Journal of Computational Physics, accepted (2011)

Bernd Freytag (Centre de Recherche Astrophysique de Lyon, UMR 5574: CNRS, Universite de Lyon, Ecole Normale Superieure de Lyon, 46 allee d'Italie, F-69364 Lyon Cedex 07, France / Istituto Nazionale di Astrofisica / Osservatorio Astronomico di Capodimonte, Via Moiariello 16, I-80131 Naples, Italy),
Matthias Steffen (Astrophysikalisches Institut Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany),
Hans-Günter Ludwig (ZAH, Landessternwarte K√∂nigstuhl, D-69117 Heidelberg, Germany),
Sven Wedemeyer-Böhm (Institute of Theoretical Astrophysics, Postboks 1029 Blindern, 0315 Oslo, Norway / Center of Mathematics for Applications University of Oslo, Postboks 1053 Blindern, N-0316 Oslo, Norway),
Werner Schaffenberger (School of Physics University of Exeter, Stocker Road, Exeter, United Kingdom, EX4 4QL / Kiepenheuer-Institut fuer Sonnenphysik, Schöneckstrasse 6, D-79104 Freiburg, Germany),
Oskar Steiner (Kiepenheuer-Institut fuer Sonnenphysik, Schöneckstrasse 6, D-79104 Freiburg, Germany)

Simulations of stellar convection with CO5BOLD

High-resolution images of the solar surface show a granulation pattern of hot rising and cooler downward-sinking material - the top of the deep-reaching solar convection zone. Convection plays a role for the thermal structure of the solar interior and the dynamo acting there, for the stratification of the photosphere, where most of the visible light is emitted, as well as for the energy budget of the spectacular processes in the chromosphere and corona. Convective stellar atmospheres can be modeled by numerically solving the coupled equations of (magneto)hydro-dynamics and non-local radiation transport in the presence of a gravity field. The CO5BOLD code described in this article is designed for so-called "realistic" simulations that take into account the detailed microphysics under the conditions in solar or stellar surface layers (equation-of-state and optical properties of the matter). These simulations indeed deserve the label "realistic" because they reproduce the various observables very well - with only minor differences between different implementations. The agreement with observations has improved over time and the simulations are now well-established and have been performed for a number of stars. Still, severe challenges are encountered when it comes to extending these simulations to include ideally the entire star or substellar object: the strong stratification leads to completely different conditions in the interior, the photosphere, and the corona. Simulations have to cover spatial scales from the sub-granular level to the stellar diameter and time scales from photospheric wave travel times to stellar rotation or dynamo cycle periods. Various non-equilibrium processes have to be taken into account. Last but not least, realistic simulations are based on detailed microphysics and depend on the quality of the input data, which can be the actual accuracy limiter. This article provides an overview of the physical problem and the numerical solution and the capabilities of CO5BOLD, illustrated with a number of applications.

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