We report the discovery of Kepler-432b, a giant planet ($M_b = 5.41^{+0.32}_{-0.18} M_{rm Jup}, R_b = 1.145^{+0.036}_{-0.039} R_{rm Jup}$) transiting an evolved star $(M_star = 1.32^{+0.10}_{-0.07} M_odot, R_star = 4.06^{+0.12}_{-0.08} R_odot)$ with an orbital period of $P_b = 52.501129^{+0.000067}_{-0.000053}$ days. Radial velocities (RVs) reveal that Kepler-432b orbits its parent star with an eccentricity of $e = 0.5134^{+0.0098}_{-0.0089}$, which we also measure independently with asterodensity profiling (AP; $e=0.507^{+0.039}_{-0.114}$), thereby confirming the validity of AP on this particular evolved star. The well-determined planetary properties and unusually large mass also make this planet an important benchmark for theoretical models of super-Jupiter formation. Long-term RV monitoring detected the presence of a non-transiting outer planet (Kepler-432c; $M_c sin{i_c} = 2.43^{+0.22}_{-0.24} M_{rm Jup}, P_c = 406.2^{+3.9}_{-2.5}$ days), and adaptive optics imaging revealed a nearby (0farcs87), faint companion (Kepler-432B) that is a physically bound M dwarf. The host star exhibits high signal-to-noise asteroseismic oscillations, which enable precise measurements of the stellar mass, radius and age. Analysis of the rotational splitting of the oscillation modes additionally reveals the stellar spin axis to be nearly edge-on, which suggests that the stellar spin is likely well-aligned with the orbit of the transiting planet. Despite its long period, the obliquity of the 52.5-day orbit may have been shaped by star-planet interaction in a manner similar to hot Jupiter systems, and we present observational and theoretical evidence to support this scenario. Finally, as a short-period outlier among giant planets orbiting giant stars, study of Kepler-432b may help explain the distribution of massive planets orbiting giant stars interior to 1 AU.
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