Final Report Summary - TOFU (Toward a new generation of multi-dimensional stellar evolution models: the TOol of the FUture) The TOFU project is devoted to multi-dimensional stellar and planetary models, based on the development of appropriate numerical tools that allows the multi-dimensional description of a complete star (or planet) interior during timescales relevant to various stellar/planetary evolutionary phases. The major scientific motivation is to improve the description of key stellar/planetary physical processes and to solve long standing problems characterising the life of stars and planets. The fully innovative aspect of the project is the development of a time implicit approach which allows the exploration of physical processes on spatial and temporal scales previously out of reach with current numerical codes. The development of the multi-D, fully compressible time implicit hydrodynamic code MUSIC was at the heart of the TOFU project. The scale of such a work is comparable to the building of a new instrument.Based on these developments, we have performed the first hydrodynamics simulations describing the multi-dimensional structure of accreting, convective low mass stars. Accretion is an important process relevant to various fields in astrophysics, from star formation to the study of compact binaries and supernovae type I. Many studies have been devoted to the effect of accretion on the structure and evolution of objects, using either simple semi-analytic approaches or simulations based on one dimensional (1D) stellar evolution codes. But no multi-dimensional numerical study has ever been devoted to the effect of accretion on the structure of accreting objects. Because of this lack of sophisticated modelling, great uncertainties still remain regarding the fraction of accretion luminosity imparted to an accreting object or radiated away, and how the accreted material is redistributed over the stellar surface and the depth it reaches. Early accretion history may impact the properties of stellar objects (luminosity, radius, and effective temperature) in star formation regions and young clusters even after several million of years when the accretion process has ceased. These effects could provide an explanation for several observed features in star-forming regions and young clusters, having important consequences on our general understanding of star formation, an active field of research in Astrophysics. Our multi-dimensional accretion simulations enable to understand the effect of so-called “hot” accretion, when the accreted material is characterised by a larger entropy than that of the bulk of the stellar material. The multi-D simulations show an accumulation of hot material at the surface that does not sink and instead produces a hot surface layer, which tends to suppress convection in the stellar envelope. These new simulations enable to derive an improved treatment of accretion in 1D stellar evolution models, based on an accretion boundary condition. Such treatment of accretion is more physical than the standard assumption of redistribution of the accreted energy within the stellar interior used in the literature. The impact of this more physical accretion boundary condition on the evolution of young low mass stars and brown dwarfs and on observations in young clusters can now be further explored in follow-up studies. These pioneering simulations show the potential of using time implicit multi-D simulations to improve our understanding of stellar physics et evolution. Our results contribute to the so-called 321D link where multi-dimensional simulations enable to improve 1D stellar evolution calculations, which are still required to produce “observables” and thus for a direct link between models and observations. Another achievement of this project is linked to a thorough study of turbulent convection in deep stellar/planetary interiors. Convection plays a crucial role on the structure and properties of stars and planets (for e.g energy transport and chemical mixing) and contribute to mixing in regions at the transition between convectively stable and unstable zones. We have performed two- and three-dimensional hydrodynamics implicit large-eddy simulations of compressible convection in a young Sun using MUSIC. We show the existence of extreme (rare) events of convective down-flows (or plumes) that penetrate much deeper in the stable region than the average plume and that could contribute substantially to mixing on the long term evolution of the star. We apply a statistical method to calculate the probability of rare events, namely extreme value theory which is usually used in finance, Earth science and climate studies. Our approach allows a quantitative estimate of the mixing in solar type stars and provides a possible explanation for the long standing problem of lithium depletion in pre-main sequence and main sequence stars (like the Sun). It can also explain a puzzling trend between rotation and depletion of lithium which is observe in many stars.
