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

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

The dynamics of correlations in open-star cluster models

Two-time and two-point (two-particle) correlations are calculated for several parameters of the stellar motions, the densities, and the phase densities of model open clusters, in the vicinities of the cluster stars. The correlation times and correlation radii are determined in spaces of the parameters considered. The distributions of the two-point correlations for the distances between stars in the coordinate and velocity spaces of the stars are calculated. The local maxima of these distributions are used to determine the parameters of density waves, the potential, and the phase density in the model clusters. Analysis of the fine structure of regions of concentration in the two-point correlations in space of mutual distances between stars suggests the formation of polarization clouds near a number of such distances between stars. The distributions of the phase-density correlations are calculated, and the dynamics of these distributions analyzed. The dispersions of these distributions depend strongly on the presence of broad "wings" in the distributions (i. e., of strong correlations in the system). These dispersions are considered as a measure of the degree of correlation of phase-density fluctuations in model clusters. A growth in the correlations with time is observed for 50% of the cluster models considered. Flows of the phase-density correlations are investigated. A dominant correlation flow from the region of strong to the region of weak correlations is identified, leading to a flow of kinetic energy toward the cluster center. The rate at which this flow heats the model cluster core is estimated. Signs of weak turbulence are detected in the stellar motions in the model cluster cores with the highest degree of non-stationary in the regular field. © 2012 Pleiades Publishing, Ltd

Non-stationarity parameters of open clusters

Estimates of a number of dynamical parameters of 103 open star clusters are presented: the density contrast in the cluster core, stellar velocity dispersion, taking into account the influence of the external field of the Galaxy and non-stationarity of the cluster, oscillation periods of the cluster and the cluster core, etc. Analytical solutions to the gross dynamical equations are obtained for simple cluster models. These solutions are used to estimate a number of quantities characterizing the degree of non-stationarity of the cluster, such as the amplitude of oscillations of the cluster virial coefficient and of the radius of the cluster core, etc. Astrophysical applications of these results are discussed. © 2012 Pleiades Publishing, Ltd