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.
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