Is the Escape Velocity in Star Clusters Linked to Extended Star
  Formation Histories? Using NGC 7252: W3 as a Test Case
  The colour-magnitude diagrams of some intermediate-age clusters (1-2 Gyr)
star clusters show unexpectedly broad main-sequence turnoffs, raising the
possibility that these clusters have experienced more than one episode of star
formation. Such a scenario predicts the existence of an extended main sequence
turn off (eMSTO) only in clusters with escape velocities above a certain
threshold ($>15$ km s$^{-1}$), which would allow them to retain or accrete gas
that eventually would fuel a secondary extended star-formation episode. This
paper presents a test of this scenario based on the study of the young and
massive cluster NGC 7252: W3. We use the HST photometry from WFPC2 and WFC3
images obtained with UV and optical filters, as well as MagE echellette
spectrograph data from the Las Campanas Clay 6.5m telescope, in order to
construct the observed UV/optical SED of NGC 7252: W3. The observations are
then compared with synthetic spectra based on different star formation
histories consistent with those of the eMSTO clusters. We find that the SED of
this cluster is best fitted by a synthetic spectrum with a single stellar
population of age $570^{+70}_{-62}$ Myr and mass $1.13^{+0.14}_{-0.13}\times
10^8$ M$_\odot$, confirming earlier works on NGC 7252: W3. We also estimate the
lower limit on the central escape velocity of 193 km s$^{-1}$. We rule out
extended star-formation histories, like those inferred for the eMSTO clusters
in the Magellanic Clouds, at high confidence. We conclude that the escape
velocity of a cluster does not dictate whether a cluster can undergo extended
periods of star formation.
