Context. The availability of asteroseismic constraints for a large sample of stars from the missions CoRoT and Kepler paves the way for various statistical studies of the seismic properties of stellar populations. Aims. We evaluate the impact of rotation-induced mixing and thermohaline instability on the global asteroseismic parameters at different stages of the stellar evolution from the zero age main sequence to the thermally pulsating asymptotic giant branch to distinguish stellar populations. Methods. We present a grid of stellar evolutionary models for four metallicities (Z = 0.0001, 0.002, 0.004, and 0.014) in the mass range from 0.85 to 6.0 M . The models are computed either with standard prescriptions or including both thermohaline convection and rotation-induced mixing. For the whole grid, we provide the usual stellar parameters (luminosity, effective temperature, lifetimes, ... ), together with the global seismic parameters, i.e. the large frequency separation and asymptotic relations, the frequency corresponding to the maximum oscillation power ν max , the maximal amplitude A max , the asymptotic period spacing of g-modes, and different acoustic radii. Results. We discuss a signature of rotation-induced mixing on the global asteroseismic quantities, that can be detected observationally. Thermohaline mixing whose effects can be identified using spectroscopic studies cannot be characterized by the global seismic parameters studied here. However, we cannot exclude that individual mode frequencies or other well chosen asteroseismic quantities might help us to constrain this mixing.

Context. Rotational splittings are currently measured for several main sequence stars and a large number of red giants with the space mission Kepler. This will provide stringent constraints on rotation profiles. Aims. Our aim is to obtain seismic constraints on the internal transport and surface loss of the angular momentum of oscillating solar-like stars. To this end, we study the evolution of rotational splittings from the pre-main sequence to the red-giant branch for stochastically excited oscillation modes. Methods. We modified the evolutionary code CESAM2K to take rotationally induced transport in radiative zones into account. Linear rotational splittings were computed for a sequence of 1.3 M models. Rotation profiles were derived from our evolutionary models and eigenfunctions from linear adiabatic oscillation calculations. Results. We find that transport by meridional circulation and shear turbulence yields far too high a core rotation rate for red-giant models compared with recent seismic observations. We discuss several uncertainties in the physical description of stars that could have an impact on the rotation profiles. For instance, we find that the Goldreich-Schubert-Fricke instability does not extract enough angular momentum from the core to account for the discrepancy. In contrast, an increase of the horizontal turbulent viscosity by 2 orders of magnitude is able to significantly decrease the central rotation rate on the red-giant branch. Conclusions. Our results indicate that it is possible that the prescription for the horizontal turbulent viscosity largely underestimates its actual value or else a mechanism not included in current stellar models of low mass stars is needed to slow down the rotation in the radiative core of red-giant stars.

Aims. In this paper we study the effects of rotation in low-mass, low-metallicity RGB stars. Methods. We present the first evolutionary models taking into account self-consistently the latest prescriptions for the transport of angular momentum by meridional circulation and shear turbulence in stellar interiors as well as the associated mixing processes for chemicals computed from the ZAMS to the upper RGB. We discuss the uncertainties associated with the physical description of the rotational mixing in detail and carefully study their effects on the rotation profile, diffusion coefficients, structural evolution, lifetimes, and chemical signatures at the stellar surface. We focus in particular on the various assumptions concerning the rotation law in the convective envelope, the initial rotation velocity distribution, the presence of µ-gradients, and the treatment of the horizontal and vertical turbulence.Results. This exploration leads to two main conclusions. (1) After completion of the first dredge-up, the degree of differential rotation (and hence mixing) is maximised in the case of a differentially rotating convective envelope (i.e., j CE (r) = const.), as anticipated in previous studies. (2) Even with this assumption, and contrary to some previous claims, the present treatment for the evolution of the rotation profile and associated meridional circulation and shear turbulence does not lead to enough mixing of chemicals to explain the abundance anomalies in low-metallicity field and globular cluster RGB stars observed around the bump luminosity. Conclusions. This study raises questions that need to be addressed in the near future. These include, for example, the interaction between rotation and convection and the trigger of additional hydrodynamical instabilities.