Improving 1D stellar atmosphere models with insights from multi-dimensional simulations II. 1D versus 3D hydrodynamically consistent model comparison for WR stars

TL;DR

This study compares 1D and 3D hydrodynamically consistent models of Wolf-Rayet stars, showing that 1D models can effectively replicate average 3D structures and wind properties when calibrated appropriately.

Contribution

It demonstrates how 1D models can incorporate insights from 3D simulations to improve accuracy in modeling WR star atmospheres and winds.

Findings

1D models reproduce average 3D density structures well.

Mass-loss rates are within 0.2 dex of 3D models after adjustments.

1D models tend to have higher terminal velocities and are more radially extended.

Abstract

Classical Wolf-Rayet (cWR) stars are evolved massive stars that have lost most of their H envelope and exhibit dense, extended atmospheres with strong, line-driven winds. Accurately modeling wind launching from optically thick layers remains a challenge. Two main approaches have advanced our understanding: 1D stationary atmosphere models with consistent hydrodynamics and time-dependent, multi-dimensional radiation-hydrodynamic simulations. Due to high computational demands, multi-dimensional models are limited in scope. Therefore, 1D hydrodynamically consistent models remain essential but must incorporate insights from 3D simulations. We compare averaged stratifications from recent multi-dimensional cWR models with 1D models computed using the hydrodynamically consistent PoWR$^{HD}$ code. We focus on winds driven by the hot iron opacity bump and explore how variations in 1D input parameters affect model outcomes. The 1D models reproduce the average 3D density structure well. While mass-loss rates are typically $\lesssim$0.2 dex higher in 1D models, small adjustments accounting for multi-dimensional dispersion reconcile the differences. 1D models tend to be more radially extended, with higher terminal velocities and lower effective temperatures. They reproduce the general velocity trends of 3D models but launch winds slightly further out and reach higher velocities during the hot iron bump. These differences also manifest in synthetic spectra computed from different 1D model approaches. Despite methodological variations, both 1D and averaged 3D models yield consistent stellar parameters when accounting for the variability seen in time-dependent simulations. For stars near the Eddington limit, reducing Doppler velocities in 1D models improves agreement in mass-loss rates, temperatures, and wind velocities. Matching temperature structures in optically thin layers remains an open challenge.