Estimation of the dynamic masses of open star clusters

The determination of star cluster masses is crucial for the study of cluster dynamics, the evaluation of gravitational binding, and the assessment of star formation efficiency. Traditional photometric approaches face challenges such as incompleteness, the problem of evaluating the uncertainty in the mass-luminosity relation, contamination by binaries, and so on. Dynamic (virial) approaches, which provide an estimate of the total cluster mass, have a difficulty in estimating the velocity dispersion. This study proposes a method to calculate the dynamic masses by using proper motions, taking into account for their observational errors. Using modern data for open clusters and samples of their probable members, we estimate dynamic masses of 833 open clusters. The resulting dynamic mass distribution is nearly log-normal with the mode of $2400\,M_\odot$.