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We examine the reasons for discrepancies between two alternative approachesto modeling small-amplitude tides in binary systems. The 'direct solution' (DS)approach solves the governing differential equations and boundary conditionsdirectly, while the 'modal decomposition' (MD) approach relies on a normal-modeexpansion. Applied to a model for the primary star in the heartbeat systemKOI-54, the two approaches predict quite different behavior of the seculartidal torque. The MD approach exhibits the pseudosynchronization phenomenon,where the torque due to the equilibrium tide changes sign at a single,well-defined and theoretically predicted stellar rotation rate. The DS approachinstead shows 'blurred' pseudosynchronization, where positive and negativetorques intermingle over a range of rotation rates.  We trace a major source of these differences to an incorrect dampingcoefficient in the profile functions describing the frequency dependence of theMD expansion coefficients. With this error corrected some differences betweenthe approaches remain; however, both are in agreement thatpseudosynchronization is blurred in the KOI-54 system. Our findings generalizeto any type of star for which the tidal damping depends explicitly orimplicitly on the forcing frequency.

Discrepant Approaches to Modeling Stellar Tides, and the Blurring of Pseudosynchronization