arXiv2010
HR\,8799 is a $λ$ Bootis, $γ$ Doradus star hosting a planetary system and a debris disk with two rings. This makes this system a very interesting target for asteroseismic studies. In particular, this work is devoted to the determination of the internal metallicity of this star, linked with its $λ$ Bootis nature, and its age, taking the advantage of its $γ$ Doradus-type pulsations. To do so we have used the equilibrium code CESAM and the non-adiabatic pulsational code GraCo. We have applied the Frequency Ratio Method and the Time Dependent Convection theory to estimate the mode identification, the Brunt-Vaïsälä frequency integral and the mode instability, making a selection of the possible models fulfilling all observational constraints. Using the position of the star in the HR diagram, the solar metallicity models is discarded. This result contradicts one of the main assumptions of the most accepted hypothesis explaining the $λ$ Bootis nature, the accretion/diffusion of gas from a star with solar metallicity. Therefore, in sight of these new results, a revision of this hypothesis is needed. The inclusion of accurate internal chemical mixing is necessary. The use of the asteroseismological constraints provides a very accurate determination of the physical characteristics of HR\,8799: an age in the ranges [1123, 1625] and [26, 430] Myr, and a mass in the ranges [1.32, 1.33] and [1.44, 1.45] $M_{\odot}$, respectively, depending on the visual angle $i$. The determination of this angle and more accurate multicolor photometric observations can definitively fix the mass, metallicity and age of this star. In particular, an accurate age estimation is needed for a correct understanding of the planetary system. In our study we have found that the age widely used for modelling the system is unlike.