Analysis of 70 Ophiuchi AB including seismic constraints

Context. The analysis of solar-like oscillations for stars belonging to a binary system provides a unique opportunity to probe the internal stellar structure and to test our knowledge of stellar physics. Such oscillations have been recently observed and characterized for the A component of the 70 Ophiuchi system. Aims. We determined the global parameters of 70 Ophiuchi AB using the new asteroseismic measurements now available for 70 Oph A and tested the input physics introduced in stellar evolution codes. Methods. Three different stellar evolution codes and two different calibration methods were used to perform a comprehensive analysis of the 70 Ophiuchi system. Results. A model of 70 Ophiuchi AB that correctly reproduces all observational constraints available for both stars is determined. An age of $6.2 \pm 1.0$ Gyr is found with an initial helium mass fraction $Y_{\mathrm{i}}=0.266 \pm 0.015$ and an initial metallicity $(Z/X)_{\mathrm{i}}=0.0300 \pm 0.0025$ when atomic diffusion is included and a solar value of the mixing-length parameter assumed. A precise and independent determination of the value of the mixing-length parameter needed to model 70 Oph A requires accurate measurement of the mean small separation, which is not available yet. Current asteroseismic observations, however, suggest that the value of the mixing-length parameter of 70 Oph A is lower or equal to the solar calibrated value. The effects of atomic diffusion and of the choice of the adopted solar mixture were also studied. We finally found that the different evolution codes and calibration methods we used led to perfectly coherent results.