Turbulent Convection and Pulsation Interaction in Stars

In many stars energy is transported from their interiors outwards by both radiation and convection. For the Sun the region where convection occurs extends from its surface down to a domain located at 30% of the distance from its uppermost layers to its centre. This outer region of a star is called stellar envelope. Convective envelopes are typical for cool stars which produce their energy directly in their centre by nuclear fusion of hydrogen or in a region located just immediately outside of it, as in the so-called red giant stars. Convection not only causes energy transport and mixing in these objects. It also excites these stars to oscillate. This has been demonstrated particularly with measurements which have been made from special satellites such as COROT, Kepler, MOST and also with the help of the BRITE satellites. Convection gives rise to processes which may excite oscillations, but it can also damp them. This competition of different processes can be analysed by continuous observations of stars preferably made over many days without any interruptions. Therefore, the pulsations, which appear as small temporal variations of stellar brightness, are measured with high precision. The strength and frequencies of the oscillations determined this way and averaged over longer periods of time allow conclusions on the basic properties of a star. Age, information about the original and current chemical composition, as well as the mass, the luminosity, and the radius of a star can be determined this way. This is of particular interest for the study of planets around other stars and the study of our Galaxy, since they allow drawing conclusions on their environment and evolution in time. To achieve the necessary accuracy for this approach, an accurate qualitative and quantitative understanding of convection and its interaction with the pulsations it drives is necessary. This is the research topic of this project for which high resolution computer simulations over sufficiently long time intervals, hundreds of oscillation periods, have to be performed. This corresponds to a total time ranging from a day up to two weeks. Thereby the flow processes for a small region at the stellar surface are investigated by approximate, numerical solution of the hydrodynamical equations and compared to predictions from simpler models derived from turbulence theory. Also the vertical oscillations that occur within such simulations will be compared to observations of their counterparts in stars. This will require both improvements of mathematical methods as well as of the simulation models. The results from this work will be an important part for the preparation of the PLATO 2.0 satellite mission which aims at an exact characterization of a very large number of stellar planetary systems.

The project "Turbulent Convection and Pulsation Interaction in Stars" investigated the interaction between two different types of motion of the plasma of which stars are made of. On the one hand these are convective flows which are driven by the large temperature difference between further outwards and further inwards lying regions in a particular star. In case of the Sun this encompasses the layers at its surface towards about 30% of the distance from its outside to its centre. On the other hand, in many stars also global, periodic motions occur. These are called pulsation. Just as vibrations in a music instrument these are excited by various physical mechanisms and similarly they are also damped which ensures a maximum extent of this motion, called amplitude, and which roughly remains constant in time. In case of the Sun this excitation of oscillations just as its damping occurs due to the convective motions themselves. Those actually cause sound waves which at certain frequencies can yield long-living, standing waves, again similar to what happens in a music instrument. Using the frequencies and amplitudes of these p-modes (pressure driven pulsation motions) the methods of helio- and asteroseismology allow drawing conclusions on the internal structure, the total mass, the radius and even the chemical composition and the age of a star. This requires data which are collected by satellite missions such as MOST, CoRoT, Kepler, BRITE, TESS, and in the future also PLATO. That research deepens also our knowledge on exoplanets which are investigated by these missions. For the case of the Sun special missions also allow the detailed study of complex, large scale structures, which are caused by convection, such as supergranulation. The project was devoted to contribute ideas that allow a better understanding of the physical processes which determine the frequencies and amplitudes of these oscillations in the Sun and in similar, pulsating stars. Consequently, the reliability of our conclusions drawn from such investigations were to be improved as well. By means of numerical simulations on supercomputers as well as by analytical work it has been possible to demonstrate that several physical processes have to be accounted for simultaneously to ensure reliable calculations of mode damping. In the long run this will lead to more accurate results from asteroseismology. Furthermore, it has been possible to demonstrate that convective flows can cause oscillations in a way that possibly explains the formation of supergranulation. The mathematical methods, which have been further developed during the project, will also be useful for applications outside astrophysics.