We have derived a new expression for the thermohaline mixing coefficient in stars, including the effects of radiative levitation and external turbulence, by solving Boussinesq equations in a quasi-incompressible fluid with a linear approximation. It
is well known that radiative levitation of individual elements can lead to their accumulation in specific stellar layers. In some cases, it can induce important effects on the stellar structure. Here we confirm that this accumulation is moderated by thermohaline convection due to the resulting inverse $mu$-gradient. The new coefficient that we have derived shows that the effect of radiative accelerations on the thermohaline instability itself is small. This effect must however be checked in all computations. We also confirm that the presence of large horizontal turbulence can reduce or even suppress the thermohaline convection. These results are important as they concern all the cases of heavy element accumulation in stars. The computations of radiative diffusion have to be revisited including thermohaline convection and its consequences. It may be one of the basic reasons for the fact that the observed abundances are always smaller than those predicted by pure atomic diffusion. In any case, these processes have to compete with rotation-induced mixing, but this competition is more complex than previously thought due to their mutual interaction.
Studying the internal structure of exoplanet-host stars compared to that of similar stars without detected planets is particularly important for the understanding of planetary formation. The observed average overmetallicity of stars with planets is a
n interesting point in that respect. In this framework, asteroseismic studies represent an excellent tool to determine the structural differences between stars with and without detected planets. It also leads to more precise values of the stellar parameters like mass, gravity, effective temperature, than those obtained from spectroscopy alone. Interestingly enough, the detection of stellar oscillations is obtained with the same instruments as used for the discovery of exoplanets, both from the ground and from space. The time scales however are very different, as the oscillations of solar type stars have periods around five to ten minutes, while the exoplanets orbits may go from a few days up to many years. Here I discuss the asteroseismology of exoplanet-host stars, with a few examples.
