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Stellar rotation rates in Kepler eccentric (heartbeat) binaries obtained from r-mode signatures

R-mode oscillations in a rotating star produce characteristic signatures in a Fourier amplitude spectrum at frequencies related with the rotation frequency, which can be, in turn, used to obtain the surface rotation rate of the star. Some binary stars observed by Kepler indicate the presence of r~modes that are probably excited by the tidal effect. In this paper, we have obtained stellar rotation periods in 20 eccentric (heartbeat) binaries with r-mode signatures. The majority of the rotation periods are found to be comparable to pseudo-synchronous periods, in which the angular velocity of rotation is similar to the angular orbital motion of the companion at periastron. In particular, for the heartbeat stars with orbital periods longer than about 8\,d, all but one agree with pseudo-synchronous rotation. In contrast to a previous investigation by Zimmerman et al., our result supports the pseudo-synchronisation theory developed by Hut.