Did the infant R136 and NGC 3603 clusters undergo residual gas
  expulsion?
  Based on kinematic data observed for very young, massive clusters that appear
to be in dynamical equilibrium, it has recently been argued that such young
systems set examples where the early residual gas-expulsion did not happen or
had no dynamical effect. The intriguing scenario of a star cluster forming
through a single starburst has thereby been challenged. Choosing the case of
the R136 cluster of the Large Magellanic Cloud, the most cited one in this
context, we perform direct N-body computations that mimic the early evolution
of this cluster including the gas-removal phase (on a thermal timescale). Our
calculations show that under plausible initial conditions as consistent from
observational data, a large fraction (> 60%) of a gas-expelled, expanding
R136-like cluster is bound to regain dynamical equilibrium by its current age.
Therefore, the recent measurements of velocity dispersion in the inner regions
of R136, that indicate that the cluster is in dynamical equilibrium, are
consistent with an earlier substantial gas expulsion of R136 followed by a
rapid re-virialization (in approx. 1 Myr). Additionally, we find that the less
massive Galactic NGC 3603 Young Cluster (NYC), with a substantially longer
re-virialization time, is likely to be found deviated from dynamical
equilibrium at its present age (approx. 1 Myr). The recently obtained stellar
proper motions in the central part of the NYC indeed suggest this and are
consistent with the computed models. This work significantly extends previous
models of the Orion Nebula Cluster which already demonstrated that the
re-virialization time of young post-gas-expulsion clusters decreases with
increasing pre-expulsion density.
