the Chang-Cooper finite-difference scheme. The variational formulation of the Fokker-Planck equation is achieved by applying a generalized variational principle based on the concept of a local potential. Our method was used to study the evolution of globular clusters with an isotropic velocity distribution. The results of our method agree well with the results of Cohn's method for both pre- and post-collapse evolution. This shows that our method is as powerful as Cohn's method. The advantage of our method is that the extension to two- or more dimensional problems is straightforward, while Cohn's direct integration method has the difficulty that no direct 2D extension of the Chang-Cooper scheme has been found.

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