The Kepler satellite has discovered a number of transiting planets around
close binary stars. These circumbinary systems have highly aligned planetary
and binary orbits. In this paper, we explore how the mutual inclination between
the planetary and binary orbits may reflect the physical conditions of the
assembly of protoplanetary disks and the interaction between protostellar
binaries and circumbinary disks. Given the turbulent nature of star-forming
molecular clouds, it is possible that the gas falling onto the outer region of
a circumbinary disk and the central protostellar binary have different axes of
rotation. Thus, the newly assembled circumbinary disk can be misaligned with
respect to the binary. However, the gravitational torque from the binary
produces a warp and twist in the disk, and the back-reaction torque tends to
align the disk and the binary orbital plane. We present a new, analytic
calculation of this alignment torque, and show that the binary-disk inclination
angle can be reduced appreciably after the binary accretes a few percent of its
mass from the disk. Our calculation suggests that in the absence of other
disturbances, circumbinary disks and planets around close (sub-AU) stellar
binaries, for which mass accretion onto the proto-binary is very likely to have
occurred, are expected to be highly aligned with the binary orbits, while disks
and planets around wide binaries can be misaligned. Measurements of the mutual
inclinations of circumbinary planetary systems can provide a clue to the birth
environments of such systems.
