  We present a search for rings or arcs in the haloes of planetary nebulae
(PNe). We discovered such structures in eight PNe, tripling the sample of PNe
with known rings. This shows that, contrary to what was believed to date, the
occurrence of mass loss fluctuations with timescales of ~100 to ~1000 yrs at
the end of the asymptotic giant branch phase (AGB) is common. We estimate a
lower limit of the occurrence rate of rings in PN haloes to be ~35%.
  Using these new detections and the cases previously known, we discuss the
statistical properties of ring systems in PNe haloes. We estimate that the mass
modulation producing the rings takes place during the last 10 or 20 kyrs of AGB
evolution. In PNe, the spacing between rings ranges from <0.01 pc to 0.06 pc,
significantly larger than those seen in proto-PNe. This, together with the
finding of a possible positive correlation of spacing with the post-AGB age of
the nebulae, suggests that the spacing of the rings increases with time.
  These properties, as well as the modest surface brightness amplitudes of
rings, are consistent with the predictions of the dust-driven wind instability
model explored by Meijerink et al. (2003), but do not immediately exclude other
proposed models.

Astrophysics