Searching for orbital decay in a heartbeat star system KIC 3766353

Theory suggests that the orbits of a large fraction of binary systems, including planet-star binary systems, shrink by few orders of magnitude after formation. But so far, only one hot Jupiter with tidally-driven orbital decay has been found by transit timing variations. We propose to search for orbital decay companions in heartbeat star systems because the orbital angular momentum is effectively transferred to the host star causing tidal dissipation. KIC 3766353 is one of the heartbeat stars with tidally excited oscillations. We acquired the primary and the secondary eclipse time variations from the \textit{Kepler} photometric light curves. Timing analysis shows that KIC 3766353 is a hierarchical triple system with a hidden third body and a red dwarf (mass $0.35\ M_{\odot}$, radius $0.34\ R_{\odot}$) in its inner orbit. The minimum mass of the third body is $\sim 0.26 \ M_{\odot}$, and the distance from the inner orbital is $\sim 111.4 \ R_{\odot}$. The period decay rate of the red dwarf is approximately 358 ms yr$^{-1}$. The combined effects of the light-travel time and the orbital decay lead to the observed timing variations. Future monitoring with a long time base-line observations is required to delve into the contributions of these two effects.