  Observations of hot Jupiters around solar-type stars with very short orbital
periods (~day) suggest that tidal dissipation in such stars is not too
efficient so that these planets can survive against rapid orbital decay. This
is consistent with recent theoretical works, which indicate that the tidal Q of
planet-hosting stars can indeed be much larger than the values inferred from
stellar binaries. On the other hand, recent measurements of Rossiter-McLaughlin
effects in transiting hot Jupiter systems not only reveal that many such
systems have misaligned stellar spin with respect to the orbital axis, but also
show that systems with cooler host stars tend to have aligned spin and orbital
axes. Winn et al. suggested that this obliquity - temperature correlation may
be explained by efficient damping of stellar obliquity due to tidal dissipation
in the star. This explanation, however, is in apparent contradiction with the
survival of these short-period hot Jupiters. We show that in the solar-type
parent stars of close-in exoplanetary systems, the effective tidal Q governing
the damping of stellar obliquity can be much smaller than that governing
orbital decay. This is because for misaligned systems, the tidal potential
contains a Fourier component with frequency equal to the stellar spin frequency
(in the rotating frame of the star). This component can excite inertial waves
in the convective envelope of the star, and the dissipation of inertial waves
then leads to a spin-orbit alignment torque, but not orbital decay. By
contrast, for aligned systems, such inertial wave excitation is forbidden since
the tidal forcing frequency is much larger than the stellar spin frequency. We
derive a general effective tidal evolution theory for misaligned binaries,
taking account of different tidal responses and dissipation rates for different
tidal forcing components.
