Abstract
The frequencies for homologous and non-homologous density flucutations in unisolated, ellipsoidal models of open clusters are determined. These fluctuations are stable. In the cases considered, the frequencies of non-homologous fluctuations are higher than those for homologous fluctuations of the ellipsoidal models. The instability of the proper fluctuations of the phase density at the center of a homogeneous ellipsoid whose central characteristics correspond to the core parameters of a dynamical, numericalmodel cluster is demonstrated. The development of instability of the phase-density flucutations at the center of such an ellipsoid leads to the domination of fluctuations with the frequency γ 1, corresponding to the growth increment γ 2 for this instability. Estimates of γ 1 and γ 2 agree with estimates obtained for the core of the corresponding dynamical, numerical model cluster. Astrophysical applications of the results are discussed.
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Original Russian Text © V.M. Danilov, 2008, published in Astronomicheskiĭ Zhurnal, 2008, Vol. 85, No. 11, pp. 986–998.