This paper emphasize the binary population: CMD fitting with the binary population synthetic model outperformed to the single population model. They used Hurley code (Hurley, Tout, and Pols (2002). Evolution of binary stars and the effect of tides on binary populations, MNRAS, 329(4), p.897-928). They mentioned that two color-color grids can disentangle the age-metallicity degeneracy via binary stellar populations. They fitted their isochrone database to M67 and NGC 1868 with the gT-grid and concluded that the database of binary stellar populations fitted the color magnitude diagrams better.

A notable sentence:

According to the work of Li and Han (2007b, arxiv/astro-ph: 0704.1202), (u-R) and (g-J) are sensitive to stellar age while (r-K) and (z-K) to stellar metallicity,

where the upper cases indicate Johnson UBVRIJHK magnitudes and the lower cases SDSS-ugriz magnitudes.

Researchers, including scientists from CHASC, working on color magnitude diagrams to infer ages, metalicities, temperatures, and other physical quantities of stars and stellar clusters may find this paper useful.

Methodologies for temperature calibration (fairly accurate estimation from V-K and a new calibration from b-y), metallicity calibration, absolute magnitude/distance calibration, interstellar reddening, and stellar ages were presented with reviews on stellar models and their parameters, astrophysical calibration errors, metalicity distribution function, age-metallicity diagram, age-velocity relation, and thin disk vs thick disk. It seems like that the previous methodologies for F and G stars need to be revised.

Despite my incapability of full understanding the theory of star formation history and the uncertainties of calibrations (looks like that all go toward regression problems to me), this paper fully manifests the complexity of the stellar models and their calibration process. From a statistical perspective, the complexity of the stellar models and calibrations comes from many predictors and only a few response variables with uncertainties (even more they are heteroskedastic). Furthermore, the relationship between predictors and response variables is sparsely known, which makes fitting the model to a star or a stellar cluster or inferencing physical information from them difficult. The mapping is considered to be highly structured black box and its required careful investigations.

I’d rather end this very technical preprint by citing a sentence:

The question of interest is therefore how well these relations and their intrinsic scatter can be determined from the observations

[hlee: Instead of determining, modeling seems to reflect the flexibilities and uncertainties.]