Entropy proxy inversions as tracers of the evolution of physical conditions at the base of the solar convective envelope

¹ STAR Institute, Université de Liège, Liège, Belgium
² Sternberg Astronomical Institute, Lomonosov Moscow State University, 119234 Moscow, Russia
³ Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, 8000 Aarhus C, Denmark

^⋆ Corresponding author.

Received: 2 May 2025
Accepted: 4 June 2025

Abstract

Context. The Sun is an important calibrator in the theory of stellar structure and evolution. However, the accuracy of our solar evolution models is tightly linked to the physical elements that enter their computations. This includes, among others, the equation of state, the opacities, the transport of chemicals, and the modelling of turbulent convection. Deriving model-independent probes of these elements is therefore crucial to further testing the quality of these ingredients and potentially revealing their shortcomings using observational data.

Aims. We aim to provide additional constraints to the thermodynamic properties of the solar plasma at the base of the solar convective zone using a revised helioseismic indicator mimicking the properties of the specific entropy in the envelope.

Methods. We derived a revised entropy proxy for the solar convective envelope, which is directly accessible when using helioseismic structure inversions. We then used solar evolutionary models with various modifications of input physics to study the properties of the proxy of the entropy in the convective envelope.

Results. We find that the entropy proxy for the solar convective envelope allows us to invalidate adiabatic overshooting as a solution to the solar modelling problem and strongly points towards the need for revised opacities. Our results show that this new indicator is a strong diagnostic of the overall evolution of the thermodynamical conditions at the base of the convective zone.

Conclusions. The new entropy proxy indicator allows for a more accurate characterisation of the conditions at the base of the solar convective zone. While it already allows us to rule out overshooting as a solution to the solar modelling problem, its sensitivity to the shape of the opacity modification and the evolution of the properties at the base of the convective zone makes it a powerful helioseismic diagnostic for solar models.