  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 (150Myr)
and M34 (250Myr). 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 to the angular
velocity expected if the primary star was synchronized (e=0) or pseudo-
synchronized (e>0) with the orbital motion. 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.
