Mathematics – Logic
Scientific paper
Jun 1990
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990mnras.244..478l&link_type=abstract
Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 244, June 1, 1990, p. 478-492.
Mathematics
Logic
24
Gravitational Collapse, Star Clusters, Stellar Cores, Stellar Models, Anisotropy, Boundary Value Problems, Eigenvalues, Homology, Partial Differential Equations
Scientific paper
A fluid-dynamical method for computing the quasi-stationary evolution of spherical star clusters is described. The model is applied to the well-understood phenomenon of core collapse in one-component star clusters. The ordinary differential equations for self-similar evolution are derived, and the eigenvalue problem for precollapse is solved. In the isotropized version, a power-law index of alpha = 2.20 and a core collapse rate xi = 2,120 are found, in reasonable agreement with existing homological models. The anisotropic model is characterized by a somewhat steeper density profile with alpha = 2.23, and a considerably reduced value xi = 1,230 for the core collapse rate. The effect of modifications of the anisotropic equations are discussed in detail, and the discrepancies between Larson's anisotropic calculations and other models, including anisotropy, are resolved.
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