Context. Colors are usually not used for constraining stellar populations because they are thought to have the well-known agemetallicity degeneracy, but some recent works show that colors can also be used. A simple stellar population synthesis model is widely used, but there is no analysis for its colors. Aims. We try to find colors that can potentially be used to determine the age and metallicity of stellar populations by the standard model. Methods. Principal component analysis and relative sensitive parameter techniques are used in this work. Results. U − K, U − H, U − J, B− K, B− H, U − I, B− J,and V − K are found to be more important for studying populations than others. Pairs of colors such as B− K and B−V are found to be able to disentangle the stellar age-metallicity degeneracy via the high-resolution model, while pairs such as U − K and R − I may be used instead when the low-resolution model is used. Furthermore, the u − g and r − i colors of the low-resolution model seem to have the same potential, but there are no such colors for the high-resolution one. Conclusions. Some colors have been shown to have the potential to determine the age and metallicity of stellar populations, but relative metallicity and age sensitivities of colors in different stellar population synthesis models are usually different. In addition, minor star formations will make star systems look younger and more metal rich than their dominating populations.

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.

This work searches for the candidates of Galactic disk star clusters in Gaia Early Data Release 3 (Gaia EDR3) and determines their basic parameters from color–magnitude diagrams (CMDs). A friends-of-friends method for membership determination and stellar population models including binary stars (ASPS) and rotating stars are adopted. As a result, 868 new star cluster candidates are found, besides 2729 known ones. When checking the CMD of each candidate, 61 new candidates show main sequences including a turnoff, which suggests that they are real star clusters. The basic parameters, including distance modulus, color excess, metallicity, age (or age range), primordial binary fraction, and rotating star fraction, are determined carefully by fitting the morphologies of CMDs of 61 newly identified star clusters and 594 known star clusters, which have relatively clear main sequences. The CMDs are fitted in considerable detail to ensure the reliability of property parameters of clusters. All final results are included in a new star cluster catalog, which is named LI team’s Star Cluster (LISC), and the catalog is available in the Zenodo repository.

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.

Using a widely used stellar‐population synthesis model, we study the possibility of using pairs of AB system colours to break the well‐known stellar age–metallicity degeneracy and to give constraints on two luminosity‐weighted stellar‐population parameters (age and metallicity). We present the relative age and metallicity sensitivities of the AB system colours that relate to the u, B, g, V, r, R, i, I, z, J, H and K bands, and we quantify the ability of various colour pairs to break the age–metallicity degeneracy. Our results suggest that a few pairs of colours can be used to constrain the above two stellar‐population parameters. This will be very useful for exploring the stellar populations of distant galaxies. In detail, colour pairs [(r–K), (u–R)] and [(r–K), (u–r)] are shown to be the best pairs for estimating the luminosity‐weighted stellar ages and metallicities of galaxies. They can constrain two stellar‐population parameters on average with age uncertainties less than 3.89 Gyr and metallicity uncertainties less than 0.34 dex for typical colour uncertainties. The typical age uncertainties for young populations (age < 4.6 Gyr) and metal‐rich populations (Z≥ 0.001) are small (about 2.26 Gyr) while those for old populations (age ≥ 4.6 Gyr) and metal‐poor populations (Z < 0.001) are much larger (about 6.88 Gyr). However, the metallicity uncertainties for metal‐poor populations (about 0.0024) are much smaller than for other populations (about 0.015). Some other colour pairs can also possibly be used for constraining the two parameters. On the whole, the estimation of stellar‐population parameters is likely to be reliable only for early‐type galaxies with small colour errors and globular clusters, because such objects contain less dust. In fact, no galaxy is totally dust‐free and early‐type galaxies are also likely have some dust [e.g. E(B–V) ∼ 0.05], which can change the stellar ages by about 2.5 Gyr and metallicities (Z) by about 0.015. When we compare the photometric estimates with previous spectroscopic estimates, we find some differences, especially when comparing the stellar ages determined by two methods. The differences mainly result from the young populations of galaxies. Therefore, it is difficult to obtain the absolute values of stellar ages and metallicities, but the results are useful for obtaining some relative values. In addition, our results suggest that colours relating to both UBVRIJHK and ugriz magnitudes are much better than either UBVRIJHK or ugriz colours for breaking the well‐known degeneracy. The results also show that the stellar ages and metallicities of galaxies observed by the Sloan Digital Sky Survey and the Two‐Micron All‐Sky Survey can be estimated via photometry data.

This paper presents the theoretically integrated spectral energy distributions (SEDs) of binary star composite stellar populations (bsCSPs) in early‐type galaxies and how the bsCSP model can be used for the spectral studies of galaxies. All bsCSPs are built based on three adjustable inputs (metallicity, ages of old and young components). The effects of binary interactions and stellar population mixture are taken into account. The results show some ultraviolet (UV) upturn SEDs naturally for bsCSPs. The SEDs of bsCSPs are affected obviously by all of the three stellar population parameters, and the effects of three parameters are degenerate. This suggests that the effects of metallicity, and the ages of the old (major in stellar mass) and young (minor) components of stellar populations should be taken into account in the SED studies of early‐type galaxies. The sensitivities of SEDs at different wavelengths to the inputs of a stellar population model are also investigated. It is shown that UV SEDs are sensitive to all of the three stellar population parameters, rather than to only stellar age. Special wavelength ranges according to some SED features that are relatively sensitive to the stellar metallicity, young‐component age and old‐component age of bsCSPs are found by this work. For example, the shapes of SEDs with the wavelength ranges of 5110–5250, 5250–5310, 5310–5350, 5830–5970 and 20 950–23 550 Å are relatively sensitive to the stellar metallicity of bsCSPs. The shapes of SEDs within 965–985, 1005–1055 and 1205–1245 Å are sensitive to the old‐component age, while SED features within the wavelength ranges of 2185–2245, 2455–2505, 2505–2555, 2775–2825 and 2825–2875 Å are sensitive to the young‐component age. The results suggest that some line indices within these special wavelength ranges are possibly better for stellar population studies compared to the others, and greater weights may be given to these special SED parts in the determination of the stellar population parameters of early‐type galaxies from fitting SEDs via bsCSPs.

We calculated the populations of core‐helium‐burning (CHeB) stars and found that secondary red‐clump (SRC) stars can form a SRC peak in the distributions of the frequency of maximum seismic amplitude (νmax) and mean large‐frequency separation (Δν) of CHeB stars when metallicity Z≥ 0.02. The νmax and Δν of CHeB stars are dependent not only on He‐core mass but also on H‐shell burning. The SRC peak is composed of CHeB stars with mass roughly between the critical mass MHeF and MHeF+ 0.2, while He‐core mass is between about 0.33 and 0.36 M⊙. The location of the SRC peak can be affected by the mixing‐length parameter α, metallicity Z and overshooting parameter δov. A decrease in α or increase in Z or δov leads to a movement of the SRC peak towards a lower frequency. The change in Z and α only slightly affects the value of MHeF, but the variation in δov can affect the value of MHeF significantly. Thus the SRC peak might aid in determining the value of MHeF and calibrating δov. In addition, the effects of convective acceleration of SRC stars and the decrease in the νmax of ‘semidegenerate’ stars with mass result in the appearance of a shoulder between about 40 and 50 μHz in the νmax distribution. However, the convective acceleration of stars with M < MHeF leads to a deficit in the νmax distribution between about 9 and 20 μHz. Moreover, the value of the parameter b of the relation between νmax and Δν for populations with M > MHeF is obviously larger than that for populations with M < MHeF.