Small convective cores on the main sequence
Michael Bazot (New York University Abu Dhabi), Jørgen Christensen-Dalsgaard (Aarhus University), Laurent Gizon (Max-Planck-Institut für Sonnensystemforschung), Othman Benomar (New York University Abu Dhabi)

Convective cores are extremely interesting objects in stellar physics. On one hand they are good age markers. On the other hand they offer ways of testing the physics of our models. One such instance is the search of small convective cores in main-sequence stars. The precise modelling of the stellar structure may strongly impact the outcome of the detection process. As a test case, we will discuss alpha Cen A, a prototypal example of star with a potential small convective core, for which we have large set of good observations (including seismic data). We will discuss the results of a thourough Bayesian analysis of this star and show the impact of overshooting, nuclear reaction rates and diffusion on the physical state at the centre of the star (does it have a convective core ? which nuclear process powers it ? what is the precise evolutionary phase of the star ?). We will show that, in probabilistic terms, it remain a very uncertain picture. We will use our conclusions to discuss the impact of Kepler data (and other space missions) for the search of small convective cores in other stars.