  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.
