Improving 1D stellar atmosphere models with insights from multidimensional simulations

II. 1D versus 3D model comparison for Wolf-Rayet stars

¹ Zentrum für Astronomie der Universität Heidelberg, Astronomisches Rechen-Institut, Mönchhofstr. 12–14, 69120 Heidelberg, Germany
² Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, 3001, Leuven, Belgium

^★ Corresponding author: gemma.gonzalez-tora@uni-heidelberg.de

Received: 13 February 2025
Accepted: 20 May 2025

Abstract

Context. Classical Wolf-Rayet (cWR) stars are evolved massive stars that have lost most of their hydrogen envelope, presenting dense, extended atmospheres with strong stellar winds. Accurate descriptions of their line-driven winds and in particular the launching of the winds in optically thick layers have long remained enigmatic. Two different approaches have recently allowed for significant progress to be made, namely, one-dimensional (1D) atmosphere models with stationary hydrodynamics and time-dependent, multidimensional, radiation-hydrodynamic models.

Aims. The computational demands and required approximations limit the applications of multidimensional, time-dependent atmospheric models. Therefore, 1D stationary atmosphere models remain an important and necessary tool, but there is also a need to incorporate reasonable approximations of the physical insights gained in multidimensional and time-dependent simulations.

Methods. We compared averaged stratifications from recent multidimensional atmosphere models for cWR stars with 1D stellar atmosphere models computed with the hydrodynamically consistent branch of the PoWR model atmosphere code. We studied models that include winds launched by the hot iron bump, while varying several of the 1D model parameters to characterize any differences that occur and to quantify their impact on the 1D solutions obtained.

Results. The 1D hydrodynamically consistent atmosphere models tested in this study match the averaged 3D density stratifications. Overall, 1D models with standard inputs obtained mass-loss rates ≲0.2 dex higher than their 3D equivalents, but minor adjustments in accordance with the mass-loss and luminosity dispersion obtained from the time-dependent multidimensional simulations are able to reconcile this difference. The 1D models are radially more extended, while displaying higher terminal velocities and lower effective temperatures. Although the 1D models reproduce the same velocity trend as the 3D calculations, they launch their winds a bit further out and reach higher velocities during the hot iron bump. The resulting differences in effective temperature and terminal velocity are also seen in the synthetic spectra computed from different 1D PoWR model approaches.

Conclusions. The overall stellar atmosphere structure profiles for 1D and 3D averaged hydrodynamically consistent models follow a similar trend, providing stellar parameters that are well matched when accounting for the dispersion of the time-dependent 3D simulations and the different methodologies. For stars closer to the Eddington Limit, decreasing the Doppler velocities in 1D models can help reconcile the mass-loss rates, effective temperatures, and velocity profiles in the outer wind. Obtaining a match for the temperature structures in optically thin regions remains an open challenge.