Tidal radius estimates for three open clusters

Abstract

A new method is developed for estimating tidal radii and masses of open star clusters (OCL) based on the sky-plane coordinates and proper motions and/or radial velocities of cluster member stars. To this end, we perform the correlation and spectral analysis of oscillations of absolute values of stellar velocity components relative to the cluster mass center along three coordinate planes and along each coordinate axis in five OCL models. Mutual correlation functions for fluctuations of absolute values of velocity field components are computed. The spatial Fourier transform of the mutual correlation functions in the case of zero time offset is used to compute wavenumber spectra of oscillations of absolute values of stellar velocity components. The oscillation spectra of these quantities contain series of local maxima at equidistant wavenumber k values. The ratio of the tidal radius of the cluster to the wavenumber difference Δk of adjacent local maxima in the oscillation spectra of absolute values of velocity field components is found to be the same for all five OCL models. This ratio is used to estimate the tidal radii and masses of the Pleiades, Praesepe, and M67 based on the proper motions and sky-plane coordinates of the member stars of these clusters. The radial dependences of the absolute values of the tangential and radial projections of cluster star velocities computed using the proper motions relative to the cluster center are determined, along with the corresponding autocorrelation functions and wavenumber spectra of oscillations of absolute values of velocity field components. The Pleiades virial mass is estimated assuming that the cluster is either isolated or non-isolated. Also derived are the estimates of the Pleiades dynamical mass assuming that it is non-stationary and non-isolated. The inferred Pleiades tidal radii corresponding to these masses are reported.