Properties that Cannot Be Explained by the Progenitors of Planetary Nebulae

I classify a large number of planetary nebulae (458) according to the process that caused their progenitors to blow axisymmetrical winds. The classification is based primarily on the morphologies of the different planetary nebulae, assuming that binary companions, stellar or substellar, are necessary in order to have axisymmetrical mass loss on the asymptotic giant branch. I propose four evolutionary classes, according to the binary-model hypothesis: (1) Progenitors of planetary nebula that did not interact with any companion. These amount to ~10% of all planetary nebulae. (2) Progenitors that interact with stellar companions that avoided a common envelope, 11⁺²₋₃% of all nebulae. (3) Progenitors that interact with stellar companions via a common envelope phase, 23⁺¹¹₋₅% of all nebulae. (4) Progenitors that interact with substellar (i.e., planets and brown dwarfs) companions via a common envelope phase, 56⁺⁵₋₈% of all nebulae. In order to define and build the different classes, I start with clarifying some relevant terms and processes related to binary evolution. I then discuss kinematical and morphological properties of planetary nebulae that appear to require the interaction of the planetary nebula progenitors and/or their winds with companions, stellar or substellar.