Wavenumber spectra of oscillations of open star cluster models

A correlation and spectral analysis of the phase-space density oscillations and oscillations of absolute values of stellar velocities is performed for six open cluster models (for cluster model 1 different smoothing parameters epsilon for force functions in equations of stellar motions is considered). The mutual correlation functions are computed for the fluctuations of phase-space density f and absolute values of stellar velocities v. The spatial Fourier transform of the correlation functions with zero time shift is used to compute the wavenumber spectra of the oscillations of f and v. The wavenumber spectrum of phase-space density oscillations has a more simple structure than the wavenumber spectrum of oscillations of absolute velocities v. The most powerful oscillations of f and v are located in the domain of small wavenumbers k (and large wavelengths lambda > 0.91-1.25 pc) with homologous cluster oscillations contributing significantly to the mean power of oscillations of f and v. Recurrent oscillations of v at equally spaced k are found in five cluster models. The wavenumber spectra of oscillations of f and v for cluster model 1 are found to depend on epsilon, and the corresponding dependences are analyzed. These wavenumber spectra are found to be appreciably less dependent on epsilon than the frequency spectra of oscillations of f. An increase of epsilon has a weaker effect on the wavenumber spectra of oscillations of f than on those of the oscillations of absolute velocity v. The slope of the wavenumber spectrum increases, on the average, with increasing epsilon because of the change of the radial structure of the cluster model. Astrophysical applications of the results (the dissimilarity of our spectra from the Kolmogorov spectrum, discrete structure of the wavelength spectrum of oscillations of v in five cluster models, widths of the spectra of the most powerful oscillations of cluster models, estimates of cluster tidal radii, etc.) are discussed.