We present rotation periods for the solar-type primary stars in 13 close (a 5 AU) single-lined spectroscopic binaries with known orbital periods (P) and eccentricities (e). All binaries are members of the open clusters M35 (NGC 2168; ~150 Myr) and M34 (NGC 1039; ~250 Myr). The binary orbital parameters and the rotation periods of the primary stars were determined from time-series spectroscopy and time-series photometry, respectively. Knowledge of the ages, orbital periods, and eccentricities of these binaries combined with the rotation periods and masses of their primary stars makes them particularly interesting systems for studying the rates of tidal circularization and synchronization. Our sample of 13 binaries includes six with orbital periods shortward of 13 days (a 0.12 AU). The stars in these binaries orbit sufficiently close that their spins and orbits have evolved toward synchronization and circularization due to tidal interactions. We investigate the degree of tidal synchronization in each binary by comparing the angular rotation velocity of the primary stars (Ω) to the angular velocity expected if the primary star was synchronized (e = 0) or pseudosynchronized (e 0) with the orbital motion (Ωps). Of the six closest binaries, two with circular orbits are not synchronized, one being subsynchronous and one being supersynchronous, and the primary stars in two binaries with eccentric orbits are rotating more slowly than pseudosynchronism. The remaining two binaries have reached the equilibrium state of both a circularized orbit and synchronized rotation. As a set, the six binaries present a challenging case study for tidal evolution theory, which in particular does not predict subsynchronous rotation in such close systems.
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