Helioseismic inferences have demonstrated very clearly the importance of including element diffusion and settling in solar modelling: models incorporating these processes are in substantially better agreement with the inferred solar sound speed than are models that neglect them. The remaining discrepancy between the models and the Sun has been taken as evidence for mixing in the region just beneath the convection zone. However, rather more serious discrepancies have resulted from a revision of solar abundances, and no obvious solution to this problem has been found so far. This perhaps demonstrates the danger of complacency when dealing with so complex a thing as a star. Hydrodynamical instabilities are likely to play a more important role than acknowledged in standard stellar modelling. An interesting example, if not relevant to modelling up to the present solar age, is the possible onset of semiconvective instability just beneath the convection zone, as first emphasized by Bahcall et al. (2001).

Gravitational settling and microscopic diffusion affects the main sequence lifetimes, main sequence turn-off luminosities and temperatures of metal-poor halo stars. As a result, the inclusion of diffusion in the stellar evolution models has important consequences for age determinations of old stars. In contrast, diffusion has little impact on the post-main sequence evolution of metal-poor stars. Observations of the heavy element abundances in turn-off and giant branch stars in the globular cluster NGC 6397 suggest that diffusion occurs in metal-poor stars, but that the diffusion must be inhibited by turbulent mixing.

We review the basic equations describing the microscopic diffusion of elements in stars. We describe the two formalisms commonly used to describe a stellar plasma, i.e., the Chapman-Enskog method and the Burgers equations. We point out the underlying assumptions about the physical state of the plasma itself. We briefly describe the different approximations which are often used to solve these equations, and discuss their validity. One of the major problems lies in the calculation of the collision integrals, and we discuss the different approaches to solving these integrals, emphasizing on their domain of validity.

Atomic diffusion can have detectable effects in many kinds of stars, each time that mixing processes are not efficient enough to prevent the build up of abundance stratifications. In this talk, after presentation of some general aspects about diffusion processes in stars, I will discuss the role of radiative acceleration which is one of the important quantities determining diffusion velocities. I will also discuss some aspects specific to stellar atmospheres, in particular for stars exhibiting strong magnetic fields.

Although it presently includes convective overshoot, microscopic diffusion, gravitational settling and radiative acceleration, the standard model of stellar structure is still unable to account for various observational facts, and there is now a large consensus that some extra mixing must occur in the radiation zones. To account for such mixing, the minimalist approach consists in introducing a parametrized turbulent diffusivity, and to adjust it so as to match the observations. A better way is to strive to implement the physical processes that may be responsible for this mixing, in particular shear-induced turbulence and large-scale meridional circulation, which both are linked with the differential rotation of the star. To describe that rotational mixing, as we call it, one has thus to follow the evolution of the internal rotation profile. By making some plausible assumptions, its is possible to reduce the advection of angular momentum through the 2-D circulation to a 1-D process, and that of the chemical elements to a vertical diffusion. It is then possible to implement these transports in a 1-D stellar evolution code.
In massive stars, angular momentum is transported mainly by the meridional circulation, and there is good agreement between the observations and the predictions based on the rotational mixing. This not so for solar-type stars where another, more efficient mechanism is required to transport angular momentum. A fossil magnetic field has been invoked, but recently it has been shown that such a field would connect with the convection zone, and imprint its differential rotation on the radiation zone, which is not observed. The other candidate is the transport of angular momentum by the internal gravity waves that are emitted at the base of the convection zone; although their treatment is still somewhat crude, it appears that they can explain both the quasi-uniform rotation of the solar interior, and the depletion of lithium observed in such stars.

With the first light of COROT, the preparation of KEPLER and the future helioseismology spatial projects such as GOLF-NG, a coherent picture of the evolution of rotating stars from their birth to their death is needed. We describe here the modelling of the macroscopic transport of angular momentum and matter in stellar interiors that we have undertaken to reach this goal. First, we recall in detail the dynamical processes that are driving these mechanisms in rotating stars and the theoretical advances we have achieved. Then, we present our new results of numerical simulations which allow us to follow in 2D the secular hydrodynamics of rotating stars, assuming that anisotropic turbulence enforces a shellular rotation law. Finally, we show how this work is leading to a dynamical vision of the Hertzsprung-Russel diagram with the support of asteroseismology and helioseismology, seismic observables giving constraints on the modelling of the internal transport and mixing processes. In conclusion, we present the different processes that should be studied in the near future to improve our description of stellar radiation zones.

Convective overshoot is a physical mechanism for which no recipe based on first principles is available; hence the necessity of assuming some parametrisations, which undermine the predictive power of the current generation of stellar models. We evidentiate the non local aspects of the convective phenomenon particularly in the proximities of the convective borders, and identify some cases when the use of a diffusive rather than the classic instantaneous approach to describe overshooting is highly recommended.

In order to prepare the theoretical interpretation of the oscillation frequencies detected by CoRoT, comparisons of results from standard stellar models by the ESTA group have proven to be very useful. The next issue which is briefly addressed here is “what are the additional physical processes that must be included in stellar models computed with different evolutionary codes for the next comparison exercises?” We therefore discuss the impact on oscillation frequencies of several physical processes which are still poorly understood and/or poorly modelled but cannot be fully discarded.


