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HR\,8799 is a $\lambda$ Bootis, $\gamma$ Doradus star hosting a planetarysystem and a debris disk with two rings. This makes this system a veryinteresting target for asteroseismic studies. In particular, this work isdevoted to the determination of the internal metallicity of this star, linkedwith its $\lambda$ Bootis nature, and its age, taking the advantage of its$\gamma$ Doradus-type pulsations. To do so we have used the equilibrium codeCESAM and the non-adiabatic pulsational code GraCo. We have applied theFrequency Ratio Method and the Time Dependent Convection theory to estimate themode identification, the Brunt-Va\"is\"al\"a frequency integral and the modeinstability, making a selection of the possible models fulfilling allobservational constraints. Using the position of the star in the HR diagram,the solar metallicity models is discarded. This result contradicts one of themain assumptions of the most accepted hypothesis explaining the $\lambda$Bootis nature, the accretion/diffusion of gas from a star with solarmetallicity. Therefore, in sight of these new results, a revision of thishypothesis is needed. The inclusion of accurate internal chemical mixing isnecessary. The use of the asteroseismological constraints provides a veryaccurate determination of the physical characteristics of HR\,8799: an age inthe 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 photometricobservations can definitively fix the mass, metallicity and age of this star.In particular, an accurate age estimation is needed for a correct understandingof the planetary system. In our study we have found that the age widely usedfor modelling the system is unlike.

Asteroseismic determination of the physical characteristics of the planetary system host HR\,8799 ($\lambda$ Bootis nature and age)