Recent progress in solar or stellar interior modelling

Acoustic modes are well-suited probes to check the internal stellar structure and bring interesting constraints on turbulence regions, mixing in stellar interiors and magnetic fields. The SOHO satellite, through the helioseismic instruments GOLF, MDI and VIRGO, has significantly improved the knowledge of these modes owing to an excellent duty cycle (greater than 90%) and the capability to detect very low amplitude modes, down to 3 mm/s. Five years of the SOHO misson guarantee an accurate view of the solar interior, weakly dependent on the turbulent surface, from the energy-generating core to the surface. The recent results allow us to verify some of the theoretical assumptions of stellar modelling. The tachocline layers, located in a narrow region at the base of the convection zone, support an hydro (or magnetohydro) dynamical instability which induces mixing and results in Li-7 depletion in accordance with photospheric observations. On the contrary, central mixing is not favoured by the present observations. Nuclear reaction rates of the pp chain are now constrained by the behaviour of the sound speed and density. Doppler velocity measurements appear as an excellent technique to follow in real time the temporal evolution of the luminosity produced in the core. Some puzzling questions about dynamical effects in stellar plasmas can now start to be addressed for the first time. The theoretical neutrino emissions can be now directly deduced from our helioseismic vision of the energy-generating core. Nowadays, helioseismology provides a dynamical vision of the external half of the Sun (20% in mass), as a result of the extraction of the sound speed, density, rotation profiles and of the time evolution of velocity measurements. Below, the classical static vision of the nuclear region persists because of the poor spatial resolution offered by acoustic modes (+/-6% in radius, 10% in mass) and the long integration time (several years). Gravity modes will be extremely useful to improve the spatial resolution in the radiative region. The extended observations with the SOHO satellite may be extremely useful to detect some of these modes.