With the advent of high-resolution high-sensitivity observations, spiral patterns have been revealed around several asymptotic giant branch (AGB) stars. Such patterns can provide possible evidence for the existence of central binary stars embedded in outflowing circumstellar envelopes. Here, we suggest the viability of explaining the previously observed incomplete ring-like patterns with the spiral-shell structure due to the motion of (unknown) binary components viewed at an inclination with respect to the orbital plane. We describe a method of extracting such spiral-shells from an incomplete ring-like pattern to place constraints on the characteristics of the central binary stars. The use of gas kinematics is essential in facilitating a detailed modeling for the three-dimensional structure of the circumstellar pattern. We show that a hydrodynamic radiative transfer model can reproduce the structure of the HC3N molecular line emission of the extreme carbon star, CIT 6. This method can be applied to other sources in the AGB phase and to the outer ring-like patterns of pre-planetary nebulae for probing the existence of embedded binary stars, which are highly anticipated with future observations using the Atacama Large Millimeter/submillimeter Array.
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