Numerical Simulation of Semiconvection in Exoplanets

During recent years the research on exoplanets has evolved into one of the most exciting areas of astrophysics. Meanwhile the existence of more than 700 planets outside our solar system has been confirmed. This list of objects keeps growing continuously. There are strong indications for the existence of more than twice as many further exoplanets from the observational data collected thus far. The combination of results from ground-based instruments with observations from satellites is pivotal for the determination of basic properties, structure, and evolution of exoplanets: only the space missions COROT and Kepler (as well as MOST and in the near future hopefully BRITE and in the long-term the proposed PLATO mission) allow extremely long series of observations under optimum conditions undisturbed by the terrestrial atmosphere. The theoretical study of structure and evolution of exoplanets is immediately linked to stellar astrophysics, but has also strong relations to geophysics. This research is challenged in a completely new way by the enormous varieties of objects and stellar systems. The change of thermodynamical quantities (temperature, pressure, and density) as well as the chemical composition and the aggregate state (gaseous, liquid, solid) from the directly observable outer layers (the atmosphere of a planet and, possibly, a solid surface) to the centre of those objects is essential to understand their formation and evolution processes. The interior of planets is not accessible to direct observations and as in stars the numerical, hydrodynamical simulation takes a key role in their investigation. The research project "Numerical Simulation of Semiconvection in Exoplanets" is supposed to study by means of such numerical, hydrodynamical simulations for gaseous giant planets the role of convective processes in mixing of matter within planets and of heat transport which is responsible for the gradual cooling of planetary interiors. Specifically, the following problems are to be investigated: are the models of layered semiconvection which are inspired by geophysics also valid in the parameter space of gaseous giants, especially in shear flows and for the case of realistic microphysics? How efficient is the transport of material in layered semiconvection? Can it be represented sufficiently accurately by parametric models? Are these models also valid in case of rapid rotation of an object? The knowledge gained from the numerical simulations is hence expected to contribute to the improvement of physical models of structure and evolution of gaseous giant planets and therefore in particular of many of the exoplanets known thus far.

The project "Numerical Simulation of Semiconvection in Exoplanets" has dealt with a special type of convection which is known in astrophysics as semiconvection. A prerequisite for its formation is that along the direction of gravity there is a difference both in temperature and also in chemical composition. If heat flows from the lower boundary into the region of interest in the physical system and if there is fluid of lower temperature located on top of it which could be water, a gas, or a plasma convection can set in. This happens in everyday live (boiling pot) as well as in phenomena of meteorology (clouds, thermals). However, if there is fluid of lower mean molecular weight, for instance hydrogen, above heavier one, such as helium, the fluid may be at first stabilized against convection provided the concentration difference of the light (or heavy) fluid is sufficiently high. Semiconvection can occur in this case now, because heat is spreading faster in the fluid by diffusion than concentration. Thus, convection finally occurs, although in a special way: frequently, though not always, layers form. Within them the fluid gets completely mixed. The layers are separated by zones which barely show any convective motions. There, a drop in concentration and heat develops and thus staircases (layers) in the fluid. This phenomenon is known from oceans and seas, but also from lakes. In astrophysics it occurs at the outer boundary of regions of thermonuclear fusion in the interior of stars, if those are convective as this causes a jump in concentration at the top of such zones. In planets known as gaseous giants (such as Jupiter or Saturn or numerous among the planets found outside our solar system and commonly known as exoplanets), this phenomenon occurs, in principle, too, since heavy material is accumulated in the core of the planet already during its formation. Semiconvection, however, is less efficient than ordinary convection. Radius and heat loss of a planet thus evolve differently. The project aimed at investigating the influence of different configurations, particularly with respect to the initial stratification, and especially also consider the consequences of additional, horizontal flows, as they form because of the rotation of the planet. In the project a large number of numerical simulations has been performed which allow a quantitative description of the influence of such effects. The influence of rotation or of a shear flow often turned out to be surprising: stabilizing and destabilizing effects can occur and require an accurate description of the physical system. The knowledge gained by this research is not only important for astrophysics, or primarily for the physics of exoplanets, but also for oceanography. During the developments necessary for these numerical simulation studies mathematical computing methods have been improved as well. They are used also outside astro- and geophysics.