Is the Escape Velocity in Star Clusters Linked to Extended Star Formation Histories? Using NGC 7252: W3 as a Test Case

Abstract: 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.