  Detailed studies of resolved young massive star clusters are necessary to
determine their dynamical state and evaluate the importance of gas expulsion
and early cluster evolution. In an effort to gain insight into the dynamical
state of the young massive cluster R136 and obtain the first measurement of its
velocity dispersion, we analyse multi-epoch spectroscopic data of the inner
regions of 30 Doradus in the Large Magellanic Cloud (LMC) obtained as part of
the VLT-FLAMES Tarantula Survey. Following a quantitative assessment of the
variability, we use the radial velocities of non-variable sources to place an
upper limit of 6 km/s on the line-of-sight velocity dispersion of stars within
a projected distance of 5 pc from the centre of the cluster. After accounting
for the contributions of undetected binaries and measurement errors through
Monte Carlo simulations, we conclude that the true velocity dispersion is
likely between 4 and 5 km/s given a range of standard assumptions about the
binary distribution. This result is consistent with what is expected if the
cluster is in virial equilibrium, suggesting that gas expulsion has not altered
its dynamics. We find that the velocity dispersion would be ~25 km/s if
binaries were not identified and rejected, confirming the importance of the
multi-epoch strategy and the risk of interpreting velocity dispersion
measurements of unresolved extragalactic young massive clusters.
