Relative evolution of eclipsing binaries: A tool for measuring globular cluster ages and He abundances

Context. Globular clusters (GCs) are among the oldest objects in the Universe for which an age can be directly measured; they thus play an important cosmological role. This age depends sensitively on the He abundance, however, which cannot be reliably measured from spectroscopy in GC stars. Detached eclipsing binaries (DEBs) near the turnoff (TO) point may play an important role in this regard. Aims. The aim of this study is to explore the possibility that, by working with differential measurements of stars that comprise a TO binary system and by assuming the two stars have the same age and He abundance, one can achieve tighter, more robust, and less model-dependent constraints on the ages and He abundances than otherwise possible by working with the absolute parameters of the stars. Methods. We compared both the absolute and differential parameters of the stars in V69, a TO DEB pair in the GC 47 Tuc, with two different sets of stellar evolutionary tracks, making use of a Monte Carlo technique to estimate the GC’s He abundance and age, along with their uncertainties. Results. We find that the relative approach can produce age and He abundance estimates that are in good agreement with those from the literature. We show that our estimates are also less model-dependent, less sensitive to [Fe/H], and more robust to inherent model systematics than those obtained with an absolute approach. On the other hand, the relative analysis results in larger statistical uncertainties than its absolute counterpart, at least in the case of V69, where the two stars have very similar properties. For binary pairs in which one of the components is less evolved than the other, the statistical uncertainty can be reduced. Conclusions. Our results suggest that the method proposed in this work can be used to robustly constrain the He abundance and ages of GCs.