Shaping bipolar Planetary Nebulae : How mass loss leads to waistline   development
  Asymptotic Giant Branch (AGB) stars generally have spherically symmetric envelopes, whereas most post-AGB stars and Planetary Nebulae (PNe) show axisymmetric circumstellar envelopes. While various mechanisms for axisymmetric circumstellar structures may explain the shapes of PNe, they do not address how the shape of the circumstellar shell evolves. Here we address the temporal changes in the axisymmetry of AGB star envelopes, and in particular the development of the torus required in the Generalized Interacting Stellar Winds (GISW) model. Assuming (1) an AGB star rotates with sufficient angular speed at the start of the AGB phase; and (2) that the rotational angular momentum of the AGB star is conserved, we demonstrate that some very important observational features of AGB star axisymmetry evolution can be reproduced. We find that, compared to the star's increasing luminosity and decreasing effective temperature, the decreasing mass of the star primarily affects the axisymmetry of the envelope. When a representative mass loss history is adopted, where most of the mass is lost near the end of the AGB phase, the envelope's axisymmetry increases over time, with the strongest increase occurring near the end of the AGB phase. This may naturally explain why most AGB stars have spherically symmetric envelopes, while axisymmetry seems common-place in the post-AGB/PNe phase. The degree of axisymmetry at the end of the AGB phase is found to increase with increasing main sequence mass, and the onset of axisymmetry occurs only after the onset of the superwind (SW) phase, in good agreement with the observations. 
Catharinus Dijkstra and Angela Speck