Smoothing of force functions and the fluctuation spectra of an open star cluster model

Abstract

We perform the correlation and spectral analysis of phase-space density and potential fluc- tuations in a model of an open star cluster for various values of the smoothing parameterof the force functions in the equations of motion of cluster stars, and compute the mutual correlation functions for the fluctuations of potential U and phase-space density f of the cluster model at different clustercentric distances. We use the Fourier transform of the mutual correlation functions to compute the power spectra and dispersion curves of the potential and phase-space density fluctuations. The spectrum of potential fluctuations proves to be less complex than that of phase-space density fluctuations. The most powerful potential fluctuations are associated with phase-space density fluctuations, and their spectrum lies in the domain of low frequencies ν 3/τv.r.), the contribution of potential fluctuations to those of the phase-space density is small or equal to zero (here τv.r. is the violent relaxation time scale of the cluster). We find a number of unstable potential fluctuations in the core of the cluster model (up to 30 pairs of fluctuations with different complex conjugate frequencies). We also find and analyze the dependences of the spectra and dispersion curves of phase-space density and potential fluctuations on � .W efind a "repeatability" (significant correlation) of the spectra at some values of parameter � . The form of the dispersion curve is unstable against small variations of � .W e discuss the astrophysical applications of our results: the break-up in the cluster core of the phase-space density wave running from the cluster periphery toward its center into several waves with frequencies commensurable to that of the external (tidal) influence; emission and reflection of phase-space and potential waves near the cluster core boundary; possible wavelength and phase discretization of the phase-space and potential waves in the cluster model.