# Characterizing a cluster's dynamic state using a single epoch of radial velocities

##### Cottaar M., Meyer MR., Parker RJ.

Context. Radial velocity measurements can be used to constrain the dynamical state of a stellar cluster. However, for clusters with velocity dispersions smaller than a few km s -1 the observed radial velocity distribution tends to be dominated by the orbital motions of binaries rather than the stellar motions through the potential well of the cluster. Aims. Our goal is to characterize the intrinsic velocity distribution of a cluster from a single epoch of radial velocity data even for a cluster with a velocity dispersion of a fraction of a km s -1 . Methods. We investigate a maximum likelihood procedure, which has been pioneered in the literature about ten years ago. Assuming a period, mass ratio, and eccentricity distribution for the binaries in the observed cluster this procedure fits a dynamical model describing the velocity distribution for the single stars and center of masses of the binaries, simultaneously with the radial velocities caused by binary orbital motions, using all the information available in the observed velocity distribution. We test the capability of this procedure to reproduce the velocity dispersion of an observed cluster, using radial velocity data of an open cluster and Monte Carlo simulations. Results. We find that the fits to the intrinsic velocity distribution depend only weakly on the binary properties assumed, so the uncertainty in the fitted parameters tends to be dominated by statistical uncertainties. Based on a large suite of Monte Carlo simulations we provide an estimate of how these statistical uncertainties vary with the velocity dispersion, binary fraction, and the number of observed stars, which can be used to estimate the sample size needed to reach a specific accuracy. Finally we test the method on the well-studied open cluster NGC 188, showing that it can successfully reproduce a velocity dispersion of only 0.5 km s -1 using a single epoch of the multi-epoch radial velocity data. Conclusions. If the binary period, mass ratio, and eccentricity distribution of the observed stars are roughly known, this procedure can be used to correct for the effect of binary orbital motions on an observed velocity distribution. This allows for the study of the dynamical state of a stellar cluster with a small velocity dispersion from a single epoch of radial velocity data. © 2012 ESO.