Constraining the helium-to-metal enrichment ratio ΔY/ΔZ from main-sequence binary stars

Aims. We aim to investigate the theoretical possibility of accurately determining the helium-to-metal enrichment ratio Delta Y/Delta Z from precise observations of double-lined eclipsing binary systems. Methods. Using Monte Carlo simulations, we drew synthetic binary systems with masses between 0.85 and 1.00 M-circle dot from a grid of stellar models. Both stars were sampled from a grid with Delta Y/Delta Z = 2.0, with a primary star at 80% of its main-sequence evolution. Subsequently, a broader grid with Delta Y/Delta Z from 1.0 to 3.0 was used in the fitting process. To account for observational uncertainties, two scenarios were explored: S1, with realistic uncertainties of 100 K in temperature and 0.1 dex in [Fe/H]; and S2, with halved uncertainties. We repeated the simulation at two baseline metallicities: [Fe/H] = 0.0 and -0.3. Results. The posterior distributions of Delta Y/Delta Z revealed significant biases. The distributions were severely biased towards the edge of the allowable range in the S1 error scenario. The situation only marginally improved when considering the S2 scenario. The effect is due to the impact of changing Delta Y/Delta Z in the stellar effective temperature and its interplay with [Fe/H] observational error, and it is therefore not restricted to the specific fitting method. Despite the presence of these systematic discrepancies, the age of the systems were recovered unbiased with 10% precision. Conclusions. Our findings indicate that the observational uncertainty in effective temperature and metallicity significantly hinders the accurate determination of the Delta Y/Delta Z parameter from main-sequence binary systems.