Testing a non-local 1-equation turbulent convection model: A solar model

TL;DR

This study tests the 1-equation Kuhfuss turbulent convection model in solar models, finding it less accurate than mixing-length theory for reproducing helioseismic data, and suggests the need for a more complex model.

Contribution

The paper evaluates the 1-equation Kuhfuss turbulent convection model's effectiveness in solar modeling, highlighting its limitations and the necessity for a 3-equation approach.

Findings

The 1-equation Kuhfuss model poorly reproduces the solar sound-speed profile.

It overestimates convective penetration below the Schwarzschild boundary.

A more complex 3-equation model is recommended for better accuracy.

Abstract

Turbulent convection models treat stellar convection more physically than standard mixing-length theory by including non-local effects. We recently successfully applied the Kuhfuss version to convective cores in main sequence stars. Its usefulness for convective envelopes remains to be tested. The solar convective envelope constitutes a viable test bed for investigating the usefulness of the 1-equation Kuhfuss turbulent convection model. We used the one-dimensional stellar evolution code GARSTEC to calculate a standard solar model with the 1-equation Kuhfuss turbulent convection model, and compared it to helioseismic measurements and a solar model using standard mixing-length theory. Additionally, we investigated the influence of the additional free parameters of the convection model on the solar structure. The 1-equation Kuhfuss model reproduces the sound-speed profile and the lower boundary of the convective region less well than the mixing-length model, because the inherent non-local effects overestimate the amount of convective penetration below the Schwarzschild boundary. We trace this back to the coupling of the temperature gradient to the convective flux in the 1-equation version of the Kuhfuss theory. The temperature stratification of the solar convective envelope is not well modelled by the 1-equation Kuhfuss turbulent convection model, and the more complex 3-equation version is needed to improve the modelling of convection in the envelopes of 1D stellar evolution models.