Numerical simulation of A-type and white dwarf stars

Convection is an important physical process for transporting heat in liquids, in gases, and in plasma. It can mix these rapidly and cause a large variety of hydrodynamical phenomena in them or modify them. This includes the formation of large upflow and downflow structures (granules and plumes), running or standing waves, and shock waves. The challenge posed by the computation of these processes in stars stems from the fact that they are highly turbulent. Deeper understanding of these processes requires the numerical solution of the physical conservation laws which provide the basis for numerical simulations of convection in stars. But even with the most powerful supercomputers it is not possible to account for all processes in such simulations. They are hence constructed to include in space and time those events which are most important to improve our physical understanding. In practice this especially requires the development and application of new numerical methods. In this project numerical simulations of parts of the surface of stars shall be performed. Stars of spectral type A and white dwarfs of spectral type DA will receive most attention. This is owed to the fact that so far it is insufficiently understood why only a fraction of the cool (main sequence) A- and (metal rich) Am-stars pulsate and the same holds for the role convection has in the excitation and damping of global oscillations in these stars in spite of all the high precision data for many of these objects from space missions such as Kepler or TESS. Likewise, convection is mixing seemingly stably stratified regions in such stars. This process is especially efficient in those types of stars which are to be investigated in this project. The role played by turbulence for this phenomenon, known under the name of overshooting (mixing beyond stability boundaries), has not yet been investigated adequately. Therefore, a whole series of numerical simulations of A-stars shall be performed such as to construct a first model grid for those objects. The key to new results is given by high spatial resolution through local grid refinement which is a feature of the ANTARES numerical simulation code to be used for this purpose. For A-stars this requires the implementation of further developed numerical procedures (based on so-called implicit- explicit Runge-Kutta methods) to avoid that the resolution in time has to become unaffordably small. With these means at hands the following topics will be investigated: what is the role of turbulence for overshooting in white dwarfs and A-type stars? How does the turbulent pressure, which results from convection, influence the presence of global oscillations in A- and Am-type stars? How does turbulent convection change the spectra of these stars? And how do spatially separate convection zones merge in the transition region for cool A-type and hot F-type stars? The predictions of the simulations will be tested with various observational methods.

The observed light of stars originates from their surface, the stellar atmosphere, since photons, the particles which light is made of, get absorbed in the stellar interior after travelling a short distance and are mostly re-emitted at different frequencies and directions. In stars energy can be transported either by radiation or convection: heat conduction mostly remains negligibly small. Within the research project "Numerical simulation of A-type and white dwarf stars" the basic equations of radiation hydrodynamics have approximately been solved numerically by means of computer simulations to study especially the following classes of objects: main sequence stars of spectral type A, characterized by having one-and-a-half to twice-and-a-half the mass of the Sun and generating energy by nuclear fusion of hydrogen in their centre. Moreover, the apart from their slightly smaller mass rather similar main sequence stars of spectral type F. Finally, white dwarfs of spectral type DA, compact remnants of stars with once a solar mass or a multiple thereof now having just one half to one solar masses, compressed to an earthsized object. Such objects have a stable interior, gradually cooling by radiation. Global stellar pulsations in A- and F-type and DA-type stars can be excited by several mechanisms. Asteroseismology has been developed to use observed pulsations, measured, for instance, as intensity variations with photometry as in ESA's PLATO mission, to constrain the interior structure of stars including their chemical composition. This also allows probing stellar models. The structural difference between A- and F-type stars, with two separate, thin convective zones in hot stars and a single, deep zone for cool stars, allows conclusive tests of our physical understanding of convection and pulsation. Equally challenging is the formation of spectral absorption lines, well understood for the Sun, but not for A-type stars. Hence, radiation hydrodynamical simulations for different stars of spectral type A, F, and DA have been performed. Very long simulation durations and large simulation grids with high resolution have been particularly challenging. To keep them affordable the simulations were initially performed for two spatial dimensions. The simpler structure of the thin, efficient convection zones of DA stars allowed a first systematic analysis of the role of turbulent mixing into stably stratified layers. High resolution, accompanied by a higher turbulence level, was found to yield faster mixing, but singular extreme events also occurred for low turbulence. Stable long duration simulations in three dimensions required developing and implementing new numerical methods, which prevent numerical instabilities and make predictions in time more reliable. The numerical studies also contributed to the development of two important improvements (energy loss by waves and non-local transport) in convection models, which are urgently required by asteroseismology and for stellar evolution calculations.