Harmonic Sums and Mellin Transforms

The finite and infinite harmonic sums form the general basis for the Mellin transforms of all individual functions $f_i(x)$ describing inclusive quantities such as coefficient and splitting functions which emerge in massless field theories. We discuss the mathematical structure of these quantities.Comment: Contribution to the Proceedings of the 7th International Workshop on Deep Inelastic Scattering and QCD, DIS99, DESY-Zeuthen, April 1999; Nucl. Phys. B (Proc. Suppl.

A spatial refractive index sensor using whispering gallery modes in an optically trapped microsphere

We propose the use of an optically trapped, dye doped polystyrene microsphere for spatial probing of the refractive index at any position in a fluid. We demonstrate the use of the dye embedded in the microsphere as an internal broadband excitation source, thus eliminating the need for a tunable excitation source. We measured the full width at half maximum of the TE and TM resonances, and their frequency spacing as a function of the refractive index of the immersion fluid. From these relations we obtained an absolute sensitivity of 5e-4 in local refractive index, even when the exact size of the microsphere was not a priori known.Comment: 3 pages, 3 figure

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

Pulsation-triggered mass loss from AGB stars: the 60-day critical period

Low- and intermediate-mass stars eject much of their mass during the late, red giant branch (RGB) phase of evolution. The physics of their strong stellar winds is still poorly understood. In the standard model, stellar pulsations extend the atmosphere, allowing a wind to be driven through radiation pressure on condensing dust particles. Here we investigate the onset of the wind, using nearby RGB stars drawn from the Hipparcos catalogue. We find a sharp onset of dust production when the star first reaches a pulsation period of 60 days. This approximately co-incides with the point where the star transitions to the first overtone pulsation mode. Models of the spectral energy distributions show stellar mass-loss rate suddenly increases at this point, by a factor of ~10 over the existing (chromospherically driven) wind. The dust emission is strongly correlated with both pulsation period and amplitude, indicating stellar pulsation is the main trigger for the strong mass loss, and determines the mass-loss rate. Dust emission does not strongly correlate with stellar luminosity, indicating radiation pressure on dust has little effect on the mass-loss rate. RGB stars do not normally appear to produce dust, whereas dust production by asymptotic giant branch stars appears commonplace, and is probably ubiquitous above the RGB-tip luminosity. We conclude that the strong wind begins with a step change in mass-loss rate, and is triggered by stellar pulsations. A second rapid mass-loss-rate enhancement is suggested when the star transitions to the fundamental pulsation mode, at a period of ~300 days.Comment: Accepted ApJ Letters, 5 pages, 2 figure

Remote Control and Experience at ESO

Remote observing can be broadly defined as those observations where the astronomer is not physically present at the telescope. Different implementations presently in use include robotic telescopes, service observing with or without eavesdropping and active remote observing. We briefly describe the terminology, the pros and cons, the observing modes, and their implementation at optical observatories. In the second part of the paper, we discuss the example of remote observing with ESO's NTT. Different aspects of the technical setup and the support given to observers, with emphasis on problems encountered, are described. With the present system, we find that the observing efficiencies for local and remote observing are identical: few projects still require local observations.Comment: Review talk given at conf. on New Observing Modes For The Next Century (Hawaii, July 1995). 9 pages, 2 (ps) figures available on request from [email protected]

Alignment of the Angular Momentum Vectors of Planetary Nebulae in the Galactic Bulge

We use high-resolution H {\alpha} images of 130 planetary nebulae (PNe) to investigate whether there is a preferred orientation for PNe within the Galactic Bulge. The orientations of the full sample have an uniform distribution. However, at a significance level of 0.01, there is evidence for a non-uniform distribution for those planetary nebulae with evident bipolar morphology. If we assume that the bipolar PNe have an unimodal distribution of the polar axis in Galactic coordinates, the mean Galactic position angle is consistent with 90{\deg}, i.e. along the Galactic plane, and the significance level is better than 0.001 (the equivalent of a 3.7{\sigma} significance level for a Gaussian distribution). The shapes of PNe are related to angular momentum of the original star or stellar system, where the long axis of the nebula measures the angular momentum vector. In old, low-mass stars, the angular momentum is largely in binary orbital motion. Consequently, the alignment of bipolar nebulae that we have found indicates that the orbital planes of the binary systems are oriented perpendicular to the Galactic plane. We propose that strong magnetic fields aligned along the Galactic plane acted during the original star formation process to slow the contraction of the star forming cloud in the direction perpendicular to the plane. This would have produced a propensity for wider binaries with higher angular momentum with orbital axes parallel to the Galactic plane. Our findings provide the first indication of a strong, organized magnetic field along the Galactic plane that impacted on the angular momentum vectors of the resulting stellar population.Comment: There are two effective parts. The main paper consists of the first 17 pages and includes 8 figures and 7 tables. The remaining 10 pages will be published as an online supplement that is made up of 4 multi-part figures. Accepted for publication in MNRAS Main Journa

Structure function evolution at next-to-leading order and beyond

Results are presented of two studies addressing the scaling violations of deep-inelastic structure functions. Factorization-scheme independent fits to all ep and mu p data on F_2 are performed at next-to-leading order (NLO), yielding alpha_s(M_Z) = 0.114 +- 0.002_exp (+0.006-0.004)_th . In order to reduce the theoretical error dominated by the renormalization-scale dependence, the next-higher order (NNLO) needs to be included. For the flavour non-singlet sector, it is shown that available calculations provide sufficient information for this purpose at x > 10^-2.Comment: 3 pages LaTeX including 4 eps-figures, uses npb.sty. Talk presented at DIS'99, DESY-Zeuthen, April 1999. To appear in the proceeding