Late AGB magnetic cycles: Magnetohydrodynamic solutions for the Hubble Space Telescope planetary nebula rings

The Hubble Space Telescope (HST) has revealed the existence of multiple, re gularly spaced, and faint concentric shells around some planetary nebulae. Here we present two- (and a half) dimensional magnetohydrodynamic numerical simulations of the effects of a solar-like magnetic cycle, with periodic p olarity inversions, in the slow wind of an asymptotic giant branch (AGB) st ar. The stellar wind is modeled with a steady mass-loss at constant velocit y. This simple version of a solar-like cycle, without mass-loss variations, is able to reproduce many properties of the observed concentric rings. The shells are formed by pressure oscillations, which drive compressions in th e magnetized wind. These pressure oscillations are due to periodic variatio ns in the field intensity. The periodicity of the shells, then, is simply a half of the magnetic cycle since each shell is formed when the magnetic pr essure goes to zero during the polarity inversion. As a consequence of the steady mass-loss rate, the density of the shells scales as r(-2), and their surface brightness has a steeper drop-off, as observed in the shells of NG C 6543, the best documented case of these HST rings. Deviations from spheri city can be generated by changing the strength of the magnetic field. For s ufficiently strong fields, a series of symmetric and equidistant blobs are formed at the polar axis, resembling the ones observed in He 2-90. These bl obs are originated by magnetic collimation within the expanding AGB wind.