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

The small separation ([delta]ν01, [delta]ν02 and [delta]ν13) between oscillations with low degree l 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]ν01, [delta]ν02 and [delta]ν13 gives a different age. Therefore, in our fitting process, we also employ the second difference, defined as νn,2 - 2νn,1+νn,0, which is 2[delta]ν01 - [delta]ν02. In addition to this, we use the frequency ratio (νn,0/νn,2). For the Sun, these expressions are equivalent and give an age of about 4.9 - 5.0 Gyr. For [alpha] 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) Z0 = 0.020, t = 3.50 Gyr and MB = 1.006 M[dotcircle] from the small separations [delta]ν01, [delta]v02 and [delta]ν13 of [alpha] Cen B; and (ii) a variety of solutions from the non-seismic constraints and [delta]ν02 of [alpha] 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 MB = 0.922 M[dotcircle] and MA = 1.115 M[dotcircle]. The differences between these masses and the corresponding observed masses are about 0.01 M[dotcircle]. [PUBLICATION ABSTRACT]