A Study in Stellar Instabilities

Hydrodynamical instabilities play a key role in the structure and evolution of stars. Convection is one such instability. It is one of the main mechanisms for energy transport and mixing inside stars and can both excite and damp other instabilities such as global stellar oscillations. Through dynamo effects it can also generate and sustain magnetic fields. Helioseismology has opened a new era of studying the solar interior in general and of solar convection in particular. Asteroseismology is now opening this "window" into the interiors of stars of spectral type A and F, among others, and also into DA type white dwarfs. Satellite missions such as COROT and MOST - to be joined soon by the BRITE Constellation and the Kepler mission - provide photometric time series of unprecedented quality on A- and F-type main sequence stars. Combined with data from ground based observations they allow in depth studies of the properties of stellar convection and pulsation. Similar progress occurs in the case of pulsating white dwarfs by means of ground based telescope networks. In the research project "A Study in Stellar Instabilities" we want to develop and perform high resolution three-dimensional hydrodynamical simulations with realistic microphysics of the near surface layers of A- and F-type main sequence stars and of DA-type white dwarfs. The particular challenge posed by modelling these types of stars is the much more efficient cooling of fluid near their surface in comparison with our Sun. We intend to reduce the resulting numerical costs by means of implicit and operator splitting techniques. Together with observational data the simulations will be used to study several among the following questions: at which effective temperature do the well separated convection zones caused by partial ionisation of hydrogen and doubly-ionised helium present in main sequence A-stars merge into one single convection zone as in our Sun? How is this related to published photometrical and spectroscopical properties of stars in this effective temperature range? What precisely determines the "red edge" of the classical instability strip, in which pulsations are excited by the opacity mechanism, in main sequence stars? Can solar-like oscillations still be observed for such effective temperatures and how can they be distinguished from opacity driven pulsations? Up to which effective temperature can we find pulsations in DA-type white dwarfs as compared to predictions based on simple convection models and what is the depth of their convection zones? The knowledge on stellar convection and stellar oscillations gained from this research is expected to provide essential contributions on how we can improve the modelling of convection in stellar evolution theory for a large range of physical parameters.

The project A Study in Stellar Instabilities has investigated hydrodynamical instabilities within stars. Convection is a special example for such a process. It is important for the transport of energy from inside stars to their surface and mixes the matter a star is made of. It can also excite global oscillations of a star as well as damp them. This occurs also inside our Sun. The study of such processes is the subject of helioseismology. It is the most important technique available to investigate the internal structure of stars. The oscillations of the Sun are low frequency standing sound waves and similar to geoseismology conclusions can be drawn from such oscillations on the distribution of mass density and chemical composition. The application of such methods to study stars other than the Sun is known as asteroseismology. It is one of the key methods in modern astrophysics and benefits tremendously from satellite missions devoted to the measurement of such oscillations. The CoRoT mission has been an example for such missions and has also been conducted with important contributions from Austria. Mathematical models are essential to understand such measurements. Due to supercomputers such as those available at the VSC (Vienna Scientific Cluster) in Vienna, where many calculations have been done during this project, it is possible to solve the basic equations of hydrodynamics and radiative transfer by mathematical methods in an approximate sense. This permits the simulation of the actions of the plasma a star is made of within a limited volume during a certain amount of time. For many stars such simulations require particular efforts, for instance, because of fast cooling processes near the stellar surface. This holds for stars of spectral type A as it does for stars with large luminosity, such as Cepheids, which are important for the measurements of distances in astronomy. To perform such simulations with a lower amount of computational efforts a new class of implicit-explicit Runge-Kutta methods with special stability properties has been developed during the project. The new methods allowed the simulation of a Cepheid, where only changes along the stellar radius were calculated (a so-called one-dimensional simulation), to be performed in one tenth of the previously required time. However, the new methods are also useful for other problems, which require the solution of mathematically similar types of equations that occur, for example, in chemistry, biomathematics, and mathematical finance. Another problem of such simulations are the so-called boundary conditions, which originate from the fact that only the simulation of parts of a star is feasible. In the case of the Sun simulation volumes extending for several 1000 km are possible with a resolution of 10 km to 20 km over the time scale of half a day. For this reason the role of the boundary conditions was investigated and improvements of them have been developed. A simulation of the solar surface of just that extent has been performed with these improved boundaries, and also a simulation of a star of spectral type F and of an evolved star of spectral type G. For the first time the damping of oscillations could be studied with such a simulation in detail as well as the role of convection for the measured frequencies of the oscillations. The latter has previously been achieved only for the case of Sun. The data about these stars had been measured by the CoRoT mission. Finally, with new simulations of a Cepheid it has been possible to show that the models of convection in these stars are insufficient and severely limit our ability to make accurate predictions of the properties of such objects. There is no way around further, extensive simulations of these objects based on the computational methods newly developed in this project, joined by the development of better physical models of convection.