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 evolution of the Mira variable R Hydrae

The Mira variable R Hydrae is well known for its declining period, which Wood & Zarro (1981) attributed to a possible recent thermal pulse. Here we investigate the long-term period evolution, covering 340 years, going back to its discovery in AD 1662. Wavelets are used to determine both the period and semi-amplitude. We show that the period decreased linearly between 1770 and 1950; since 1950 the period has stabilized at 385 days. The semi-amplitude closely follows the period evolution. Detailed analysis of the oldest data shows that before 1770 the period was about 495 days. We find no evidence for an increasing period during this time as found by Wood & Zarro. IRAS data shows that the mass loss dropped dramatically around AD 1750. The decline agrees with the mass-loss formalism from Vassiliadis & Wood, but is much larger than predicted by the Bloecker mass-loss law. An outer detached IRAS shell suggests that R Hya has experienced such mass-loss interruptions before. The period evolution can be explained by a thermal pulse occuring around AD 1600, or by an non-linear instability leading to an internal relaxation of the stellar structure. The elapsed time between the mass-loss decline giving rise to the outer detached shell, and the recent event, of approximately 5000 yr suggests that only one of these events could be due to a thermal pulse. Further monitoring of R Hya is recommended, as both models make strong predictions for the future period evolution. R Hya-type events, on time scales of 10^2-10^3 yr, could provide part of the explanation for the rings seen around some AGB and post-AGB stars.Comment: 13 pages. MNRAS, accepted for publicatio

Symmetry transformations in Batalin-Vilkovisky formalism

This short note is closely related to Sen-Zwiebach paper on gauge transformations in Batalin-Vilkovisky theory (hep-th 9309027). We formulate some conditions of physical equivalence of solutions to the quantum master equation and use these conditions to give a very transparent analysis of symmetry transformations in BV-approach. We prove that in some sense every quantum observable (i.e. every even function $H$ obeying $\Delta_{\rho}(He^S)=0$) determines a symmetry of the theory with the action functional $S$ satisfying quantum master equation $\Delta_{\rho}e^S=0$ \endComment: 3 page