The age of 47 Tuc from self-consistent isochrone fits to colour–magnitude diagrams and the eclipsing member V69

Abstract

Our aim is to derive a self-consistent age, distance and composition for the globular cluster $47\,$Tucanae ($47\,$Tuc; NGC104). First, we reevaluate the reddening towards the cluster resulting in a nominal $E(B-V)=0.03\pm0.01$ as the best estimate. The $T_{\rm eff}$ of the components of the eclipsing binary member V69 is found to be $5900\pm72$ K from both photometric and spectroscopic evidence. This yields a true distance modulus $(m-M)_0=13.21\pm0.06$(random)$ \pm0.03 $(systematic) to $47\,$Tuc when combined with existing measurements of V69 radii and luminosity ratio. We then present a new completely self-consistent isochrone fitting method to ground based and $\textit{HST}$ cluster colour-magnitude diagrams and the eclipsing binary member V69. The analysis suggests that the composition of V69, and by extension one of the populations of $47\,$Tuc, is given by [Fe/H]$\sim-0.70$, [O/Fe]$\sim+0.60$, and $Y\sim0.250$ on the solar abundance scale of Asplund, Grevesse & Sauval. However, this depends on the accuracy of the model $T_{\rm eff}$ scale which is 50-75 K cooler than our best estimate but within measurement uncertainties. Our best estimate of the age of $47\,$Tuc is 11.8 Gyr, with firm ($3 \sigma$) lower and upper limits of 10.4 and 13.4 Gyr, respectively, in satisfactory agreement with the age derived from the white dwarf cooling sequence if our determination of the distance modulus is adopted.