SIMBAD references

We argue that relative to nonspherical planetary nebulae (PNs), spherical PNs are about an order of magnitude less likely to be detected at distances of several kiloparsecs. Noting the structure similarity of halos around nonspherical PNs to that of observed spherical PNs, we assume that most unobserved spherical PNs are also similar in structure to the spherical halos around nonspherical PNs. The fraction of nonspherical PNs with detected spherical halos around them, taken from a recent study, leads us to the claim of a large (relative to that of nonspherical PNs), hidden population of spherical PNs in the visible band. Building a toy model for the luminosity evolution of PNs, we show that the claimed detection fraction of spherical PNs based on halos around nonspherical PNs is compatible with observational sensitivities. We use this result to update earlier studies on the different PN-shaping routes in the binary model. We estimate that ∼30% of all PNs are spherical, namely, that their progenitors did not interact with any binary companion. This fraction is to be compared with the ∼3% fraction of observed spherical PNs among all observed PNs. From all PNs, ∼15% owe their moderate elliptical shape to the interaction of their progenitors with planets, while ∼55% of all PNs owe their elliptical or bipolar shapes to the interaction of their progenitors with stellar companions.