Backflow in Post-Asymptotic Giant Branch Stars

We derive the conditions for a backflow toward the central star(s) of circumstellar material to occur during the post-asymptotic giant branch (AGB) phase. The backflowing material may be accreted by the post-AGB star and/or its companion, if such exists. Such a backflow may play a significant role in shaping the descendant planetary nebula, by, among other things, slowing down the post-AGB evolution, and by forming an accretion disk which may blow two jets. We consider three forces acting on a slowly moving mass element: the gravity of the central system, radiation pressure, and fast wind ram pressure. We find that for a significant backflow to occur, a slow dense flow should exsist, such that the relation between the total mass in the slow flow, M, and the solid angle it covers, Omega, is given by (4*pi*M/Omega)>0.1Mo. The requirement for both high mass loss rate per unit solid angle and a very slow wind, such that it can be decelerated and flow back, probably requires close binary interaction.Comment: Submitted to MNRA

The Formation of Slow-Massive-Wide Jets

I propose a model for the formation of slow-massive-wide (SMW) jets by accretion disks around compact objects. This study is motivated by claims for the existence of SMW jets in some astrophysical objects such as in planetary nebulae (PNs) and in some active galactic nuclei in galaxies and in cooling flow clusters. In this model the energy still comes from accretion onto a compact object. The accretion disk launches two opposite jets with velocity of the order of the escape velocity from the accreting object and with mass outflow rate of ~1-20% of the accretion rate as in most popular models for jet launching; in the present model these are termed fast-first-stage (FFS) jets. However, the FFS jets encounter surrounding gas that originates in the mass accretion process, and are terminated by strong shocks close to their origin. Two hot bubbles are formed. These bubbles accelerate the surrounding gas to form two SMW jets that are more massive and slower than the FFS jets. There are two conditions for this mechanism to work. Firstly, the surrounding gas should be massive enough to block the free expansion of the FFS jets. Most efficiently this condition is achieved when the surrounding gas is replenished. Secondly, the radiative energy losses must be small.Comment: Accepted by New Astronom

Linear lambda terms as invariants of rooted trivalent maps

The main aim of the article is to give a simple and conceptual account for the correspondence (originally described by Bodini, Gardy, and Jacquot) between $\alpha$-equivalence classes of closed linear lambda terms and isomorphism classes of rooted trivalent maps on compact oriented surfaces without boundary, as an instance of a more general correspondence between linear lambda terms with a context of free variables and rooted trivalent maps with a boundary of free edges. We begin by recalling a familiar diagrammatic representation for linear lambda terms, while at the same time explaining how such diagrams may be read formally as a notation for endomorphisms of a reflexive object in a symmetric monoidal closed (bi)category. From there, the "easy" direction of the correspondence is a simple forgetful operation which erases annotations on the diagram of a linear lambda term to produce a rooted trivalent map. The other direction views linear lambda terms as complete invariants of their underlying rooted trivalent maps, reconstructing the missing information through a Tutte-style topological recurrence on maps with free edges. As an application in combinatorics, we use this analysis to enumerate bridgeless rooted trivalent maps as linear lambda terms containing no closed proper subterms, and conclude by giving a natural reformulation of the Four Color Theorem as a statement about typing in lambda calculus.Comment: accepted author manuscript, posted six months after publicatio

Detecting Planets in Planetary Nebulae

We examine the possibility of detecting signatures of surviving Uranus-Neptune-like planets inside planetary nebulae. Planets that are not too close to the stars, orbital separation larger than about 5 AU, are likely to survive the entire evolution of the star. As the star turns into a planetary nebula, it has a fast wind and a strong ionizing radiation. The interaction of the radiation and wind with a planet may lead to the formation of a compact condensation or tail inside the planetary nebula, which emits strongly in Halpha, but not in [OIII]. The position of the condensation (or tail) will change over a time of about 10 years. Such condensations might be detected with currently existing telescopes.Comment: Latex, uses aasms4.sty, 10 pages, preprin