Abstract In our previous work on the 3-dimensional dynamical structure of planetary nebulae the effect of magnetic field was not considered. Recently Jordan et al. have directly detected magnetic fields in the central stars of some planetary nebulae. This discovery supports the hypothesis that the non-spherical shape of most planetary nebulae is caused by magnetic fields in AGB stars. In this study we focus on the role of initially weak toroidal magnetic fields embedded in a stellar wind in altering the shape of the PN. We found that magnetic pressure is probably influential on the observed shape of most PNe.
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