Binary central stars of planetary nebulae

This paper reviews our knowledge on binary central stars of planetary nebulae and presents some personal opinions regarding their evolution. Three types of interactions are distinguished: type I, where the binary companion induces the mass loss; type II, where it shapes the mass loss but does not enhance it; type III, where a wide orbit causes the centre of mass to move, leading to a spiral embedded in the wind. Surveys for binary central stars are discussed, and the separations are compared to the distribution for binary post-AGB stars. The effect of close binary evolution on nebular morphology is discussed. Post-common-envelope binaries are surrounded by thin, expanding disks, expelled in the orbital plane. Wider binaries give rise to much thicker expanding torii. Type I binary evolution predicts a wide distribution of masses of central stars, skewed towards low masses. Comparison with observed mass distributions suggests that this is unlikely to be the only channel leading to the formation of a planetary nebula. A new sample of compact Bulge nebulae shows about 40% of nebulae with binary-induced morphologies.Comment: Invited review, in 'Evolution and chemistry of symbiotic stars and related objects', Wierzba, August 2006. To appear in Baltic Astronom

The Immunity of Polymer-Microemulsion Networks

The concept of network immunity, i.e., the robustness of the network connectivity after a random deletion of edges or vertices, has been investigated in biological or communication networks. We apply this concept to a self-assembling, physical network of microemulsion droplets connected by telechelic polymers, where more than one polymer can connect a pair of droplets. The gel phase of this system has higher immunity if it is more likely to survive (i.e., maintain a macroscopic, connected component) when some of the polymers are randomly degraded. We consider the distribution $p(\sigma)$ of the number of polymers between a pair of droplets, and show that gel immunity decreases as the variance of $p(\sigma)$ increases. Repulsive interactions between the polymers decrease the variance, while attractive interactions increase the variance, and may result in a bimodal $p(\sigma)$.Comment: Corrected typo