Kepler-93: A testbed for detailed seismic modelling and orbital evolution of super-Earths around solar-like stars

Abstract

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 Mp = 4.01 ± 0.67 M⊕, Rp = 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 (Mp, 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.

Probing stellar cores from inversions of frequency separation ratios

“…This also allows to estimate the impact of the resolution limit. This advanced modelling strategy provided the optimal model of Kepler-93 (which was confirmed by a more elaborated modelling procedure, Bétrisey et al 2022).…”

“…From a pure statistical point of view, the precision is of the order ∼ 0.1% to 0.2%, which is negligible in comparison to the systematic uncertainty due to the choice of the physical ingredients, and the resolution limit of the inversion. In practice, a modelling strategy similar to that of Bétrisey et al (2022) should be considered. An extensive set of models with various physical ingredients should be constructed, and the precision is measured with the standard deviation of the inversion results.…”

“…that are difficult to treat for this type of stars. Because the entropy differences are localised in the very central stellar regions that are difficult to probe even with the ratios, we found that a modelling strategy similar to that of Bétrisey et al (2022) should be considered in a practical application of the method. An extensive set of models should be constructed, and inferences about the properties of the core can be deducted from the global behaviour of the inversion on the models of the set.…”

“…In practice, this limitation can be translated into a systematic uncertainty (see e.g. Bétrisey et al 2022), but it can become significant enough to prevent the inversion of accurately correcting.…”

“…Therefore, inversions based on so-called indicators were developed (Reese et al 2012;Buldgen et al 2015bBuldgen et al ,a, 2018, and applied to various cases (e.g. Buldgen et al 2016aBuldgen et al ,b, 2017aBuldgen et al , 2019bBétrisey et al 2022).…”