The Kepler Problem: Orbit Cones and Cylinders

Planetary orbits, being conic sections, may be obtained as the locus of intersection of planes and cones. The planes involved are familiar to anyone who has studied the classical Kepler problem. We focus here on the cones

DeBruijn Strings, Double Helices, and the Ehrenfeucht-Mycielski Mechanism

We revisit the pseudo-random sequence introduced by Ehrenfeucht and Mycielski and its connections with DeBruijn strings

A novel technique for wide-field polarimetry with a radiotelescope array

We report the use of the Australia Telescope Compact Array (ATCA) to conduct polarimetric observations of the sky at 5 GHz. The ATCA is normally operated as an interferometer array, but these observations were conducted in a split array mode in which the antenna elements were used as single-dishes with their beams staggered to simultaneously cover a wide area of sky with a resolution of 10 arcmin. The linearly polarized sky radiation was fully characterized from measurements, made over a range of parallactic angles, of the cross correlated signals from the orthogonal linear feeds. We describe the technique and present a polarimetric image of the Vela supernova remnant made as a test of the method. The development of the techniques was motivated by the need for wide-field imaging of the foreground contamination of the polarized component of the cosmic microwave background signal.Comment: 13 pages, 2 figures, accepted for publication in A

Radicals of 0-regular algebras

We consider a generalisation of the Kurosh--Amitsur radical theory for rings (and more generally multi-operator groups) which applies to 0-regular varieties in which all operations preserve 0. We obtain results for subvarieties, quasivarieties and element-wise equationally defined classes. A number of examples of radical and semisimple classes in particular varieties are given, including hoops, loops and similar structures. In the first section, we introduce 0-normal varieties (0-regular varieties in which all operations preserve 0), and show that a key isomorphism theorem holds in a 0-normal variety if it is subtractive, a property more general than congruence permutability. We then define our notion of a radical class in the second section. A number of basic results and characterisations of radical and semisimple classes are then obtained, largely based on the more general categorical framework of L. M\'arki, R. Mlitz and R. Wiegandt as in [13]. We consider the subtractive case separately. In the third section, we obtain results concerning subvarieties and quasivarieties based on the results of the previous section, and also generalise to subtractive varieties some results for multi-operator group radicals defined by simple equational rules. Several examples of radical and semisimple classes are given for a range of fairly natural 0-normal varieties of algebras, most of which are subtractive

GRAPE - A Balloon-Borne Gamma-Ray Polarimeter Experiment

This paper reviews the development status of GRAPE (the Gamma-Ray Polarimeter Experiment), a hard X-ray Compton Polarimeter. The purpose of GRAPE is to measure the polarization of hard X-rays in the 50-300 keV energy range. We are particularly interested in X-rays that are emitted from solar flares and gamma-ray bursts (GRBs), although GRAPE could also be employed in the study of other astrophysical sources. Accurately measuring the polarization of the emitted radiation will lead to a better understating of both emission mechanisms and source geometries. The GRAPE design consists of an array of plastic scintillators surrounding a central high-Z crystal scintillator. The azimuthal distribution of photon scatters from the plastic array into the central calorimeter provides a measure of the polarization fraction and polarization angle of the incident radiation. The design of the detector provides sensitivity over a large field-of-view (>pi steradian). The design facilitates the fabrication of large area arrays with minimal deadspace. This paper presents the latest design concept and the most recent results from laboratory tests of a GRAPE science model.Comment: 6 pages; paper presented at the FRASCATI Workshop 2005 on Multifrequency Behaviour of High Energy Cosmic Sources; submitted to Chinese Journal of Astronomy and Astrophysic

Radial Trends in IMF-Sensitive Absorption Features in Two Early-Type Galaxies: Evidence for Abundance-Driven Gradients

Samples of early-type galaxies show a correlation between stellar velocity dispersion and the stellar initial mass function (IMF) as inferred from gravity-sensitive absorption lines in the galaxies' central regions. To search for spatial variations in the IMF, we have observed two early-type galaxies with Keck/LRIS and measured radial gradients in the strengths of absorption features from 4000-5500 \AA $\,$ and 8000-10,000 \AA. We present spatially resolved measurements of the dwarf-sensitive spectral indices NaI (8190 \AA) and Wing-Ford FeH (9915 \AA), as well as indices for species of H, C$_2$, CN, Mg, Ca, TiO, and Fe. Our measurements show a metallicity gradient in both objects, and Mg/Fe consistent with a shallow gradient in \alpha-enhancement, matching widely observed trends for massive early-type galaxies. The NaI index and the CN$_1$ index at 4160 \AA $\,$ exhibit significantly steeper gradients, with a break at $r \sim 0.1 r_{\rm eff}$ ($r \sim 300$ pc). Inside this radius NaI strength increases sharply toward the galaxy center, consistent with a rapid central rise in [Na/Fe]. In contrast, the ratio of FeH to Fe index strength decreases toward the galaxy center. This behavior cannot be reproduced by a steepening IMF inside $0.1 r_{\rm eff}$ if the IMF is a single power law. While gradients in the mass function above $\sim 0.4 M_\odot$ may occur, exceptional care is required to disentangle these IMF variations from the extreme variations in individual element abundances near the galaxies' centers.Comment: Accepted for publication in ApJ. Updates from v1 include an expanded comparison of measured index strengths to SPS models. 20 page body + 7 page appendix + references. Includes 25 figure

SONTRAC—a scintillating plastic fiber tracking detector for neutron and proton imaging spectroscopy

SONTRAC (SOlar Neutron TRACking imager and spectrometer) is a conceptual instrument intended to measure the energy and incident direction of 20–150 MeV neutrons produced in solar flares. The intense neutron background in a low-Earth orbit requires that imaging techniques be employed to maximize an instrument’s signal-to-noise ratio. The instrument is comprised of mutually perpendicular, alternating layers of parallel, scintillating, plastic fibers that are viewed by optoelectronic devices. Two stereoscopic views of recoil proton tracks are necessary to determine the incident neutron’s direction and energy. The instrument can also be used as a powerful energetic proton imager. Data from a fully functional 3-d prototype are presented. Early results indicate that the instrument’s neutron energy resolution is approximately 10% with the neutron incident direction determined to within a few degrees

The 2000 Periastron Passage of PSR B1259-63

We report here on a sequence of 28 observations of the binary pulsar system PSR B1259-63/SS2883 at four radio frequencies made with the Australia Telescope Compact Array around the time of the 2000 periastron passage. Observations made on 2000 Sep 1 show that the pulsar's apparent rotation measure (RM) reached a maximum of $-14800 \pm 1800$ rad m$^{-2}$, some 700 times the value measured away from periastron, and is the largest astrophysical RM measured. This value, combined with the dispersion measure implies a magnetic field in the Be star's wind of 6 mG. We find that the light curve of the unpulsed emission is similar to that obtained during the 1997 periastron but that differences in detail imply that the emission disc of the Be star is thicker and/or of higher density. The behaviour of the light curve at late times is best modelled by the adiabatic expansion of a synchrotron bubble formed in the pulsar/disc interaction. The expansion rate of the bubble $\sim 12$ km s$^{-1}$ is surprisingly low but the derived magnetic field of 1.6 G close to that expected.Comment: 8 pages, 6 figures, 3 tables, LaTeX (mn.sty). Accepted for publication in the Monthly Notices of the Royal Astronomical Society. Also available at http://astronomy.swin.edu.au/staff/tconnors/publications.htm