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Failure of rotation and notable success of age spread to reproduce the CMDs of star clusters NGC 1831, NGC 1868 and NGC 2249

We study the high-quality CMDs of three star clusters, NGC 1831, NGC 1868 and NGC 2249 in detail, via the two most likely causes (stellar rotation and age spread) for CMDs with extended main-sequence turn-offs. The results show evident failure of stellar rotation (including resolved and unresolved binary stars) to interpret the CMDs of three star clusters, and the unexpected success of age spread. In particular, the special structures of turn-off and red clump parts cannot be generated by stellar rotation, but age spread perfectly reproduces the observed features. This suggests that these three clusters contain multiple populations of stars, rather than a single population of rotating stars and binaries. The thick subgiant branch of NGC 1831 gives the strongest support to this. The results demonstrate that stellar rotation cannot save the widely accepted view (simple population) of star clusters, and an extended star formation history is needed for explaining the observed CMDs. In addition, this work shows that a narrow subgiant branch does not correspond to a simple population. The judgement of simple population in NGC 1651 by a previous work is not necessarily reliable. We anticipate our assay to be a starting point for more precise study of Hertzsprung-Russell diagrams of star clusters. This involves many factors, such as binaries, rotating stars, and star formation history (SFH).