Morphology and kinematics of the gas envelope of the variable AGB star $pi^1$ Gruis

Observations of the $^{12}$CO(3-2) emission of the circumstellar envelope (CSE) of the variable star $pi^1$ Gru using the compact array (ACA) of the ALMA observatory have been recently made accessible to the public. An analysis of the morphology and kinematics of the CSE is presented with a result very similar to that obtained earlier for $^{12}$CO(2-1) emission by Chiu et al. (2006) using the Sub-Millimeter Array. A quantitative comparison is made using their flared disk model. A new model is presented that provides a significantly better description of the data, using radial winds and smooth evolutions of the radio emission and wind velocity from the stellar equator to the poles.