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Explanation of a special color-magnitude diagram of star cluster NGC 1651 from different models

The color-magnitude diagram (CMD) of globular cluster NGC1651 has special structures including a broad main sequence, an extended main sequence turn-off and an extended red giant clump. The reason for such special CMDs remains unclear. In order to test how different the results from various stellar population assumptions are, we study a high-quality CMD of NGC1651 from the Hubble Space Telescope archive via eight kinds of models. Distance modulus, extinction, age ranges, star formation mode, fraction of binaries, and fraction of rotational stars are determined and then compared. The results show that stellar populations both with and without age spread can reproduce the special structure of the observed CMD. A composite population with extended star formation from 1.8\,Gyrs ago to 1.4\,Gyrs ago, which contains 50 per cent binaries and 70 per cent rotational stars, fits the observed CMD best. Meanwhile, a 1.5\,Gyr-old simple population that consists of rotational stars can also fit the observed CMD well. The results of CMD fitting are shown to depend strongly on stellar population type (simple or composite), and fraction of rotators. If the member stars of NGC1651 formed in a single star burst, the effect of stellar rotation should be very important for the explanation of observed CMDs. Otherwise, the effect may be small. It is also possible that the special observed CMD is a result of the combined effects of stellar binarity, rotation and age spread. Therefore, further work on stellar population type and fraction of rotational stars of intermediate-age clusters are necessary to understand their observed CMDs.