Axisymmetric Self-Similar Equilibria of Self-Gravitating Isothermal Systems

All axisymmetric self-similar equilibria of self-gravitating, rotating, isothermal systems are identified by solving the nonlinear Poisson equation analytically. There are two families of equilibria: (1) Cylindrically symmetric solutions in which the density varies with cylindrical radius as R^(-alpha), with 0 <= alpha <= 2. (2) Axially symmetric solutions in which the density varies as f(theta)/r^2, where `r' is the spherical radius and `theta' is the co-latitude. The singular isothermal sphere is a special case of the latter class with f(theta)=constant. The axially symmetric equilibrium configurations form a two-parameter family of solutions and include equilibria which are surprisingly asymmetric with respect to the equatorial plane. The asymmetric equilibria are, however, not force-free at the singular points r=0, infinity, and their relevance to real systems is unclear. For each hydrodynamic equilibrium, we determine the phase-space distribution of the collisionless analog.Comment: 13 pages, 7 figures, uses emulateapj.sty. Submitted to Ap

The Milky Way Galaxy as a Strong Gravitational Lens

We study the gravitational lensing effects of spiral galaxies by taking a model of the Milky Way and computing its lensing properties. The model is composed of a spherical Hernquist bulge, a Miyamoto-Nagai disc and an isothermal halo. As a strong lens, a spiral galaxy like the Milky Way can give rise to four different imaging geometries. They are (i) three images on one side of the galaxy centre (`disc triplets'), (ii) three images with one close to the centre (`core triplets'), (iii) five images and (iv) seven images. Neglecting magnification bias, we show that the core triplets, disc triplets and fivefold imaging are roughly equally likely. Even though our models contain edge-on discs, their image multiplicities are not dominated by disc triplets. The halo has a small effect on the caustic structure, the time delays and brightnesses of the images. The Milky Way model has a maximum disc (i.e., the halo is not dynamically important in the inner parts). Strong lensing by nearly edge-on disc galaxies breaks the degeneracy between the relative contribution of the disc and halo to the overall rotation curve. If a spiral galaxy has a sub-maximum disc, then the astroid caustic shrinks dramatically in size, whilst the radial caustic shrinks more modestly. This causes changes in the relative likelihood of the image geometries, specifically (i) core triplets are now 9/2 times more likely than disc triplets, (ii) the cross section for threefold imaging is reduced by a factor of 2/3, whilst (iii) the cross section for fivefold imaging is reduced by 1/2. Although multiple imaging is less likely (the cross sections are smaller), the average total magnification is greater.Comment: MNRAS, in pres

Planetary Stability Zones in Hierarchical Triple Star Systems

A symplectic integrator algorithm suitable for hierarchical triple systems is formulated and tested. The positions of the stars are followed in hierarchical Jacobi coordinates, whilst the planets are referenced purely to their primary. The algorithm is fast, accurate and easily generalised to incorporate collisions. There are five distinct cases -- circumtriple orbits, circumbinary orbits and circumstellar orbits around each of the stars in the hierarchical triple -- which require a different formulation of the symplectic integration algorithm. As an application, a survey of the stability zones for planets in hierarchical triples is presented, with the case of a single planet orbiting the inner binary considered in detail. Fits to the inner and outer edges of the stability zone are computed. Considering the hierarchical triple as two decoupled binary systems, the earlier work of Holman & Wiegert on binaries is shown to be applicable to triples, except in the cases of high eccentricities and close or massive stars. Application to triple stars with good data in the multiple star catalogue suggests that more than 50 per cent are unable to support circumbinary planets, as the stable zone is almost non-existent.Comment: 16 pages, MNRAS, in pres

Radiation Induced Fermion Resonance

The Dirac equation is solved for two novel terms which describe the interaction energy between the half integral spin of a fermion and the classical, circularly polarized, electromagnetic field. A simple experiment is suggested to test the new terms and the existence of radiation induced fermion resonance.Comment: latex, 4 pages, no figure

Comparison of different methods for estimating snowcover in forested, mountainous basins using LANDSAT (ERTS) images

Snow-covered areas on LANDSAT (ERTS) images of the Santiam River basin, Oregon, and other basins in Washington were measured using several operators and methods. Seven methods were used: (1) Snowline tracing followed by measurement with planimeter, (2) mean snowline altitudes determined from many locations, (3) estimates in 2.5 x 2.5 km boxes of snow-covered area with reference to snow-free images, (4) single radiance-threshold level for entire basin, (5) radiance-threshold setting locally edited by reference to altitude contours and other images, (6) two-band color-sensitive extraction locally edited as in (5), and (7) digital (spectral) pattern recognition techniques. The seven methods are compared in regard to speed of measurement, precision, the ability to recognize snow in deep shadow or in trees, relative cost, and whether useful supplemental data are produced

Construction of ATS Cloud Console Final Report

ATS cloud console for rapid analysis of cloud image sequence

Analysis of ERTS imagery using special electronic viewing/measuring equipment

An electronic satellite image analysis console (ESIAC) is being employed to process imagery for use by USGS investigators in several different disciplines studying dynamic hydrologic conditions. The ESIAC provides facilities for storing registered image sequences in a magnetic video disc memory for subsequent recall, enhancement, and animated display in monochrome or color. Quantitative measurements of distances, areas, and brightness profiles can be extracted digitally under operator supervision. Initial results are presented for the display and measurement of snowfield extent, glacier development, sediment plumes from estuary discharge, playa inventory, phreatophyte and other vegetative changes

A Note on the Relativistic Covariance of the B−B- Cyclic Relations

It is shown that the Evans-Vigier modified electrodynamics is compatible with the Relativity Theory.Comment: ReVTeX file, 14pp., no figure