From proper motions to star cluster dynamics: measuring velocity dispersion in deconvolved distribution functions

Abstract

We investigate the effect that the usually large errors associated with ground-based proper motion (PM) components have on the determination of a star cluster's velocity dispersion (\sv). Rather than histograms, we work with PM distribution functions (PMDFs), taking the $1\sigma$ uncertainties formally into account. In this context, a cluster's intrinsic PMDF is broadened by the error distribution function (eDF) that, given the average error amplitude, has a width usually comparable to the cluster PMDF. Thus, we apply a Richardson-Lucy (RL) deconvolution to the PMDFs of a set of relatively nearby and populous open clusters (OCs), using the eDFs as point spread functions (PSFs). The OCs are NGC\,1039 (M\,34), NGC\,2477, NGC\,2516, NGC\,2682 (M\,67), and NGC\,7762. The deconvolved PMDFs are approximately Gaussian in shape, with dispersions lower than the observed ones by a factor of 4-10. NGC\,1039 and NGC\,2516, the nearest OCs of the sample, have deconvolved \sv\ compatible with those of bound OCs of mass $\sim10^3$\,\ms. NGC\,2477 and NGC\,2682 have deconvolved PMDFs with a secondary bump, shifted towards higher average velocities, which may be an artefact of the RL deconvolution when applied to asymmetric profiles. Alternatively, it may originate from cluster merger, large-scale mass segregation or, least probably, binaries.