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 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, using a 2-component, 2-dimensional
model that takes into account the uncertainties on the measurements. This gives
a 3-dimensional velocity dispersion of $\sigma_{3D} = 17.8 \pm 0.6$ km/s
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.
