Turbulent convection models for stars

We propose to develop the non-local hydrodynamic moment equations into a new and powerful tool for the treatment of convection in stellar modelling. During the preceeding project P11882-PHY "Convection in Stars" we have studied the numerical properties of the moment equations and their capability to recover the mean structure and energy transport found in numerical simulations of convection zones. We have performed such simulations and developed a new simulation code with advanced numerics. We have also developed software for automatic and fast computation of mode atmosphere grids and applied this software to compare traditional convection models with observations. The moment equations passed our tests surprisingly well. We consider them an excellent convection treatment applicable to stellar convection, as they fulfill the requirements of a proven performance record (reliability), of versatility, and of manageability, which altogether are necessary to provide substantial progress on a whole variety of unsolved astrophysical problems related to convection. In the new project, we propose to implement the hydrodynamic moment equations into a next generation of stellar model atmospheres, to test these model atmospheres by comparing them with observations and numerical simulations, and to support scientific collaborators implementing such convection models into stellar interior models. Our new code will be used to produce grids of model atmospheres for spectral line profile calculation as well as synthetic photometry. We will compare these synthetic data with photometric observations and Balmer line profiles of galactic clusters and standard stars. Moreover, we will compare the new model atmospheres with realistic 3D numerical simulations of the solar photosphere and for selected A and F main sequence stars and we also will produce new numerical simulation data. If these applications are successful, we will also try to reproduce observed spectral line bi-sectors over the HR diagram. Succeeding to do so would provide a new, flexible, and inexpensive tool to study velocity and temperature fields in stars. It would allow a physical modelling of convective line broadening in everyday applications and without fudge parameters which presently have to be tuned individually for each star. We also plan to organize an international workshop in Vienna bringing together the experts in stellar convection modelling. Important goals of this workshop are a comparison of available methods for convection treatment and the development of a road map for turbulent convection modelling in astrophysics for the next decade.

A better understanding of turbulent flows is of vital interest for a large number of research fields, including not only astrophysics, but also geophysics (atmospheric sciences, meteoro-logy, oceanography), climatology, engineering sciences, and even branches of biology and medicine. Everyday examples from engineering include combustion processes in motors of cars or the flow of air along wing and hull of a commercial jet at cruising speed. Key uncertainties in climatology are caused by the turbulent nature of flows in the oceans. Research in this field is crucial for a better understanding of the dynamics of the oceans and their exchange of energy with the atmosphere of the earth, the most important part of any climate model. The turbulent nature of the flows in the earth`s atmosphere is also one of the causes of uncertainty in weather predictions. Most of these flows have counterparts in astrophysics: from the atmospheres of other planets to the convective envelopes and cores of different types of stars to even supernovae, the giant explosions some stars experience during their final stages of evolution. Project P13936-TEC has focussed on the problem of how to improve the modelling of stel-lar convection. Its starting point has been a new generation of turbulence models which had previously and successfully been applied to various engineering problems and to geophysical flows. As our work intended to use these models for physical conditions quite different from cases encountered on the earth, extensive computer simulations had to be made to study these ideas in a "numerical laboratory" at conditions more close to stellar ones, before selecting the most promising competitors for applications in models of stars. As a result of this procedure, it was possible to provide some feedback to the geophysical community. We were able to confirm the poor performance of some models already held in lower esteem, add others to this list, and finally identify a model, which at least for those types of stars we have studied in detail (stars of spectral type "A", some types of white dwarfs) yields a dramatic improvement over any of the models previously used. While the latter fail many observational tests we have been looking at, and also in comparisons to numerical simulations performed for such cases by other researchers, the new model succeeds in these challenges without specific readjustments. The higher degree of universality of this model is also good news for geophysicists. In addition, several specific improvements of the model have been devised on the basis of our own numerical simulations which may find application elsewhere. The new model is the first to permit realistic quantitative predictions of surface velocity fields and mixing effects due to convection in envelopes of A type stars (among them Vega, e.g., represents the "hot end"). If similar results can be obtained for other types of stars, the new model will be very useful in improving our understanding of the structure, evolution, and observable properties of stars. The project also supported other FwF projects conducted at the Institute for Astronomy of the University of Vienna which were devoted to research in neighbouring fields. The project has also, indirectly, contributed to the satellite projects COROT and Eddington where Austrian researchers participate in. Finally, during the project a new, generally applicable code for hydrodynamical simulations has been developed as well as software for computer based code generation, providing a basis for further research in the field.