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 year baseline and have typical precisions < 1 mas/yr .
We calculate the velocity dispersion in the two axes to be \sigma _ { \alpha } ( c ) = 13.0 ^ { +0.8 } _ { -0.7 } and \sigma _ { \delta } ( c ) = 9.1 ^ { +0.5 } _ { -0.5 } km s ^ { -1 } , using a 2-component , 2-dimensional model that takes into account the uncertainties on the measurements .
This gives a 3-dimensional velocity dispersion of \sigma _ { 3 D } = 17.8 \pm 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 _ { \odot } , 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 .