Exploring B4: A Pulsating sdB star, in a Binary, in the Open Cluster NGC 6791

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We report on Kepler photometry of the hot sdB star B4 in the open cluster NGC 6791. We confirm that B4 is a reflection effect binary with an sdB component and a low-mass main sequence companion with a circular 0.3985 d orbit. The sdB star is a g-mode pulsator (a V1093 Her star) with periods ranging from 2384 s to 7643 s. Several of the pulsation modes show symmetric splitting by 0.62 microHz. Attributing this to rotational splitting, we conclude that the sdB component has a rotation period of approximately 9.63 d, indicating that tidal synchronization has not been achieved in this system. Comparison with theoretical synchronization time provides a discriminant between various theoretical models.