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

Context. In the context of the space missions CoRoT, Kepler, Gaia, TESS, and PLATO, precise and accurate stellar ages, masses, and radii are of paramount importance. For instance, they are crucial for constraining scenarii of planetary formation and evolution. Aims. We aim at quantifying how detailed stellar modelling can improve the accuracy and precision on age and mass of individual stars. To that end, we adopt a multifaceted approach where we carefully examine how the number of observational constraints as well as the uncertainties on observations and on model input physics affect the results of age-dating and weighing. Methods. We modelled in detail the exoplanet host-star HD 52265, a main-sequence, solar-like oscillator that CoRoT observed for four months. We considered different sets of observational constraints (Hertzsprung-Russell data, metallicity, various sets of seismic constraints). For each case, we determined the age, mass, and properties of HD 52265 inferred from stellar models, and we quantified the impact of the model input physics and free parameters. We also compared model ages with ages derived by empirical methods or Hertzsprung-Russell diagram inversion. Results. For our case study HD 52265, our seismic analysis provides an age A = 2.10-2.54 Gyr, a mass M = 1.14-1.32 M-circle dot, and a radius R = 1.30-1.34 R-circle dot, which corresponds to age, mass, and radius uncertainties of similar to 10, similar to 7, and similar to 1.5 per cent, respectively. These uncertainties account for observational errors and current state-of-the-art stellar model uncertainties. Our seismic study also provides constraints on surface convection properties through the mixing-length, which we find to be 12-15 per cent lower than the solar value. On the other hand, because of helium-mass degeneracy, the initial helium abundance is determined modulo the mass value. Finally, we evaluate the seismic mass of the exoplanet to be M-p sin i = 1.17-1.26 M-Jupiter, much more precise than what can be derived by Hertzsprung-Russell diagram inversion. Conclusions. We demonstrate that asteroseismology allows us to substantially improve the age accuracy that can be achieved with other methods. We emphasize that the knowledge of the mean properties of stellar oscillations - such as the large frequency separation - is not enough to derive accurate ages. We need precise individual frequencies to narrow the age scatter that is a result of the model input physics uncertainties. Further progress is required to better constrain the physics at work in stars and the stars helium content. Our results emphasize the importance of precise classical stellar parameters and oscillation frequencies such as will be obtained by the Gaia and PLATO missions.