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The S-type asymptotic giant branch (AGB) star $pi^{1}$ Gruis has a known companion at a separation of $approx$400 AU. The envelope structure, including an equatorial torus and a fast bipolar outflow, is rarely seen in the AGB phase and is particularly unexpected in such a wide binary system. Therefore a second, closer companion has been suggested, but the evidence is not conclusive. The new ALMA $^{12}$CO and $^{13}$CO $J$=3-2 data, together with previously published $^{12}$CO $J$=2-1 data from the Submillimeter Array (SMA), and the $^{12}$CO $J$=5-4 and $J$=9-8 lines observed with Herschel/Heterodyne Instrument for the Far-Infrared (HIFI), is modeled with the 3D non-LTE radiative transfer code SHAPEMOL. The data analysis clearly confirms the torus-bipolar structure. The 3D model of the CSE that satisfactorily reproduces the data consists of three kinematic components: a radially expanding torus with velocity slowly increasing from 8 to 13 km s$^{-1}$ along the equator plane; a radially expanding component at the center with a constant velocity of 14 km s$^{-1}$; and a fast, bipolar outflow with velocity proportionally increasing from 14 km s$^{-1}$ at the base up to 100 km s$^{-1}$ at the tip, following a linear radial dependence. The results are used to estimate an average mass-loss rate during the creation of the torus of 7.7$times$10$^{-7}$ M$_{odot}$ yr$^{-1}$. The total mass and linear momentum of the fast outflow are estimated at 7.3$times$10$^{-4}$ M$_{odot}$ and 9.6$times$10$^{37}$ g cm s$^{-1}$, respectively. The momentum of the outflow is in excess (by a factor of about 20) of what could be generated by radiation pressure alone, in agreement with recent findings for more evolved sources. The best-fit model also suggests a $^{12}$CO/$^{13}$CO abundance ratio of 50. Possible shaping scenarios for the gas envelope are discussed
The AGB star $pi^{1}$ Gruis has a known companion (at a separation of ~400 AU) which cannot explain the strong deviations from the spherical symmetry of the CSE. Recently, hydrodynamic simulations of mass transfer in closer binary systems have succes
Observation of CO emission around asymptotic giant branch (AGB) stars is the primary method to determine gas mass-loss rates. While radiative transfer models have shown that molecular levels of CO can become mildly inverted, causing maser emission, C
One of the major puzzles in the study of stellar evolution is the formation process of bipolar and multi-polar planetary nebulae. There is growing consensus that collimated jets create cavities with dense walls in the slowly-expanding (10--20 ~km~s$^
Asymptotic giant branch (AGB) stars lose their envelopes by means of a stellar wind whose driving mechanism is not understood well. Characterizing the composition and thermal and dynamical structure of the outflow provides constraints that are essent
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