Self-consistent Analysis of Stellar Clusters: An Application to HST Data of the Halo Globular Cluster NGC 6752

The Bayesian isochrone fitting using the Markov chain Monte Carlo algorithm is applied, to derive the probability distribution of the parameters age, metallicity, reddening, and absolute distance modulus. We introduce the SIRIUS code by means of simulated color-magnitude diagrams (CMDs), including the analysis of multiple stellar populations (MPs). The population tagging is applied from the red giant branch to the bottom of the main sequence. Through sanity checks using synthetic Hubble Space Telescope CMDs of globular clusters we verify the code reliability in the context of simple and MPs. In such tests, the formal uncertainties in age or age difference, metallicity, reddening, and absolute distance modulus can reach 400 Myr, 0.03 dex, 0.01 mag, and 0.03 mag, respectively. We apply the method to analyze NGC 6752, using Dartmouth stellar evolutionary models. Assuming a single stellar population, we derive an age of 13.7 +/- 0.5 Gyr and a distance of d(circle dot) = 4.11 +/- 0.08 kpc, with the latter in agreement within 3 sigma with the inverse Gaia parallax. In the analysis of the MPs, three populations are clearly identified. From the Chromosome Map and UV/Optical two-color diagrams inspection, we found a fraction of stars of 25 +/- 5, 46 +/- 7, and 29 +/- 5%, for the first, second, and third generations, respectively. These fractions are in good agreement with the literature. An age difference of 500 +/- 410 Myr between the first and the third generation is found, with the uncertainty decreasing to 400 Myr when the helium enhancement is taken into account.