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We present a detailed comparative study of the arcs and fragmented ring-likefeatures in the haloes of the planetary nebulae (PNe) NGC 6543, NGC 7009, andNGC 7027 and the spiral pattern around the carbon star AFGL 3068 usinghigh-quality multi-epoch HST images. This comparison allows us to investigatethe connection and possible evolution between the regular patterns surroundingAGB stars and the irregular concentric patterns around PNe. The radial propermotion of these features, ~15 km/s, are found to be consistent with the AGBwind and their linear sizes and inter-lapse times (500-1900 yr) also agree withthose found around AGB stars, suggesting a common origin. We find evidenceusing radiative-hydrodynamic simulations that regular patterns produced at theend of the AGB phase become highly distorted by their interactions with theexpanding PN and the anisotropic illumination and ionization patterns caused byshadow instabilities. These processes will disrupt the regular (mostly spiral)patterns around AGB stars, plausibly becoming the arcs and fragmented ringsobserved in the haloes of PNe.

Rings and arcs around evolved stars. II. The Carbon Star AFGL 3068 and the Planetary Nebulae NGC 6543, NGC 7009 and NGC 7027