Constraints on the structure of 16 Cygni A and 16 Cygni B using inversion techniques

Context. Constraining additional mixing processes and chemical composition is a central problem in stellar physics as their impact on determining stellar age leads to biases in our studies of stellar evolution, galactic history and exoplanetary systems. In two previous papers, we have shown how seismic inversion techniques could be used to offer strong constraints on such processes by pointing out weaknesses in current theoretical models. The theoretical approach having been tested, we now wish to apply our technique to observations. In that sense, the solar analogues 16CygA and 16CygB, being amongst the best targets in the Kepler field, are probably currently the most well suited stars to test the diagnostic potential of seismic inversions. Aims. We wish to use seismic indicators obtained through inversion techniques to constrain additional mixing processes in the components of the binary system 16Cyg. The combination of various seismic indicators will help to point out the weaknesses of stellar models and thus obtain more constrained and accurate fundamendal parameters for these stars. Methods. First, we used the latest seismic, spectroscopic and interferometric observational constraints in the literature for this system to independently determine suitable reference models for both stars. We then carried out seismic inversions of the acoustic radius, the mean density and a core conditions indicator. These additional constraints will be used to improve the reference models for both stars. Results. The combination of seismic, interferometric and spectroscopic constraints allows us to obtain accurate reference models for both stars. However, we note that it is possible to achieve similar accuracy for a range of model parameters. Namely, changing the diffusion coefficient or the chemical composition within the observational values could lead to a 5% uncertainty in mass, a 3% uncertainty in radius and up to an 8% uncertainty in age. We used acoustic radius and mean density inversions to further improve our reference models and then carried out inversions for a core conditions indicator, denoted tu. Thanks to the sensitivity of this indicator to microscopic diffusion and chemical composition mismatches, we were able to reduce the mass uncertainties to 2%, namely between [0.96 M⊙, 1.0 M⊙], the radius uncertainties to 1%, namely between [1.188 R⊙, 1.200 R⊙] and the age uncertainties to 3%, namely between [7.0 Gy, 7.4 Gy], for 16CygA. For 16CygB, tu offered a consistency check for the models but could not be used to independently reduce the initial scatter observed for the fundamental parameters. Nonetheless, assuming consistency with the age of 16CygA can help to further constrain its mass and radius. We thus find that the mass of 16CygB should be between 0.93 M⊙ and 0.96 M⊙ and its radius between 1.08 R⊙ and 1.10 R