The Formation of Globules in Planetary Nebulae

We discuss the formation of globules in planetary nebulae, typified by those observed in the Helix Nebula. We show that the properties of the globules, their number, mass, separation, and overall geometry strongly support a scenario in which globules are formed by the fragmentation of a swept-up shell as opposed to models in which the knots form in the AGB wind. We show that the RT or other instabilities which lead to the break-up of shells formed in the nebulae by fast winds or ionization fronts can produce arrays of globules with the overall geometry and within the mass range observed. We also show that the presence of a magnetic field in the circumstellar gas may play an important role in controlling the fragmentation process. Using field strengths measured in the precursor AGB envelopes, we find that close to the central star where the fields are relatively strong, the wavelengths of unstable MRT modes are larger than the shell dimensions, and the fragmentation of the shell is suppressed. The wavelength of the most unstable MRT mode decreases with increasing distance from the star, and when it becomes comparable to the shell thickness, it can lead to the sudden, rapid break-up of an accelerating shell. For typical nebula parameters, the model results in numerous fragments with a mass scale and a separation scale similar to those observed. Our results provide a link between global models of PN shaping in which shells form via winds and ionization fronts, and the formation of small scale structures in the nebulae.Comment: 4 pages, 2 figures, to appear in IAU Symp. 234, Planetary Nebulae in Our Galaxy and Beyond, eds. M. J. Barlow, R. H. Mende

Experimental investigations of the effects of cutting angle on chattering of a flexible manipulator

When a machine tool is mounted at the tip of a robotic manipulator, the manipulator becomes more flexible (the natural frequencies are lowered). Moreover, for a given flexible manipulator, its compliance will be different depending on feedback gains, configurations, and direction of interest. Here, the compliance of a manipulator is derived analytically, and its magnitude is represented as a compliance ellipsoid. Then, using a two-link flexible manipulator with an abrasive cut off saw, the experimental investigation shows that the chattering varies with the saw cutting angle due to different compliance. The main work is devoted to finding a desirable cutting angle which reduces the chattering

Circumstellar chemistry

The study of the outer envelopes of cool evolved stars has become an active area of research. The physical properties of CS envelopes are presented. Observations of many wavelengths bands are relevant. A summary of observations and a discussion of theoretical considerations concerning the chemistry are summarized. Recent theoretical considerations show that the thermal equilibrium model is of limited use for understanding the chemistry of the outer CS envelopes. The theoretical modeling of the chemistry of CS envelopes provides a quantitive test of chemical concepts which have a broader interest than the envelopes themselves

The Shapes of AGB Envelopes as Probes of Binary Companions

We describe how the large scale geometry of the circumstellar envelopes of asymptotic giant branch stars can be used to probe the presence of unseen stellar companions. A nearby companion modifies the mass loss by gravitationally focusing the wind towards the orbital plane, and thereby determines the shape of the envelope at large distances from the star. Using available simulations, we develop a prescription for the observed shapes of envelopes in terms of the binary parameters, envelope orientation, and type of observation. The prescription provides a tool for the analysis of envelope images at optical, infrared, and millimetre wavelengths, which can be used to constrain the presence of companions in well observed cases. We illustrate this approach by examining the possible role of binary companions in triggering the onset of axi-symmetry in planetary nebula formation. If interaction with the primary leads to axi-symmetry, the spherical halos widely seen around newly formed nebulae set limits on the companion mass. Only low mass objects may orbit close to the primary without observable shaping effects: they remain invisible until the interaction causes a sudden change in the mass loss geometry.Comment: 11 pages, 7 figures, to appear in MNRA