Age and helium content of the open cluster NGC 6791 from multiple eclipsing binary members I. Measurements, methods, and first results

Context. Models of stellar structure and evolution can be constrained by measuring accurate parameters of detached eclipsing binaries in open clusters. Multiple binary stars provide the means to determine helium abundances in these old stellar systems, and in turn, to improve age estimates. Aims. Earlier measurements of the masses and radii of the detached eclipsing binary V20 in the open cluster NGC 6791 were accurate enough to demonstrate that there are significant differences between current stellar models. Here we improve on those results and add measurements of two additional detached eclipsing binaries, the cluster members V18 and V80. The enlarged sample sets much tighter constraints on the properties of stellar models than has hitherto been possible, thereby improving both the accuracy and precision of the cluster age. Methods. We employed (i) high-resolution UVES spectroscopy of V18, V20 and V80 to determine their spectroscopic effective temperatures, [Fe/H] values, and spectroscopic orbital elements; and (ii) time-series photometry from the Nordic Optical Telescope to obtain the photometric elements. Results. The masses and radii of the V18 and V20 components are found to high accuracy, with errors on the masses in the range 0.27-0.36% and errors on the radii in the range 0.61-0.92%. V80 is found to be magnetically active, and more observations are needed to determine its parameters accurately. The metallicity of NGC 6791 is measured from disentangled spectra of the binaries and a few single stars to be [Fe/H] = +0.29 +/- 0.03 (random) +/- 0.07 (systematic). The cluster reddening and apparent distance modulus are found to be E(B - V) = 0.160 +/- 0.025 and (m - M)(V) = 13.51 +/- 0.06. A first model comparison shows that we can constrain the helium content of the NGC 6791 stars, and thus reach a more accurate age than previously possible. It may be possible to constrain additional parameters, in particular the C, N, and O abundances. This will be investigated in Paper II. Conclusions. Using multiple, detached eclipsing binaries for determining stellar cluster ages, it is now possible to constrain parameters of stellar models, notably the helium content, which were previously out of reach. By observing a suitable number of detached eclipsing binaries in several open clusters, it will be possible to calibrate the age-scale and the helium enrichment parameter Delta Y/Delta Z, and provide firm constraints that stellar models must reproduce.