  Recent observations of strikingly well-defined spirals in the circumstellar
envelopes of asymptotic giant branch (AGB) stars point to the existence of
binary companions in these objects. In the case of planet or brown dwarf mass
companions, we investigate the observational properties of the spiral-onion
shell wakes due to the gravitational interaction of these companions with the
outflowing circumstellar matter. Three dimensional hydrodynamical simulations
at high resolution show that the substellar mass objects produce detectable
signatures at 100 AU distance, for the wake induced by a Jupiter to brown dwarf
mass object orbiting a solar mass AGB star. In particular, the arm pattern
propagates with a speed depending on the local wind and sound speeds, implying
possible variations in the arm separation in the wind acceleration region
and/or in a slow wind with significant temperature variation. The pattern
propagation speeds of the inner and outer boundaries differ by twice the sound
speed, leading to the overlap of high density boundaries in slow winds and
producing a subpattern of the spiral arm feature. Vertically, the wake forms
concentric arcs with angular sizes anticorrelated to the wind Mach number. We
provide an empirical formula for the peak density enhancement as a function of
the mass, orbital distance, and velocity of the object as well as the wind and
local sound speeds. In typical condition of AGB envelopes, the arm-interarm
density contrast can be greater than 30 % of the background density within a
distance of ~10(M_p/M_J) AU for the object mass M_p in units of Jupiter mass
M_J. These results suggest that such features may probe unseen substellar mass
objects embedded in the winds of AGB stars and may be useful in planning future
high sensitivity/resolution observations with ALMA.
