Based on the theoretical CMDs of bsSSPs, we fit the CMDs of our sample clusters and derive some
basic parameters of these clusters in this section. In order to get reliable results, big ranges are
used for the stellar ages and metallicities of theoretical populations when fitting the observational
CMDs of star clusters. In detail, the stellar age and metallicity ranges are taken as 0.1 – 15 Gyr
and 0.0001 – 0.03, respectively. These are just the default ranges of the isochrone database used by
this work. Although the largest metallicity of the theoretical populations is only 0.03, it is enough for
studying the CMDs of most globular clusters, as globular clusters are usually metal-poor (Z ≤ 0.03).
Because the observational data of stars with high luminosities have less observational uncertainties,
a magnitude-weighted method is taken in this work. This can possibly enhance the reliability of the
fitting results. To be clear, we compare the observational and best-fit theoretical CMDs of 12 GCs in
Figures 1, 2 and 3. The best-fit CMDs are found by comparing the distribution of stars in theoretical
CMDs to that in observational CMDs. The advantage of such a method is that both the shape and
luminosity function are compared at the same time.