A 3D radiative transfer framework

VII. Arbitrary velocity fields in the Eulerian frame

¹ Hamburger Sternwarte, Gojenbergsweg 112 21029 Hamburg, Germany
e-mail: aseelmann@hs.uni-hamburg.de; yeti@hs.uni-hamburg.de
² Dept. of Physics and Astronomy, University of Oklahoma, 440 W. Brooks, Rm 100, Norman, OK 73019, USA
e-mail: baron@ou.edu
³ Computational Research Division, Lawrence Berkeley National Laboratory, MS 50F-1650, 1 Cyclotron Road, CA 94720-8139, USA

Received: 17 February 2010
Accepted: 17 July 2010

Abstract

Aims. A solution of the radiative-transfer problem in 3D with arbitrary velocity fields in the Eulerian frame is presented. The method is implemented in our 3D radiative transfer framework and used in the PHOENIX/3D code. It is tested by comparison to our well-tested 1D co-moving frame radiative transfer code, where the treatment of a monotonic velocity field is implemented in the Lagrangian frame. The Eulerian formulation does not need much additional memory and is useable on state-of-the-art computers, even large-scale applications with 1000’s of wavelength points are feasible.

Methods. In the Eulerian formulation of the problem, the photon is seen by the atom at a Doppler-shifted wavelength depending on its propagation direction, which leads to a Doppler-shifted absorption and emission. This leads to a different source function and a different Λ_∗ operator in the radiative transfer equations compared to the static case.

Results. The results of the Eulerian 3D spherical calculations are compared to our well-tested 1D Lagrangian spherical calculations, the agreement is, up to v_max = 1 × 10³   km   s^-1 very good. Test calculation in other geometries are also shown.