Mathematics – Logic
Scientific paper
Jan 1979
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979mnras.186..155h&link_type=abstract
Monthly Notices of the Royal Astronomical Society, vol. 186, Jan. 1979, p. 155-176.
Mathematics
Logic
7
Astronomical Models, Gravitational Collapse, Star Clusters, Equations Of Motion, Fokker-Planck Equation, Spatial Distribution, Star Distribution, Stellar Motions, Thermodynamic Equilibrium
Scientific paper
This paper is concerned with core collapse in isolated clusters of identical point masses. Equations are derived which determine the evolution of the core which would result from given deviations from a Maxwellian distribution. Assuming certain forms for the deviations, the predicted evolution of the core is compared with the results of Monte Carlo calculations. The deviations corresponding to stars moving in nearly radial orbits appear ultimately to dominate the evolution of the core. The deviations are maintained because stars of high energy cannot relax fast enough to thermalize with the evolving core. Under certain crude approximations, the deviations for stars in radial orbits can approach a homological form. In a better approximation, it is shown that the Fokker-Planck equation for the deviations admits an essentially unique homological solution which also determines the evolution of the core. Remaining approximations prevent definitive comparison with Monte Carlo calculations, but the qualitative agreement is satisfactory.
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