Lensing Properties of Cored Galaxy Models

A method is developed to evaluate the magnifications of the images of galaxies with lensing potentials stratified on similar concentric ellipses. A simple contour integral is provided which enables the sums of the magnifications of even parity or odd parity or the central image to be easily calculated. The sums for pairs of images vary considerably with source position, while the signed sums can be remarkably uniform inside the tangential caustic in the absence of naked cusps. For a family of models in which the potential is a power-law of the elliptic radius, the number of visible images is found as a function of flattening, external shear and core radius. The magnification of the central image depends on the core radius and the slope of the potential. For typical source and lens redshifts, the missing central image leads to strong constraints; the mass distribution in the lensing galaxy must be nearly cusped, and the cusp must be isothermal or stronger. This is in accord with the cuspy cores seen in high resolution photometry of nearby, massive, early-type galaxies, which typically have the surface density falling like distance^{-1.3} outside a break radius of a few hundred parsecs. Cuspy cores by themselves can provide an explanation of the missing central images. Dark matter at large radii may alter the slope of the projected density; provided the slope remains isothermal or steeper and the break radius remains small, then the central image remains unobservable. The sensitivity of the radio maps must be increased fifty-fold to find the central images in abundance.Comment: 42 pages, 11 figures, ApJ in pres

Millimeter-wave antenna system

Parabolic reflectors fabricated from Carbon Fiber Reinforced Plastic (CFRP) composite material will not distort their shape by more than 3 percent of millimeter wavelength, despite large temperature differences on reflector surfaces. CFRP has zero thermal expansion. It is derived from charred polyacrylonitrite plastic filaments that are combined with epoxy resin

Cuspy Dark-Matter Haloes and the Galaxy

The microlensing optical depth to Baade's Window constrains the minimum total mass in baryonic matter within the Solar circle to be greater than 3.9 x 10^{10} solar masses, assuming the inner Galaxy is barred with viewing angle of roughly 20 degrees. From the kinematics of solar neighbourhood stars, the local surface density of dark matter is about 30 +/- 15 solar masses per square parsec. We construct cuspy haloes normalised to the local dark matter density and calculate the circular-speed curve of the halo in the inner Galaxy. This is added in quadrature to the rotation curve provided by the stellar and ISM discs, together with a bar sufficiently massive so that the baryonic matter in the inner Galaxy reproduces the microlensing optical depth. Such models violate the observational constraint provided by the tangent-velocity data in the inner Galaxy (typically at radii 2-4 kpc). The high baryonic contribution required by the microlensing is consistent with implications from hydrodynamical modelling and the pattern speed of the Galactic bar. We conclude that the cuspy haloes favoured by the Cold Dark Matter cosmology (and its variants) are inconsistent with the observational data on the Galaxy.Comment: 5 pages, 1 figures, MNRAS (submitted

Jamming transitions and avalanches in the game of Dots-and-Boxes

We study the game of Dots-and-Boxes from a statistical point of view. The early game can be treated as a case of Random Sequential Adsorption, with a jamming transition that marks the beginning of the end-game. We derive set of differential equations to make predictions about the state of the lattice at the transition, and thus about the distribution of avalanches in the end-game.Comment: 7 pages, 8 figures, revtex