About seventy percent of intermediate-age star clusters in the Large Magellanic Clouds have been confirmed to have broad main sequence, multiple or extended turn-offs and dual red giant clumps. The observed result seems against the classical idea that such clusters are simple stellar populations. Although many models have been used for explaining the results via factors such as prolonged star formation history, metallicity spread, differential redenning, selection effect, observational uncertainty, stellar rotation, and binary interaction, the reason for the special color-magnitude diagrams is still uncertain. We revisit this question via the combination of stellar rotation and binary effects. As a result, it shows "golf club" color-magnitude diagrams with broad or multiple turn-offs, dual red clump, blue stragglers, red stragglers, and extended main sequences. Because both binaries and massive rotators are common, our result suggests that most color-magnitude diagrams including extended turn-off or multiple turn-offs can be explained using simple stellar populations including both binary and stellar rotation effects, or composite populations with two components.

The color-magnitude diagram (CMD) of globular cluster NGC 1651 has special structures including a broad main sequence, an extended main sequence turn-off, and an extended red giant clump. The reason for such a special CMDremains unclear. In order to test the difference amongthe results from various stellar population assumptions, we study a high-quality CMD of NGC 1651 from the Hubble Space Telescope archive using 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% binaries and 70% 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 NGC 1651 formed in a single star burst, the effect of stellar rotation should be very important for explaining the 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.

Stellar rotation, age spread and binary stars are thought to be three most possible causes of the peculiar color-magnitude diagrams (CMDs) of some star clusters, which exhibit extended main-sequence turn-offs (eMSTOs). It is far from getting a clear answer. This paper studies the effects of three above causes on the CMDs of star clusters systematically. A rapid stellar evolutionary code and a recently published database of rotational effects of single stars have been used, via an advanced stellar population synthesis technique. As a result, we find a consistent result for rotation to recent works, which suggests that rotation is able to explain, at least partially, the eMSTOs of clusters, if clusters are not too old (< 2.0 Gyr). In addition, an age spread of 200 to 500 Myr reproduces extended turn-offs for all clusters younger than 2.5 Gyr, in particular, for those younger than 2.2 Gyr. Age spread also results in extended red clumps (eRCs) for clusters younger than 0.5 Gyr. The younger the clusters, the clearer the eRC structures. Moreover, it is shown that binaries (including interactive binaries) affect the spread of MSTO slightly for old clusters, but they can contribute to the eMSTOs of clusters younger than 0.5 Gyr. Our result suggests a possible way to disentangle the roles of stellar rotation and age spread, i.e., checking the existence of CMDs with both eMSTO and eRC in clusters younger than 0.5 Gyr.

Binaries are very common in galaxies, and more than half of Galactic hot subdwarf stars, which are thought as a possible origin of UV-upturn of old stellar populations, are found in binaries. Previous works showed that binary evolution can make the spectra of binary star populations significantly different from those of single star populations. However, the effect of binary evolution has not been taken into account in most works of spectral fitting of galaxies. This paper studies the role of binary evolution in spectral fitting of early-type galaxies, via a stellar population synthesis model including both single and binary star populations. Spectra from ultraviolet to optical band are fitted to determine a few parameters of galaxies. The results show that the inclusion of binaries in stellar population models may lead to obvious change in the determination of some galaxy parameters and therefore it is potentially important for spectral studies. In particular, the ages of young components of composite stellar populations become much older when using binary star population models instead of single star population models. This implies that binary star population models will measure significantly different star formation histories (SFHs) for galaxies compared to single star population models. In addition, stellar population models with binary interactions measure larger dust extinctions than single star population models on average. It suggests that when using binary star population models instead of single star population models, negative extinctions are possibly unnecessary in spectral fitting of early-type galaxies.

We present a new tool for colour-magnitude diagram (CMD) studies, P owerf ul CM D. This tool is built on the basis of the advanced stellar population synthesis (ASPS) model, in which single stars, binary stars, rotating stars, and star formation history have been taken into account. Via P owerf ul CM D, the distance modulus, colour excess, metallicity, age, binary fraction, rotating star fraction, and star formation history of star clusters can be determined simultaneously from observed CMDs. The new tool is tested via both simulated and real star clusters. Five parameters of clusters NGC6362, NGC6652, NGC6838 and M67 are determined and compared to other works. It is shown that this tool is useful for CMD studies, in particular for those with the data of the Hubble Space Telescope (HST). Moreover, we find that the inclusion of binaries in theoretical stellar population models may lead to smaller colour excess compared to the case of single star population models.