Validating a non-local stellar convection model with 3D hydrodynamics simulations

¹ Heidelberger Institut für Theoretische Studien Schloss-Wolfsbrunnenweg 35 69118 Heidelberg, Germany
² Max-Planck-Institut für Astrophysik Karl-Schwarzschild-Straße 1 85748 Garching, Germany
³ Zentrum für Astronomie der Universität Heidelberg, Astronomisches Rechen-Institut Mönchhofstr. 12–14 69120 Heidelberg, Germany
⁴ Zentrum für Astronomie der Universität Heidelberg, Institut für Theoretische Astrophysik Philosophenweg 12 69120 Heidelberg, Germany

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 1 April 2025
Accepted: 3 October 2025

Abstract

Context. The efficient transport of energy and chemical elements by convective motions has a profound effect on the structure and evolution of stars. These motions occur on the relatively short dynamical timescale of convection and are intrinsically multi-dimensional. Stellar models usually rely on the one-dimensional mixing-length approximation of these processes, which is known to break down at convective boundaries. The Kuhfuß, R. (1987, Dissertation, Technische Universität München, München) convection model has been shown to handle convective boundaries in a more consistent way.

Aims. We test the assumptions that enter the Kuhfuß model using multi-dimensional hydrodynamics simulations, and we compare the results with existing one-dimensional models. Where possible, we also aim to calibrate the parameters of the Kuhfuß model using the simulations.

Methods. We computed one-dimensional stellar models employing the Kuhfuß model of a 3 M_⊙ main-sequence star. These models were compared to three-dimensional hydrodynamic simulations obtained with the code called SEVEN-LEAGUE HYDRO and using the Reynolds-averaged Navier Stokes analysis. We analysed the global convective variables and individual contributions to the equations of the convection model.

Results. The turbulent kinetic energy as predicted by the Kuhfuß model agrees well with the simulation results. Towards the boundary of the convective core, the simulations show a layer of a positive entropy gradient that coincides with a positive convective flux, as predicted by the convection model. The terms involving pressure fluctuations are found to have a non-negligible magnitude.

Conclusions. The agreement of the turbulent kinetic energy equation for the convection model and the simulation is an important sign that the convection model is physically accurate. The gradient of the mean entropy that we found in the multi-dimensional simulations and in the Kuhfuß model confirms the existence of a Deardorff layer, that is, of a layer with a subadiabtic temperature stratification and positive convective flux. This is not predicted by the mixing-length theory. The assumption that turbulence is isotropic and that pressure fluctuations are negligible needs to be revisited in the convection model.