Deep near-infrared photometry of the globular cluster 47 Tucanae. Reconciling theory and observations

Context. The Galactic globular cluster 47 Tucanae is central to studies of Galaxy formation, and a test-bed for theoretical models, distance determination and extragalactic age-dating techniques. Independent parallax-based distance determinations in the optical spectral range provide discrepant results; also, star counts along the Red Giant Branch from optical data have disclosed a worrying disagreement with theoretical predictions, that impacts not only the theory of red giant stars, but also the calibration of the age scale of extragalactic systems. Aims. Our new near-infrared data for 47 Tuc set constraints on its distance and test the reliability of theoretical red giant branch star counts, independently of previous conclusions from optical work. Methods. We have obtained deep near-infrared imaging of 47 Tuc using SOFI at the ESO New Technology Telescope. Colour-magnitude diagrams, isochrones and synthetic horizontal branch modelling have been used to determine the distance of 47 Tuc and constrain its age. We have also constructed a luminosity function of red giant stars, which has been compared with theoretical predictions of stellar evolution models. Results. We obtain a distance (m-M)0 = 13.18 ± 0.03 (random) ± 0.04 $(systematic$), for [Fe/H] = -0.7 ± 0.1 and E($B-V$) = 0.04 ± 0.02. This supports the shorter end of the range of distances obtained from optical studies. The mean horizontal branch star mass is between 0.65 and 0.66 $M_{\odot}$, and its 1σ Gaussian dispersion is between 0.010 and 0.012 $M_{\odot}$. The cluster age can only be approximately estimated from the data, and is between ~10 and ~13 Gyr. The luminosity function of red giant branch (and early-asymptotic giant branch) stars does not show a statistically significant discrepancy with theory. The brightness of the red giant branch bump in the near-infrared is possibly fainter than the models, although the uncertainty on the spectroscopic metallicity and age prevents to reach a firm conclusion on this issue