Improving 1D stellar atmosphere models with insights from multi-dimensional simulations
Authors: González-Torà G. , Sander A. A. C. , Sundqvist J. O. , Debnath D. , Delbroek L. , Josiek J. , Lefever R. R. , Moens N. , Van der Sijpt C. , Verhamme O. 
Published: January 2025

Context. The outer layers and the spectral appearance of massive stars are inherently affected by radiation pressure. Recent multidimensional, radiation-hydrodynamical (RHD) simulations of massive stellar atmospheres have shed new light on the complexity involved in the surface layers and the onset of radiation-driven winds. These findings include the presence of sub-surface, radiatively driven turbulent motion. For some regimes, the velocities associated with this turbulence and their localisation significantly exceed earlier estimates drawn from stellar structure models. This prompts the question of whether spectral diagnostics obtained with the typical assumptions in 1D spherically symmetric and stationary atmospheres are still sufficient.
Aims. For the foreseeable future, the inherent computation costs and necessary approximations will pose challenges to the common usage of multi-dimensional, time-dependent atmosphere models in the quantitative spectral analysis of populations of stars. Therefore, suitable approximations of multi-dimensional simulation results need to be implemented into 1D atmosphere models.
Methods. We compared current 1D and multi-dimensional atmosphere modelling approaches to understand their strengths and shortcomings. We calculated the averaged stratifications from selected multi-dimensional calculations for O stars – corresponding to spectral types O8, O4, and O2, with log 𝑔 ∼ 3.7 – to approximate them with 1D stellar atmosphere models using the PoWR model atmosphere code and assuming a fixed β–law for the wind regime. We then studied the effects of our approximations and assumptions on current spectral diagnostics. In particular, we focus on the impact of an additional turbulent pressure in the subsonic layers of the 1D models.
Results. To match the 2D averages, the 1D stellar atmosphere models need to account for turbulent pressure in the hydrostatic equation. Moreover, an adjustment of the connection point between the (quasi)hydrostatic regime and the wind regime is required. The improvement between the density stratification of the 1D model and 2D average can be further increased if the mass-loss rate of the 1D model is not identical to that of the 2D simulation; rather, it is typically ∼0.2 dex higher. Especially in the case of an early-type star, this would imply a significantly more extended envelope with a lower effective temperature.
Conclusions. Already, the inclusion of a constant turbulence term in the solution of the hydrostatic equation is shown to sufficiently reproduce the 2D-averaged model density stratifications. The addition of a significant turbulent motion also smoothens the slope of the radiative acceleration term in the (quasi)hydrostatic domain, with several potential implications on the total mass-loss rate inferred from 1D modelling. Concerning the spectral synthesis, the addition of a turbulence term in the hydrostatic equation mimics the effect of a lower surface gravity, potentially presenting a solution to the ‘mass discrepancy problem’ between the evolutionary and spectroscopy mass determinations.