Hydrodynamical model atmospheres and 3D spectral synthesis

1 Radiation-hydrodynamics modeling – overview In this paper we discuss three issues in the context of three-dimensional (3D) hydrodynamical model atmospheres for late-type stars, related to spectral line shifts, radiative transfer in metal-poor 3D models, and the solar oxygen abundance. To establish the context we start by giving a brief overview about the model construction, taking the radiation-hydrodynamics code CO 5 BOLD (COnservative COde for the COmputation of COmpressible COnvection in a BOx of L Dimensions with L=2,3; [3]) and the related spectral synthesis package Linfor3D as examples. Based on a Godunov-type finite volume approach, CO 5 BOLD provides the time-dependent solution for a one-component compressible radiating fluid in an external gravity field on a fixed, non-staggered 3D Cartesian grid (allowing variable spacing). Operator splitting separates Eulerian hydrodynamics, optional tensor viscosity, and radiation transport. Directional splitting decomposes the 3D hydrodynamics problem into 1D sub-steps which are treated by an approximate Riemann solver of Roe type, modified to work with an arbitrary equation of state, and to properly handle an external gravity field. This scheme is very robust and well adapted to handle transonic flows and shocks in a highly stratified medium. By design, the code guarantees the numerical conservation of mass, momentum, and energy. For any prescribed chemical composition, CO 5 BOLD uses a tabulated equation of state taking into account partial ionization of H I, He I, and He II, as well as the formation and dissociation of H 2 molecules. The role of radiation in the hydrodynamical simulations is to describe the energy balance due to radiative heating and cooling. The radiative energy exchange is computed from the solution of the non-local transfer equation on a system of a large number of rays traversing the computational volume under different azimuthal and polar angles. Realistic stellar opacities are used, optionally based on ATLAS or MARCS opacity data. The frequency dependence of the radiation field is treated in a multi-group approximation – the so-called opacity binning method (OBM; [9, 7, 10]) – where frequencies are sorted into a small number of bins (typically 4. .. 6) according to the ratio