Numerical Modelling of Semiconvection (Stellar Physics)

In 1987 a supernova has appeared in the Magellanic Clouds, the dwarf galaxies which accompany our own galaxy. Since hundreds of years this was the first `nearby` supernova. Due to its proximity, the precursor star could easily be identified on archive material. Contrary to expectations, it turned out to be a blue giant star, not a red one as predicted by the stellar evolution calculations at this time. - This pointed to major flaws in the understanding of late type stars. One of the main suspects was (and is) ill known semiconvection. This is a mixing process in which not only temperature matters as in ordinary convection (hot material rising) but also chemical composition; deep within a star chemical composition may be different from the outer parts due to nuclear reactions. There are theories of semiconvection which, however, rest upon simplified equations the validity of which is difficult to assess. We want therefore set out from essentially the full equations (or rather the `Low Mach Number Approximation` which can expected to hold under the specific circumstances) and perform a numerical modelling of the process. Due to the difficulties of the matter, there are only very few (2-3) previous investigations along those lines. The problem is, among others, that the relevant time scales are very long. Thus, only very specific software (based on `Low Mach` or so) can be expected to yield results. In addition it may happen that narrow interfaces develop which, by no means, are allowed to be smeared by numerics. Since years we have developed our hydrodynamics code ANTARES (A Numerical Tool for Astrophysical RESearch) and our visualization package VIVAT (VIennese Visualization and Analysis Tool). Properly extending these codes, we want to investigate the questions mentioned. We will tightly cooperate with the group of F. Kupka at the Max Planck Institute for Astrophysics in Garching, Germany. The German group will work on the `global` approach, i.e., assume that a pattern of motion ensues which spans all of the semiconvective zone. We, in contrast, will focus on the `local` scenario which holds that a large number of layers develops, stacked atop of each other. Within each layer there are convective motions; across the layer boundaries, material is transported by diffusive processes. (Such a situation is observed in suitable laboratory experiments.) That presently we do not know whether the `global` or the `local` scenario applies in the stellar case testifies sufficiently how little we know about these processes. - We hope to figure out which one of the scenarios holds true and to continue therefore our research in the correct direction.

The process of convection is well known in daily live: warm air ascends above a heater, releases its energy, cools and sinks down again. Another example is readily seen in cumulus clouds. In the interiors of a large fraction of the stars convection transports, in specific zones, practically all the energy generated deep in the interior by nuclear reactions.Semiconvection is somewhat more subtle. In principle, warm material would ascend and keep ascending for some distance in certain layers of specific varieties of stars were it not for the fact that the star is chemically inhomogenous because of nuclear reactions during its earlier life. So, the material deeper down may contain more heavy elements which inhibits buoyancy to a degree and, thus, ordinary convection. Due to its history of nuclear burning in the interior, a star in later phases of its lifetime may consist of shells of varying chemical composition. The question whether these shells may get mixed is decisive for its ongoing nuclear reactions and, therefore, further evolution. When in 1987 a supernova (the violent explosion marking, for some types of stars, their end of life as normal stars) in the Magellanic Clouds exploded (the first relatively nearby supernova since about 400 years), its predecessor could be investigated on photographs taken earlier. Contrary to what stellar evolution theory predicted at that time, it was a blue giant instead of a read giant. If mixing larger than anticipated at that time was assumed, theory could be reconciled with observations.It has become customary to ascribe that extra mixing to mixing in semiconvective zones and recipes have been developed to account for this. However, these recipes lack stringent physical justification. It is namely difficult to investigate semiconvection in a parameter range relevant for the astrophysical case by experiments. It is also difficult but more promising to model it on computers in the way one models flows e.g. for airplane construction or weather prediction. Only recently, first advances have been made in that field. Just because of the difficulty of semiconvection modelling we have developed resp. improved numerical methods for optimal efficiency. Then, we have commenced the construction and analysis of models. They have been applied to deliver suggestions resp. checks to the development of a different type of models (H. Spruit, Garching) which then, allowed with more confidence to extrapolate the results to the truely astrophysical regime which is still not accessible to simulations. As a result, it seems that semiconvection in itself does not yield the extra rate of mixing sought for. It may well be that it does so, however, in concert with other processes. So, there is ample room for further research. Ultimately, such work should lead to a better understanding of the late stages of stellar evolution and, as a consequence, of the cosmic matter circuit, where, from one generation of stars, material is processed by nuclear reactions, the processed material then used in the formation of the next generation of stars (and planets, by the way), etc.