  Observations of increasingly higher spatial resolution reveal the existence
of asymmetries in the circumstellar envelopes of a small fraction of asymptotic
giant branch (AGB) stars. Although there is no general consensus for their
origin, a binary companion star may be responsible. Within this framework, we
investigate the gravitational effects associated with a sufficiently wide
binary system, where Roche lobe overflow is unimportant, on the outflowing
envelopes of AGB stars using three dimensional hydrodynamic simulations. The
effects due to individual binary components are separately studied, enabling
investigation of the stellar and circumstellar characteristics in detail. The
reflex motion of the AGB star alters the wind velocity distribution, thereby,
determining the overall shape of the outflowing envelope. On the other hand,
the interaction of the companion with the envelope produces a gravitational
wake, which exhibits a vertically thinner shape. The two patterns overlap and
form clumpy structures. To illustrate the diversity of shapes, we present the
numerical results as a function of inclination angle. Not only is spiral
structure produced by the binary interaction, but arc patterns are also found
that represent the former structure when viewed at different inclinations. The
arcs reveal a systematic shift of their centers of curvature for cases when the
orbital speed of the AGB star is comparable to its wind speed. They take on the
shape of a peanut for inclinations nearly edge-on. In the limit of slow orbital
motion of the AGB star relative to the wind speed, the arc pattern becomes
nearly spherically symmetric. We find that the aspect ratio of the overall
oblate shape of the pattern is an important diagnostic probe of the binary as
it can be used to constrain the orbital velocity of the AGB star, and moreover
the binary mass ratio.
