Correlations, spectra, and instability of phase-space density fluctuations in open-cluster models

Abstract

The dynamical evolution of six open star cluster models is analyzed using the correlation and spectral analysis of phase-space density fluctuations. The two-time and mutual correlation functions are computed for the fluctuations of the phase-space density of cluster models. The data for two-time and two-particle correlations are used to determine the correlation time for phase-space density fluctuations ((0.1-1) τ v.r., where τ v.r. is the violent relaxation time of the model) and the average phase velocities of the propagation of such fluctuations in cluster models. These velocities are 2-20 times smaller than the root mean square velocities of the stars in the cluster core. The power spectra and dispersion curves of phase-space density fluctuations are computed using the Fourier transform of mutual correlation functions. The results confirm the presence of known unstable phase-space density fluctuations due to homologous fluctuations of the cluster cores. The models are found to exhibit a number of new unstable phase-space density fluctuations (up to 32-41 pairs of fluctuations with different complex conjugate frequencies in each model; the e-folding time of the amplitude growth of such fluctuations is (0.4-10) τ v.r. and their phases are distributed rather uniformly). Astrophysical applications of the obtained results (irregular structure of open star clusters, formation and decay of quasi-stationary states in such clusters) are discussed. © 2013 Pleiades Publishing, Ltd.