Context. The advent of space-based photometry missions such as CoRoT, Kepler and TESS has sparkled the rapid development of asteroseismology and its synergies with exoplanetology. In the near future, the advent of PLATO will further strengthen such multi-disciplinary studies. In that respect, testing asteroseismic modelling strategies and their importance for our understanding of planetary systems is crucial.
Aims. We carried out a detailed modelling of Kepler-93, an exoplanet host star observed by the Kepler satellite for which high-quality seismic data are available. This star is particularly interesting because it is a solar-like star very similar to the PLATO benchmark target (G spectral type, ∼6000 K, ∼1 M ⊙ and ∼1 R ⊙ ) and provides a real-life testbed for potential procedures to be used in the PLATO mission.
Methods. We used global and local minimisation techniques to carry out the seismic modelling of Kepler-93, for which we varied the physical ingredients of the given theoretical stellar models. We supplemented this step by seismic inversion techniques of the mean density. We then used these revised stellar parameters to provide new planetary parameters and to simulate the orbital evolution of the system under the effects of tides and atmospheric evaporation.
Results. We provide the following fundamental parameters for Kepler-93: ρ̄ ⋆ = 1.654 ± 0.004 g cm −3 , M ⋆ = 0.907 ± 0.023 M ⊙ , R ⋆ = 0.918 ± 0.008 R ⊙ , and Age = 6.78 ± 0.32 Gyr. The uncertainties we report for this benchmark star are well within the requirements of the PLATO mission and give confidence in the ability of providing precise and accurate stellar parameters for solar-like exoplanet-host stars. For the exoplanet Kepler-93b, we find M p = 4.01 ± 0.67 M ⊕ , R p = 1.478 ± 0.014 R ⊕ , and a semi-major axis a = 0.0533 ± 0.0005 AU. According to our simulations of the orbital evolution of the system, it seems unlikely that Kepler-93b formed with a mass high enough ( M p, initial > 100 M ⊕ ) to be impacted on its orbit by stellar tides.
Conclusions. For the benchmark case of a solar twin of the PLATO mission, detailed asteroseismic modelling procedures will be able to provide fundamental stellar parameters within the requirements of the PLATO mission. We also illustrate the synergies that can be achieved regarding the orbital evolution and atmospheric evaporation of exoplanets when these parameters are obtained. We also note the importance of the high-quality radial velocity follow-up, which here is a limiting factor, for providing precise planetary masses and mean densities to constrain the formation scenarii of exoplanets.
