Analysis of the linear approximation of seismic inversions for various structural pairs

Abstract

Thanks to space-based photometry missions CoRoT and Kepler, we benefit from a wealth of seismic data for stars other than the sun. In the future, K2, Tess, and Plato will complement this data and provide observations in addition to those already at hand. The availability of this data leads to questions on how it is feasible to extend linear structural inversion techniques to stars other than the sun. Linked to this problem is the question of the validity of the linear assumption. In this study, we analyse its limitations with respect to changes of structural variables.We wish to provide a more extended theoretical background to structural linear inversions by doing a study of the validity of the linear assumption for various structural variables. First, we recall the origins of the linear assumption for structural stellar inversions and explain its importance for asteroseismic studies. We recall the impact of unknown structural quantities such as the mass and the radius of the star on structural inversion results. We explain how kernels for new structural variables can be derived using two methods, one suited to asteroseismic targets, the other to helioseismic targets. For this second method, we present a new structural pair, namely the (A, Y) structural kernels. The kernels are tested in various numerical experiments that enable us to evaluate the weaknesses of different pairs and the domains of validity of their respective linear regime. The numerical tests we carry out allow us to disentangle the impact of various uncertainties in stellar models on the verification of the linear integral relations. We show the importance of metallicity, the equation of state, extra-mixing, and inaccuracies in the microphysics. We discuss the limitations of the method of conjugated functions due to the lack of extremely precise determinations of masses or radii in the asteroseismology.

arXiv comment14 pages. Accepted for publication in Astronomy and Astrophysics

References in corpus (11)

• The chemical composition of the Sun
• Low Temperature Opacities
• The PLATO 2.0 Mission
• Element Diffusion in the Solar Interior
• Updated Electron-Conduction Opacities: The Impact on Low-Mass Stellar Models
• Helioseismology and Solar Abundances
• CLES, Code Liegeois d'Evolution Stellaire
• The Liege Oscillation Code
• Using seismic inversions to obtain an internal mixing processes indicator for main-sequence solar-like stars
• Asteroseismology of solar-type stars with K2
• Stable higher order finite-difference schemes for stellar pulsation calculations

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• Asteroseismic Inference of the Central Structure in a Subgiant Star
• Seismic Solar Models from Ledoux discriminant inversions
• Asteroseismic Inversions for Internal Sound Speed Profiles of Main-sequence Stars with Radiative Cores
• Influence of the magnetic activity cycle on mean density and acoustic radius inversions
• Stellar Inversion Techniques
• Probing stellar cores from inversions of frequency separation ratios