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Context. Determining stellar characteristics such as the radius, the mass orthe age is crucial when studying stellar evolution, exoplanetary systems orcharacterising stellar populations in the Galaxy. Asteroseismology is thegolden path to accurately obtain these characteristics. In this context, a keyquestion is how to make these methods less model-dependant. Aims. Building onthe work of Reese et al. (2012), we wish to extend the SOLA inversion techniqueto new stellar global characteristics in addition to the mean density. The goalis to provide a general framework in which to estimate these characteristics asaccurately as possible in low mass main sequence stars. Methods. First, wedescribe our framework and discuss the reliability of the inversion techniqueand the possible sources of error.We then apply this methodology to theacoustic radius, an age indicator based on the sound speed derivative and themean density and compare it to estimates based on the average large and smallfrequency separations. These inversions are carried out for several test caseswhich include: various metallicities, different mixing-lengths, non-adiabaticeffects and turbulent pressure. Results. We observe that the SOLA method yieldsaccurate results in all test cases whereas results based on the large and smallfrequency separations are less accurate and more sensitive to surface effectsand structural differences in the models. If we include the surface correctionsof Kjeldsen et al. (2008), we obtain results of comparable accuracy for themean density. Overall, the mean density and acoustic radius inversions are morerobust than the inversions for the age indicator. Moreover, the currentapproach is limited to relatively young stars with radiative cores. Increasingthe number of observed frequencies improves the reliability and accuracy of themethod.

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