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

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 (sigma(v)). 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. 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 2516, the nearest OCs of the sample, have deconvolved sigma(v) compatible with those of bound OCs of mass similar to 10(3) M-circle dot. NGC 2477 and 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.