The GeMS/GSAOI Galactic Globular Cluster Survey (G4CS) II: Characterization of 47 Tuc with Bayesian Statistics

We present a photometric analysis of globular cluster 47 Tuc (NGC\,104), using near-IR imaging data from the GeMS/GSAOI Galactic Globular Cluster Survey (G4CS) which is in operation at Gemini-South telescope.~Our survey is designed to obtain AO-assisted deep imaging with near diffraction-limited spatial resolution of the central fields of Milky Way globular clusters.~The G4CS near-IR photometry was combined with an optical photometry catalog obtained from Hubble Space Telescope survey data to produce a high-quality color-magnitude diagram that reaches down to K$_s\approx$ 21 Vega mag.~We used the software suite BASE-9, which uses an adaptive Metropolis sampling algorithm to perform a Markov chain Monte Carlo (MCMC) Bayesian analysis, and obtained probability distributions and precise estimates for the age, distance and extinction cluster parameters.~Our best estimate for the age of 47 Tuc is 12.42$^{+0.05}_{-0.05}$ $\pm$ 0.08 Gyr, and our true distance modulus estimate is (m$-$M)$_0$=13.250$^{+0.003}_{-0.003}$ $\pm$ 0.028 mag, in tight agreement with previous studies using Gaia DR2 parallax and detached eclipsing binaries.