On the structure of the Sun and alpha Centauri A and B in the light of seismic and non-seismic constraints

The small separation (delta nu(01), delta nu(02) and delta nu(13)) between oscillations with low degree I is dependent primarily on the sound speed profile within the stellar core, where nuclear evolution occurs. The detection of such oscillations in a star offers a very good opportunity to determine the stage of its nuclear evolution, and hence its age. In this context, we investigate the Sun and alpha Cen A and B. For alpha Cen A and B, each of the small separations delta nu(01), delta nu(02) and delta nu(13) gives a different age. Therefore, in Our fitting process, we also employ the second difference, defined as nu(n,2) - 2 nu(n,1) + nu(n,0), which is 2 delta nu(01) - delta nu(02). In addition to this, we use the frequency ratio (nu(n,0)/nu(n,2)). For the Sun, these expressions are equivalent and give all age of about 4.9-5.0 Gyr. For a Cen A and B, however, the small separation and the second difference give very different ages. This conflict may be resolved by the detection of oscillation frequencies that can be measured much more precisely than the current frequencies. When we fit the models to the observations, we find that (i) Z(0) = 0.020, t = 3.50 Gyr and M(B) = 1.006 M(circle dot) from the small separations delta nu(01), delta nu(02) and delta nu(13) of a Cen B; and (ii) a variety of solutions from the non-seismic constraints and delta nu(02) of a Cen A and B, in which the masses of alpha Cen A and B are slightly modified and the age of the system is about 5.2-5.3 Gyr. For Z = 0.025, the closest masses we find to the observed masses are M(B) = 0.922 M(circle dot) and M(A) = 1.115 M(circle dot). The differences between these masses and the corresponding observed masses are about 0.01 M(circle dot).