2D simulations of the line-driven instability in hot-star winds

II. Approximations for the 2D radiation force

¹ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Strasse 1, 85748 Garching bei Munchen, Germany e-mail: luc@as.arizona.edu
² Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA
³ Bartol Research Institute of the University of Delaware, Newark, DE 19716, USA

Received: 27 January 2005
Accepted: 19 March 2005

Abstract

We present initial attempts to include the multi-dimensional nature of radiation transport in hydrodynamical simulations of the small-scale structure that arises from the line-driven instability in hot-star winds. Compared to previous 1D or 2D models that assume a purely radial radiation force, we seek additionally to treat the lateral momentum and transport of diffuse line-radiation, initially here within a 2D context. A key incentive is to study the damping effect of the associated diffuse line-drag on the dynamical properties of the flow, focusing particularly on whether this might prevent lateral break-up of shell structures at scales near the lateral Sobolev angle of ca. 1^o. Based on 3D linear perturbation analyses that show a viscous diffusion character for the damping at these scales, we first explore nonlinear simulations that cast the lateral diffuse force in the simple, local form of a parallel viscosity. We find, however, that the resulting strong damping of lateral velocity fluctuations only further isolates azimuthal zones, leading again to azimuthal incoherence down to the grid scale. To account then for the further effect of lateral mixing of radiation associated with the radial driving, we next explore models in which the radial force is azimuthally smoothed over a chosen scale, and thereby show that this does indeed translate to a similar scale for the resulting density and velocity structure. Accounting for both the lateral line-drag and the lateral mixing in a more self-consistent way thus requires a multi-ray computation of the radiation transport. As a first attempt, we explore further a method first proposed by Owocki (1999), which uses a restricted 3-ray approach that combines a radial ray with two oblique rays set to have an impact parameter within the stellar core. From numerical simulations with various grid resolutions (and p), we find that, compared to equivalent 1-ray simulations, the high-resolution 3-ray models show systematically a much higher lateral coherence. This first success in obtaining a lateral coherence of wind structures in physically consistent 2D simulations of the radiative instability motivates future development of more general multi-ray methods that can account for transport along directions that do not intersect the stellar core.