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.
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