We analyze an asteroseismic binary system : KIC 7107778 , a non-eclipsing , unresolved target , with solar-like oscillations in both components .
We used Kepler short cadence time series spanning nearly two years to obtain the power spectrum .
Oscillation mode parameters were determined using Bayesian inference and a nested sampling Monte Carlo algorithm with the DIAMONDS package .
The power profiles of the two components fully overlap , indicating their close similarity .
We modelled the two stars with MESA and calculated oscillation frequencies with GYRE .
Stellar fundamental parameters ( mass , radius and age ) were estimated by grid modelling with atmospheric parameters and the oscillation frequencies of l = 0 , 2 modes as constraints .
Most l = 1 mixed modes were identified with models searched using a bisection method .
Stellar parameters for the two sub-giant stars are : M _ { A } = 1.42 \pm 0.06 M _ { \astrosun } , M _ { B } = 1.39 \pm 0.03 M _ { \astrosun } , R _ { A } = 2.93 \pm 0.05 R _ { \astrosun } , R _ { B } = 2.76 \pm 0.04 R _ { \astrosun } , t _ { A } = 3.32 \pm 0.54 Gyr and t _ { B } = 3.51 \pm 0.33 Gyr .
The mass difference of the system is \sim 1 % .
The results confirm their simultaneous birth and evolution , as is expected from binary formation .
KIC 7107778 comprises almost identical twins , and is the first asteroseismic sub-giant binary to be detected .