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 \texttt{SIRIUS} code by means of simulated color-magnitude diagrams, including the analysis of multiple stellar populations. The population tagging is applied from the red giant branch to the bottom of the main sequence. Through sanity checks using synthetic {\it HST} color-magnitude diagrams of globular clusters we verify the code reliability in the context of simple and multiple stellar populations. 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 analyse NGC 6752, using Dartmouth stellar evolutionary models. Assuming a single stellar population, we derive an age of $13.7\pm0.5$ Gyr and a distance of $d_{\odot}=4.11\pm 0.08$ kpc, with the latter in agreement within $~3σ$ with the inverse Gaia parallax. In the analysis of the multiple stellar populations, three {populations} are clearly identified. From the Chromosome Map and UV/Optical two-color diagrams inspection, we found a fraction of stars of $25\pm5$, $46\pm7$, and $29\pm5$ per cent, for the first, second, and third generations, respectively. These fractions are in good agreement with the literature. An age difference of $500\pm410$ 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.

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