Abstract

We present a 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 eight clusters for which new data were obtained. We find that 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 the 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 of less than or similar to 1.35 Gyr; (2) the width of the pseudo-age distributions of eMSTO clusters is correlated with their central escape velocity v(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; and (3) we find that v(esc) >= 15 km s(-1) out to ages of at least 100 Myr for all clusters featuring eMSTOs, and v(esc) <= 12 km s(-1) at all ages for two lower-mass clusters in the same age range that do 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(-1) is consistent with wind velocities of intermediate-mass asymptotic giant branch stars and massive binary stars in the literature.