Using seismic inversions to obtain an indicator of internal mixing processes in main-sequence solar-like stars

Context. Currently, seismic modelling is one of the best ways of building accurate stellar models, thereby providing accurate ages. However, current methods are affected by simplifying assumptions concerning stellar mixing processes. In this context, providing new structural indicators that are less model-dependent and more sensitive to mixing processes is crucial. Aims. We wish to build a new indicator for core conditions (i.e. mixing processes and evolutionary stage) on the main sequence. This indicator tu should be more sensitive to structural differences and applicable to older stars than the indicator t presented in a previous paper. We also wish to analyse the importance of the number and type of modes for the inversion, as well as the impact of various constraints and levels of accuracy in the forward modelling process that is used to obtain reference models for the inversion. Methods. First, we present a method of obtaining new structural kernels in the context of asteroseismology. We then use these new kernels to build a new indicator of central conditions in stars, denoted tu, and test it for various effects including atomic diffusion, various initial helium abundances, and various metallicities, following the seismic inversion method presented in our previous paper. We then study the indicator's accuracy for seven different pulsation spectra including those of 16CygA and 16CygB and analyse how it depends on the reference model by using different constraints and levels of accuracy for its selection. Results. We observe that the inversion of the new indicator tu using the SOLA method provides a good diagnostic for additional mixing processes in central regions of stars. Its sensitivity allows us to test for diffusive processes and chemical composition mismatch. We also observe that using modes of degree 3 can improve the accuracy of the results, as well as using modes of low radial order. Moreover, we note that individual frequency combinations should be considered to optimise the accuracy of the results.