Stellar rotation and magnetism are two phenomena which intervene in many pulsating stars. As a result, calculating their effects on stellar pulsations has been the subject of active research for a number of years, and many results have emerged. For instance, slow stellar rotation lifts mode degeneracy and leads to evenly spaced frequency multiplets. At rapid rotation rates, a new organisation of the frequency spectrum appears, in which the centrifugal force plays a dominant role. Stellar magnetism plays an important role on pulsation frequencies both directly and indirectly. Various studies show how magnetism can shift frequencies and play on mode excitation and selection. Magnetism also introduces other types of waves with a different frequency spectrum organisation.


The present work is placed in the framework of the preparation for the interpretation of the seismic space data from the space mission CoRoT. In this context, rotation have become one of the most limiting factors when analysing the observed spectra of stars. A general view on the effects of rotation on the oscillations is given from the point of view of a linear perturbation analysis. As well, the latest results about the effect of shellular rotation on adiabatic oscillation frequencies are addressed. Finally, the role of rotation on asteroseismic diagnostics is discussed. In particular, échélle diagrams and analysis of rotation profile variations are examined.

Low-frequency oscillations are unstable in a wide range of stellar models and have been detected in a number of B-type stars. For such modes, even a moderate rotation significantly affects amplitude distribution over stellar surface and hence their visibility conditions. Adopting the traditional approximation, we study effects of rotation on relative amplitudes in photometric passbands and in radial velocity. We present numerical results for unstable modes in a selected stellar model of a 6 M๏ main sequence star. The goal is to show how observable amplitudes, which are tools for mode identification, depend on the rotation rate and on the aspect angle.

The approximation known as Frozen Convection has been widely used in the context of stellar oscillations due to the lack of a Time Dependent Convection theory. This approximation supposes to neglect the interaction between convection and oscillations and there are different ways to do it. The choice can affect theoretical predictions concerning the non-adiabatic treatment of the stellar oscillations. In fact, fictitious excitation or damping of the pulsation modes can be produced depending on the approximation used.

Three-dimensional Large Eddy Simulations (LES) of the convection-radiation transition layer of solar-type stars predict a different temperature stratification compared to models that use standard mixing-length theory. When these structural changes are taken into account theoretical oscillation frequencies are modified. Here, we compare the changes to the seismic spectra as predicted by the LES with those arising from diffusion and settling of helium and heavier elements. It is shown that turbulence effects in the modelling of the star α Centauri A change the large frequency separations twice as much as compared to those arising from gravitational settling, giving rise to a frequency shift opposite to what would have been expected from gravitational settling alone.

We present recent work undertaken by the Evolution and Seismic Tools Activity (ESTA) team of the CoRoT Seismology Working Group. The new ESTA-Task 3 aims at testing, comparing and optimising stellar evolution codes which include microscopic diffusion of the chemical elements resulting from pressure, temperature and concentration gradients. The results already obtained are globally satisfactory, but some differences between the different numerical tools appear that require further investigations.

We present the results of comparing three different implementations of the microscopic diffusion process in the stellar evolution codes CESAM and CLES. For each of these implementations we computed models of 1.0, 1.2 and 1.3 M๏. We analyse the differences in their internal structure at three selected evolutionary stages, as well as the variations of helium abundance and depth of the stellar convective envelope. The origin of these differences and their effects on the seismic properties of the models are also considered.

The ESTA activity under the CoRoT project aims at testing the tools for computing stellar models and oscillation frequencies that will be used in the analysis of asteroseismic data from CoRoT and other large-scale upcoming asteroseismic projects. Here I report results of comparisons between calculations using the Aarhus code (ASTEC) and two other codes, for models that include diffusion and settling. It is found that there are likely deficiencies, requiring further study, in the ASTEC computation of models including convective cores.

A report on the current status of the ESTA- Task 2 (oscillation frequencies comparison) is presented. Several types of comparisons have been made using the frequencies provided by different numerical codes. The equilibrium model is the same for all of them, and additionally some requirements such as boundary conditions, no re-meshing, etc, are also imposed. Some unexpected differences appear in the frequency and large separation comparisons. In the high frequency region these differences can be due to the order of the integration scheme used to solve the partial differential equations (or to the lack of number of mesh points in the outer layers). In the region around the fundamental radial mode and the low frequency region, important differences appear for the avoided crossing and the trapped modes respectively, the reason maybe due to the different sensitivity of each code to the profile of the Brunt-Väisälä frequency. The next step will be to test the accuracy of the codes using a model with a larger number of mesh points and with a better described Brunt-Väisälä frequency.

I present the software tool of the HELAS NA5 Workpackage Frequency Analysis and Mode Identification for Asteroseismology. We term this tool FAMIAS. It will be a collection of software tools for the frequency analysis and mode identification of photometric as well as spectroscopic data of oscillating stars packed into a graphical user interface. The workpackage is currently in the stage of development and will be made publicly available in a well documented form at the end of 2007. The creation of this data analysis tool is one of the objectives of the NA5 workpackage “Asteroseismology” within HELAS. For the spectroscopic mode identification, the moment method as well as various methods based on the Doppler broadening of the line profile will be implemented. The photometric mode identification will be based on the method of amplitude ratios and phase differences in different passbands. Therefore, pre-computed grids with the frequency values and their non-adiabatic eigenfunctions in the outer atmosphere for different kinds of stars will be included in the package.