Asteroseismology for "à la carte" stellar age-dating and weighing: Age and mass of the CoRoT exoplanet host HD 52265

In the context of CoRoT, Kepler, Gaia, TESS, and PLATO, precise and accurate stellar ages, masses and radii are of paramount importance. They are crucial to constrain scenarii of planetary formation and evolution.We aim at quantifying how detailed stellar modeling improves the accuracy and precision on age and mass of individual stars. We adopt a multifaceted approach where we examine how the number of observational constraints as well as the uncertainties on observations and on model input physics impact the age-dating and weighing. We modelled the exoplanet host-star HD52265, a MS, solar-like oscillator observed by CoRoT. We considered different sets of observational constraints (HR data, metallicity, seismic constraints). For each case, we determined the age, mass, and properties of HD52265 inferred from models, and quantified the impact of the models inputs. Our seismic analysis provides an age A=2.10-2.54 Gyr, a mass M=1.14-1.32 Msun, and a radius R=1.30-1.34 Rsun, which corresponds to uncertainties of 10, 7, and 1.5% respectively. Our seismic study provides constraints on surface convection, through the mixing-length found to be 12-15% smaller than the solar one. Because of helium-mass degeneracy, the initial He abundance is determined modulo the mass. The seismic mass of the exoplanet is found to be Mp sin i=1.17-1.26 MJup, much more precise than what can be derived by HR diagram inversion. We demonstrate that asteroseismology allows to improve the age accuracy compared to other methods. We emphasize that the knowledge of the mean properties of oscillations -as the large frequency separation- is not enough for deriving accurate ages. We need precise individual frequencies to narrow the age scatter due to model uncertainties. This strengthen the case for precise classical stellar parameters and frequencies as will be obtained by Gaia and PLATO.