%0 Journal Article %T Extended Main Sequence Turnoffs in Intermediate-Age Star Clusters: A Correlation Between Turnoff Width and Early Escape Velocity %A Paul Goudfrooij %A Leo Girardi %A Vera Kozhurina-Platais %A Jason S. Kalirai %A Imants Platais %A Thomas H. Puzia %A Matteo Correnti %A Alessandro Bressan %A Rupali Chandar %A Leandro Kerber %A Paola Marigo %A Stefano Rubele %J Physics %D 2014 %I arXiv %R 10.1088/0004-637X/797/1/35 %X We present color-magnitude diagram analysis of deep Hubble Space Telescope imaging of a mass-limited sample of 18 intermediate-age (1 - 2 Gyr old) star clusters in the Magellanic Clouds, including 8 clusters for which new data was obtained. We find that ${\it all}$ star clusters in our sample feature extended main sequence turnoff (eMSTO) regions that are wider than can be accounted for by a simple stellar population (including unresolved binary stars). FWHM widths of the MSTOs indicate age spreads of 200-550 Myr. We evaluate dynamical evolution of clusters with and without initial mass segregation. Our main results are: (1) the fraction of red clump (RC) stars in secondary RCs in eMSTO clusters scales with the fraction of MSTO stars having pseudo-ages $\leq 1.35$ Gyr; (2) the width of the pseudo-age distributions of eMSTO clusters is correlated with their central escape velocity $v_{\rm esc}$, both currently and at an age of 10 Myr. We find that these two results are unlikely to be reproduced by the effects of interactive binary stars or a range of stellar rotation velocities. We therefore argue that the eMSTO phenomenon is mainly caused by extended star formation within the clusters; (3) we find that $v_{\rm esc} \geq 15$ km/s out to ages of at least 100 Myr for ${\it all}$ clusters featuring eMSTOs, while $v_{\rm esc} \leq 12$ km/s at all ages for two lower-mass clusters in the same age range that do ${\it not}$ show eMSTOs. We argue that eMSTOs only occur for clusters whose early escape velocities are higher than the wind velocities of stars that provide material from which second-generation stars can form. The threshold of 12-15 km/s is consistent with wind velocities of intermediate-mass AGB stars in the literature. %U http://arxiv.org/abs/1410.3840v3