The Zeta Herculis binary system revisited. Calibration and seismology

Abstract

We have revisited the calibration of the visual binary system Zeta Herculis with the goal to give the seismological properties of the G0 IV sub-giant Zeta Her A. We have used the most recent physical and observational data. For the age we have obtained 3387 Myr, for the masses respectively 1.45 and 0.98 solar mass, for the initial helium mass fraction 0.243, for the initial mass ratio of heavy elements to hydrogen 0.0269 and for the mixing-length parameters respectively 0.92 and 0.90 using the Canuto & Mazitelli (1991, 1992) convection theory. Our results do not exclude that Zeta Her A is itself a binary sub-system; the mass of the hypothetical unseen companion would be smaller than 0.05 solar mass. The adiabatic oscillation spectrum of Zeta Her A is found to be a complicated superposition of acoustic and gravity modes; some of them have a dual character. This greatly complicates the classification of the non-radial modes. The echelle diagram used by the observers to extract the frequencies will work for ell=0, 2, 3. The large difference is found to be of the order of 42 mu Hz, in agreement with the Martic et al. (2001) seismic observations.