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We analyze an asteroseismic binary system: KIC 7107778, a non-eclipsing,unresolved target, with solar-like oscillations in both components. We used\emph{Kepler} short cadence time series spanning nearly two years to obtain thepower spectrum. Oscillation mode parameters were determined using Bayesianinference and a nested sampling Monte Carlo algorithm with the\texttt{DIAMONDS} package. The power profiles of the two components fullyoverlap, indicating their close similarity. We modelled the two stars with\texttt{MESA} and calculated oscillation frequencies with \texttt{GYRE}.Stellar fundamental parameters (mass, radius and age) were estimated by gridmodelling with atmospheric parameters and the oscillation frequencies of$l=0,2$ modes as constraints. Most $l=1$ mixed modes were identified withmodels searched using a bisection method. Stellar parameters for the twosub-giant stars are: $M_A=1.42\pm0.06$ $M_{\astrosun}$, $M_B=1.39\pm0.03$$M_{\astrosun}$, $R_A=2.93\pm0.05$ $R_{\astrosun}$, $R_B=2.76\pm0.04$$R_{\astrosun}$, $t_A=3.32\pm0.54$ Gyr and $t_B=3.51\pm0.33$ Gyr. The massdifference of the system is $\sim$1\%. The results confirm their simultaneousbirth and evolution, as is expected from binary formation. KIC 7107778comprises almost identical twins, and is the first asteroseismic sub-giantbinary to be detected.

Asteroseismology of KIC 7107778: a binary comprising almost identical subgiants