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

Abstract

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. DOI: 10.1134/S199034131302003X Keywords: stars: kinematics and dynamics-Galaxy: open clusters and associations: general INTRODUCTIONRecently, Chavanis [1-3] derived theoretical estimates for the fluctuations of phase-space density (PSD) and the corresponding correlation functions for spatially uniform and nonuniform systems with long-range interactions (including self-gravitating systems). To this end, the above author used kinetic equations written with a number of simplifying assumptions. The formulas for the correlation functions derived by Chavanis [1-3] have a rather complex form making them difficult to use for analyzing dynamic processes in such systems. In our opinion, it is more productive to compute the correlation functions directly by numerically integrating the equations of motion of gravitating particles in the problems of clustering of galaxies and the evolution of the Universe (see, e.g., [4][5][6]), and also when modeling the dynamics of open star clusters (OCl) [7].In one of our previous papers [7] we computed the two-time correlation functions for r = |r|, v = |v|, and the energy ε per unit star mass, as well as twoparticle correlations of r, v, ε, stellar number density n = n(r, t) and PSD f = f (r, v, t) for open star

Noise and waves: a unified kinetic theory for stellar systems

“…Some damped wave modes in star clusters and galaxies can be very long-lasting, decaying on a timescale |γ| −1 10 2 tcross (Weinberg 1991;Weinberg 1994;Sellwood & Pryor 1998;Ideta 2002). Hence in 'intermediate-N ' systems such as open clusters (Danilov & Putkov 2012, 2013 or the N = 10 3 -body simulations of Lau & Binney (2019), the assumption |γ| −1 t relax can be violated. Additionally, waves can be important in systems with very large N .…”

Radial Velocity Dispersions of Star Groups in M67

“…To understand the influence of instability on the dynamics and kinematics of the star groups inside the OC, one can analyse the phase density fluctuations and their spectra. This method gives an indication of the formation of the density waves and groups of stars with different kinematic and dynamic characteristics (Danilov & Putkov 2013Danilov 2015).…”