A toy model for testing opacity effects on stellar structure computations
Year: 2026
Type: article
Abstract: New multi-dimensional modelling of stellar evolution requires a new formulation of the mathematical problem; instead of the classical Lagrangian approach of 1D stellar models, multi-dimensional ones, such as Evolution STEllaire en Rotation (ESTER) models, use an Eulerian description of fluid flows. In this approach a spectral discretisation of the equations is used. However, ESTER models are presently restricted to early-type stars since numerical difficulties arise when dealing with low-mass or solar-type stars. This study is aimed at analysing the origin of these numerical difficulties and offering new strategies to circumvent them. After showing that the difficulties of ESTER in the low-mass star range are associated with the strong variations of opacities with temperature, we designed a toy model based on a simple plane-parallel fluid layer in hydrostatic equilibrium, equipped with an opacity law that reproduces the temperature dependence of solar opacity well. We took the Sun as the typical example of a low-mass star. The toy model clearly reproduces the difficulties faced by ESTER models when the surface effective temperature drops below 10 000 K. In this case the non-linear differential equation that determines the temperature profile becomes stiff and the number of the Newton solver iterations increases dramatically. As this model allows for the introduction of an adiabatic layer when destabilising temperature gradients are met, we show that one additional difficulty is the determination of the interfaces between this layer and the neighbouring radiative layers. It is shown that convergence towards the solution is efficient if interface positions are updated only when Newton corrections are small enough. The toy model also indicates that for low-mass stars, Newton iterations should be initialised with a fully isentropic layer. Convergence is then faster and more robust than with an initial fully radiative model, as is actually the case for ESTER models. This toy model opens a pathway to 2D or 3D models describing the stellar evolution of low-mass stars. This path has now to be assessed.
Source: Astronomy and Astrophysics
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,865
OpenAlex ID: W7221064138