Radiative transfer with scattering for domain-decomposed 3D MHD simulations of cool stellar atmospheres

Numerical methods and application to the quiet, non-magnetic, surface of a solar-type star

¹ Max Planck Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany e-mail: [hayek,asplund,remo]@mpa-garching.mpg.de
² Research School of Astronomy & Astrophysics, Cotter Road, Weston Creek 2611, Australia
³ Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029 Blindern, 0315 Oslo, Norway e-mail: [mats.carlsson,b.v.gudiksen,viggo.hansteen]@astro.uio.no
⁴ JILA, University of Colorado, 440 UCB, Boulder, CO 80309-0440, USA e-mail: trampeda@lcd.colorado.edu
⁵ Astronomical Institute, Utrecht University, Postbus 80 000, 3508 TA Utrecht, The Netherlands e-mail: j.leenaarts@uu.nl

Received: 5 February 2010
Accepted: 28 April 2010

Abstract

Aims. We present the implementation of a radiative transfer solver with coherent scattering in the new BIFROST code for radiative magneto-hydrodynamical (MHD) simulations of stellar surface convection. The code is fully parallelized using MPI domain decomposition, which allows for large grid sizes and improved resolution of hydrodynamical structures. We apply the code to simulate the surface granulation in a solar-type star, ignoring magnetic fields, and investigate the importance of coherent scattering for the atmospheric structure.

Methods. A scattering term is added to the radiative transfer equation, requiring an iterative computation of the radiation field. We use a short-characteristics-based Gauss-Seidel acceleration scheme to compute radiative flux divergences for the energy equation. The effects of coherent scattering are tested by comparing the temperature stratification of three 3D time-dependent hydrodynamical atmosphere models of a solar-type star: without scattering, with continuum scattering only, and with both continuum and line scattering.

Results. We show that continuum scattering does not have a significant impact on the photospheric temperature structure for a star like the Sun. Including scattering in line-blanketing, however, leads to a decrease of temperatures by about 350 K below log₁₀ τ₅₀₀₀ –4. The effect is opposite to that of 1D hydrostatic models in radiative equilibrium, where scattering reduces the cooling effect of strong LTE lines in the higher layers of the photosphere. Coherent line scattering also changes the temperature distribution in the high atmosphere, where we observe stronger fluctuations compared to a treatment of lines as true absorbers.