Combining multiple structural inversions to constrain the solar modelling problem

¹ School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK
e-mail: g.buldgen@bham.ac.uk
² STAR Institute, Université de Liège, Allée du Six Août 19C, 4000 Liège, Belgium
³ Dipartimento di Fisica e Astronomia, Università degli Studi di Padova, vicolo dell’Osservatorio 3, 35122 Padova, Italy
⁴ Sternberg Astronomical Institute, Lomonosov Moscow State University, 119234 Moscow, Russia
⁵ Observatoire de Genève, Université de Genève, 51 Ch. Des Maillettes, 1290 Sauverny, Suisse
⁶ Institute of Problems of Chemical Physics RAS, 142432 Chernogolovka, Russia
⁷ Tomsk State University, 634050 Tomsk, Russia
⁸ Joint Institute for High Temperatures RAS, 125412 Moscow, Russia
⁹ Moscow Institute of Physics and Technology, 141701 Dolgoprudnyi, Russia
¹⁰ LUPM, Université de Montpellier, CNRS, Place E. Bataillon, 34095 Montpellier Cedex, France
¹¹ Troitsk Institute for Innovation and Fusion Research, 142190 Troitsk, Russia

Received: 27 July 2018
Accepted: 24 September 2018

Abstract

Context. The Sun is the most studied of all stars, which serves as a reference for all other observed stars in the Universe. Furthermore, it also serves the role of a privileged laboratory of fundamental physics and can help us better understand processes occuring in conditions irreproducible on Earth. However, our understanding of our star is currently lessened by the so-called solar modelling problem, resulting from comparisons of theoretical solar models to helioseismic constraints. These discrepancies can stem from various causes, such as the radiative opacities, the equation of state as well as the mixing of the chemical elements.

Aims. By analysing the potential of combining information from multiple seismic inversions, our aim is to help disentangle the origins of the solar modelling problem.

Methods. We combined inversions of the adiabatic sound speed, an entropy proxy and the Ledoux discriminant with other constraints such as the position of the base of the convective zone and the photospheric helium abundance. First, we tested various combinations of standard ingredients available for solar modelling such as abundance tables, equation of state, formalism for convection and diffusion and opacity tables. Second, we studied the diagnostic potential of the inversions on models including ad hoc modifications of the opacity profile and additional mixing below the convective envelope.

Results. We show that combining inversions provides stringent constraints on the required modifications to the solar ingredients, far beyond what can be achieved from sound speed inversions alone. We constrain the form and amplitude of the opacity increase required in solar models and show that a 15% increase at log T = 6.35 provides a significant improvement, but is insufficient on its own. A more global increase in the opacity, within the uncertainties of the current tables, coupled with a localized additional mixing at the bottom of the convective zone provides the best agreement for low-metallicity models. We show that high-metallicity models do not satisfy all the inversion results. We conclude that the solar modelling problem likely occurs from multiple small contributors, as other ingredients such as the equation of state or the formalism of convection can induce small but significant changes in the models and that using phase shift analyses combined with our approach is the next step for a better understanding of the inaccuracies of solar models just below the convective envelope.