Stellar acoustic radii, mean densities, and ages from seismic inversion techniques

Context. Determining stellar characteristics such as the radius, mass or age is crucial when studying stellar evolution or exoplanetary systems, or when characterising stellar populations in the Galaxy. Asteroseismology is the golden path to accurately obtain these characteristics. In this context, a key question is how to make these methods less model-dependent. Aims: Building on the previous work of Daniel Reese, we wish to extend the Substractive Optimally Localized Averages (SOLA) inversion technique to new stellar global characteristics beyond the mean density. The goal is to provide a general framework in which to estimate these characteristics as accurately as possible in low-mass main-sequence stars. Methods: First, we describe our framework and discuss the reliability of the inversion technique and possible sources of error. We then apply this methodology to the acoustic radius, an age indicator based on the sound speed derivative and the mean density, and compare it to estimates based on the average large and small frequency separations. These inversions are carried out for several test cases including various metallicities, different mixing-lengths, non-adiabatic effects, and turbulent pressure. Results: We observe that the SOLA method yields accurate results in all test cases whereas results based on the large and small frequency separations are less accurate and more sensitive to surface effects and structural differences in the models. If we include the surface corrections of Kjeldsen et al. (2008, ApJ, 683, L175), we obtain results of comparable accuracy for the mean density. Overall, the mean density and acoustic radius inversions are more robust than the inversions for the age indicator. Moreover, the current approach is limited to relatively young stars with radiative cores. Increasing the number of observed frequencies improves the reliability and accuracy of the method