Effects of rotational mixing on the asteroseismic properties of solar-type stars

Context. Observations of solar-like oscillations obtained either from the ground or from space stimulated the study of the effects of various physical processes on the modelling of solar-type stars. Aims. The influence of rotational mixing on the evolution and asteroseismic properties of solar-type stars is studied. Methods. Global and asteroseismic properties of models of solar-type stars computed with and without a comprehensive treatment of shellular rotation are compared. The effects of internal magnetic fields are also discussed in the framework of the Tayler-Spruit dynamo. Results. Rotational mixing changes the global properties of a solar-type star with a significant increase of the effective temperature resulting in a shift of the evolutionary track to the blue part of the HR diagram. These differences observed in the HR diagram are related to changes of the chemical composition, because rotational mixing counteracts the effects of atomic diffusion leading to larger helium surface abundances for rotating models than for non-rotating ones. Higher values of the large frequency separation are then found for rotating models than for non-rotating ones at the same evolutionary stage, because the increase of the effective temperature leads to a smaller radius and hence to an increase of the stellar mean density. In addition to changing the global properties of solar-type stars, rotational mixing also has a considerable impact on the structure and chemical composition of the central stellar layers by bringing fresh hydrogen fuel to the central stellar core, thereby enhancing the main-sequence lifetime. The increase of the central hydrogen abundance together with the change of the chemical profiles in the central layers result in a significant increase of the values of the small frequency separations and of the ratio of the small to large separations for models including shellular rotation. This increase is clearly seen for models with the same age sharing the same initial parameters except for the inclusion of rotation as well as for models with the same global stellar parameters and in particular the same location in the HR diagram. By computing rotating models of solar-type stars including the effects of a dynamo that possibly occurs in the radiative zone, we find that the efficiency of rotational mixing is strongly reduced when the effects of magnetic fields are taken into account, in contrast to what happens in massive stars.