Asteroseismology of KIC 7107778: a binary comprising almost identical subgiants

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 the power spectrum. Oscillation mode parameters were determined using Bayesian inference and a nested sampling Monte Carlo algorithm with the \texttt{DIAMONDS} package. The power profiles of the two components fully overlap, 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 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: $M_A=1.42\pm0.06$ $M_{\astrosun}$, $M_B=1.39\pm0.03$ $M_{\astrosun}$, $R_A=2.93\pm0.05$ $R_{\astrosun}$, $R_B=2.76\pm0.04$ $R_{\astrosun}$, $t_A=3.32\pm0.54$ Gyr and $t_B=3.51\pm0.33$ Gyr. The 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.