The Gaia-ESO Survey: kinematical and dynamical study of four young open
  clusters
  Context. The origin and dynamical evolution of star clusters is an important
topic in stellar astrophysics. Several models have been proposed to understand
the formation of bound and unbound clusters and their evolution, and these can
be tested by examining the kinematical and dynamical properties of clusters
over a wide range of ages and masses. Aims. We use the Gaia-ESO Survey products
to study four open clusters (IC 2602, IC 2391, IC 4665, and NGC 2547) that lie
in the age range between 20 and 50 Myr. Methods. We employ the gravity index
$\gamma$ and the equivalent width of the lithium line at 6708 $\AA$, together
with effective temperature $\rm{T_{eff}}$, and the metallicity of the stars in
order to discard observed contaminant stars. Then, we derive the cluster radial
velocity dispersions $\sigma_c$, the total cluster mass $\rm{M}_{tot}$, and the
half mass radius $r_{hm}$. Using the $Gaia$-DR1 TGAS catalogue, we
independently derive the intrinsic velocity dispersion of the clusters from the
astrometric parameters of cluster members. Results. The intrinsic radial
velocity dispersions derived by the spectroscopic data are larger than those
derived from the TGAS data, possibly due to the different masses of the
considered stars. Using $\rm{M}_{tot}$ and $r_{hm}$ we derive the virial
velocity dispersion $\sigma_{vir}$ and we find that three out of four clusters
are supervirial. This result is in agreement with the hypothesis that these
clusters are dispersing, as predicted by the "residual gas expulsion" scenario.
However, recent simulations show that the virial ratio of young star clusters
may be overestimated if it is determined using the global velocity dispersion,
since the clusters are not fully relaxed.
