A test of time-dependent theories of stellar convection

TL;DR

This study evaluates two 1-D time-dependent convection models against 2-D nonlinear simulations of Cepheid stars, revealing limitations of TDC models and favoring Stellingwerf's approach for better accuracy.

Contribution

It provides a direct comparison of two TDC models with 2-D simulations, highlighting their limitations and identifying the more accurate model for stellar convection simulations.

Findings

Stellingwerf's model shows better agreement with simulations.

TDC models have inherent limits due to variable free parameters.

Non-universality of TDC parameters affects model reliability.

Abstract

Context: In Cepheids close to the red edge of the classical instability strip, a coupling occurs between the acoustic oscillations and the convective motions close to the surface.The best topical models that account for this coupling rely on 1-D time-dependent convection (TDC) formulations. However, their intrinsic weakness comes from the large number of unconstrained free parameters entering in the description of turbulent convection. Aims: We compare two widely used TDC models with the first two-dimensional nonlinear direct numerical simulations (DNS) of the convection-pulsation coupling in which the acoustic oscillations are self-sustained by the kappa-mechanism. Methods: The free parameters appearing in the Stellingwerf and Kuhfuss TDC recipes are constrained using a chi2-test with the time-dependent convective flux that evolves in nonlinear simulations of highly-compressible convection with kappa-mechanism. Results: This work emphasises some inherent limits of TDC models, that is, the temporal variability and non-universality of their free parameters. More importantly, within these limits, Stellingwerf's formalism is found to give better spatial and temporal agreements with the nonlinear simulation than Kuhfuss's one. It may therefore be preferred in 1-D TDC hydrocodes or stellar evolution codes.