The small separation ( \delta \nu _ { 01 } , \delta \nu _ { 02 } and \delta \nu _ { 13 } ) between the 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 for 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 also use frequency ratio ( \nu _ { n, 0 } / \nu _ { n, 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 solved 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 ( i ) Z _ { 0 } = 0.020 , t = 3.50 Gyr and M _ { B } = 1.006 M _ { \odot } from the small separations \delta \nu _ { 01 } , \delta \nu _ { 02 } and \delta \nu _ { 13 } of \alpha Cen B ; and ( ii ) a variety of solutions from the non-seismic constraints and \delta \nu _ { 02 } 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 M _ { B } =0.922 M _ { \odot } and M _ { A } =1.115 M _ { \odot } .
The differences between these masses and the corresponding observed masses are about 0.01 M _ { \odot } .