The zeta Herculis binary system revisited - Calibration and seismology

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. The sum of masses and the mass fraction are derived from the mo st recent astrometric data mostly based on the hipparcos ones. We have deri ved the effective temperatures, the luminosities and the metallicities from available spectroscopic data and tycho photometric data and calibrations. For the calculations of evolutionary models we have used updated physics an d the most recent physical data. A chi (2) minimization is performed to app roach the most reliable modeling parameters which reproduce the observation s within their error bars. For the age of the zeta Her binary system we hav e obtained t(zeta) (Her) = 3387 Myr, for the masses m(zeta) (Her) (A) = 1.4 5 M. and m(zeta) (Her) (B) = 0.98 M., for the initial helium mass fraction Y-i = 0.243, for the initial mass ratio of heavy elements to hydrogen (Z/X) (i) = 0.0269 and for the mixing-length parameters Lambda (zeta) (Her) (A) = 0.92 and Lambda (zeta) (Her) (B) = 0.90 using the Canuto & Mazitelli (1991 , 1992) convection theory. Our results do not exclude that zeta Her A is it self a binary sub-system as has been suspected many times in the past centu ry; the mass of the hypothetical unseen companion would be m(zeta) (Her) (A ) less than or similar to 0.5 M., a value significantly smaller than previo us determinations. A calibration made with an overshoot of the convective c ore of zeta Her A leads to similar results but with a slight increase of ap proximate to +250 Myr for the age. The adiabatic oscillation spectrum of ze ta Her A is found to be a complicated superposition of acoustic and gravity modes. Some of these waves have a dual character. This greatly complicates the classification of the non-radial modes. For l = 1 the modes all have b oth energy in the core and in the envelope; they are mixed modes. For l = 2 , 3 there is a succession of modes with energy either in the core or in the envelope with a few mixed modes. The echelle diagram used by the observers to extract the frequencies will work for l = 0; 2; 3. The large difference is found to be of the order of <(<Delta>nu (0))over bar> approximate to 42 mu Hz, in agreement with the Martic et al. (2001) seismic observations.