Analysis of density fluctuations in models of open clusters

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 γ1, corresponding to the growth increment γ2 for this instability. Estimates of γ1 and γ2 agree with estimates obtained for the core of the corresponding dynamical, numerical model cluster. Astrophysical applications of the results are discussed.