Cygnus OB2 DANCe: A high-precision proper motion study of the Cygnus OB2 association

We present a high-precision proper motion study of 873 X-ray and spectroscopically selected stars in the massive OB association Cygnus OB2 as part of the DANCe project. These were calculated from images spanning a 15 yr baseline and have typical precisions < 1 mas yr(-1). We calculate the velocity dispersion in the two axes to be (c) = 13.0(-0.7)(+0.8) sigma delta(c) = 9.1(-0.5)(+0.5) km s(-1), using a two-component, two-dimensional model that takes into account the uncertainties on the measurements. This gives a three-dimensional velocity dispersion of sigma(3D) = 17.8 +/- 0.6 km s(-1) implying a virial mass significantly larger than the observed stellar mass, confirming that the association is gravitationally unbound. The association appears to be dynamically unevolved, as evidenced by considerable kinematic substructure, non-isotropic velocity dispersions and a lack of energy equipartition. The proper motions show no evidence for a global expansion pattern, with approximately the same amount of kinetic energy in expansion as there is in contraction, which argues against the association being an expanded star cluster disrupted by process such as residual gas expulsion or tidal heating. The kinematic substructures, which appear to be close to virial equilibrium and have typical masses of 40-400 M-aS (TM), also do not appear to have been affected by the expulsion of the residual gas. We conclude that Cyg OB2 was most likely born highly substructured and globally unbound, with the individual subgroups born in (or close to) virial equilibrium, and that the OB association has not experienced significant dynamical evolution since then.