Gravity Modes Reveal the Internal Rotation of a Post-mass Transfer Gamma Doradus/Delta Scuti Hybrid Pulsator in Kepler Eclipsing Binary KIC 9592855

We report the discovery of a post-mass transfer Gamma Doradus/Delta Scuti hybrid pulsator in the eclipsing binary KIC~9592855. This binary has a circular orbit, an orbital period of 1.2 days, and contains two stars of almost identical masses ($M_1=1.72M_{\odot}, M_2=1.71M_{\odot}$). However, the cooler secondary star is more evolved ($R_2=1.96R_{\odot}$) while the hotter primary is still on the zero-age-main-sequence ($R_1=1.53R_{\odot}$). Coeval models from single star evolution cannot explain the observed masses and radii, and binary evolution with mass-transfer needs to be invoked. After subtracting the binary light curve, the Fourier spectrum shows low-order pressure-mode pulsations, and more dominantly, a cluster of low-frequency gravity modes at about $2$ day$^{-1}$. These g-modes are nearly equally-spaced in period, and the period spacing pattern has a negative slope. We identify these g-modes as prograde dipole modes and find that they stem from the secondary star. The frequency range of unstable p-modes also agrees with that of the secondary. We derive the internal rotation rate of the convective core and the asymptotic period spacing from the observed g-modes. The resulting values suggest that the core and envelope rotate nearly uniformly, i.e., their rotation rates are both similar to the orbital frequency of this synchronized binary.