2001A&A...379..245M

We have revisited the calibration of the visual binary system ζHerculis with the goal to give the seismological properties of the G0IV sub-giant ζHerA. The sum of masses and the mass fraction are derived from the most recent astrometric data mostly based on the hipparcos ones. We have derived 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 and the most recent physical data. A χ² minimization is performed to approach the most reliable modeling parameters which reproduce the observations within their error bars. For the age of the ζ Her binary system we have obtained t_ζ Her_=3387Myr, for the masses m_ζ HerA_=1.45M☉_ and m_ζ HerB_=0.98M☉_, 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 Λ_ζ HerA_=0.92 and Λ_ζ HerB_=0.90 using the Canuto & Mazitelli (1991ApJ...370..295C, 1992ApJ...389..724C) convection theory. Our results do not exclude that ζ HerA is itself a binary sub-system as has been suspected many times in the past century; the mass of the hypothetical unseen companion would be m_ζ HerA_0.05M☉_, a value significantly smaller than previous determinations. A calibration made with an overshoot of the convective core of ζ HerA leads to similar results but with a slight increase of ≃+250Myr for the age. The adiabatic oscillation spectrum of ζ HerA 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 both 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 <Δν₀≥∼42µHz, in agreement with the Martic et al. (2001, Observing Solar Like Oscillations: α CMi, η Cas, ζ Her A, ed. A. Wilson, ESA Publications Division, ESA SP-464, 431) seismic observations.