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

Gravitational Lenses With More Than Four Images: I. Classification of Caustics

We study the problem of gravitational lensing by an isothermal elliptical density galaxy in the presence of a tidal perturbation. When the perturbation is fairly strong and oriented near the galaxy's minor axis, the lens can produce image configurations with six or even eight highly magnified images lying approximately on a circle. We classify the caustic structures in the model and identify the range of models that can produce such lenses. Sextuple and octuple lenses are likely to be rare because they require special lens configurations, but a full calculation of the likelihood will have to include both the existence of lenses with multiple lens galaxies and the strong magnification bias that affects sextuple and octuple lenses. At optical wavelengths these lenses would probably appear as partial or complete Einstein rings, but at radio wavelengths the individual images could probably be resolved.Comment: 30 pages, including 12 postscript figures; accepted for publication in Ap

A search for continuous fluorescence in reflection nebulae

Photometric and spectrophotometric observations were made of the reflection nebulae NGC1435, NGC2068, NGC7023, and IC1287 in an attempt to detect continuous fluorescence by dust grains. Several effects of importance for observations of such faint objects are discussed, including instrumental light scattering, a photographic effect, and a time delay effect which can occur if the illuminating star is a spectrum variable. It is found that continuous fluorescence by interstellar grains is not likely to exist and that it cannot account for more than 10 percent of the total surface brightness of these reflection nebulae. No evidence of diffuse interstellar features is found in the spectra of these nebulae

Semiclassical and Quantum Black Holes and their Evaporation, de Sitter and Anti-de Sitter Regimes, Gravitational and String Phase Transitions

An effective string theory in physically relevant cosmological and black hole space times is reviewed. Explicit computations of the quantum string entropy, partition function and quantum string emission by black holes (Schwarzschild, rotating, charged, asymptotically flat, de Sitter dS and AdS space times) in the framework of effective string theory in curved backgrounds provide an amount of new quantum gravity results as: (i) gravitational phase transitions appear with a distinctive universal feature: a square root branch point singularity in any space time dimensions. This is of the type of the de Vega - Sanchez transition for the thermal self-gravitating gas of point particles. (ii) There are no phase transitions in AdS alone. (iii) For $dS$ background, upper bounds of the Hubble constant H are found, dictated by the quantum string phase transition.(iv) The Hawking temperature and the Hagedorn temperature are the same concept but in different (semiclassical and quantum) gravity regimes respectively. (v) The last stage of black hole evaporation is a microscopic string state with a finite string critical temperature which decays as usual quantum strings do in non-thermal pure quantum radiation (no information loss).(vi) New lower string bounds are given for the Kerr-Newman black hole angular momentum and charge, which are entirely different from the upper classical bounds. (vii) Semiclassical gravity states undergo a phase transition into quantum string states of the same system, these states are duals of each other in the precise sense of the usual classical-quantum (wave-particle) duality, which is universal irrespective of any symmetry or isommetry of the space-time and of the number or the kind of space-time dimensions.Comment: review paper, no figures. to appear in Int Jour Mod Phys

Zur Androgenrezeptor-Hypothese der amyotrophen Lateralsklerose

Unter Annahme einer möglichen Funktionsstörung des Androgenrezeptors bei der amyotrophen Lateralsklerose (ALS) wurde die repetitive CAG-Trinukleotidsequenz seines ersten Exons bei 12 Patienten untersucht, da eine abnorme Verlängerung dieses Genabschnitts zur ALS-ähnlichen bulbospinalen Neuronopathie führt. Nach den Ergebnissen kommt dieser Typ vom Androgenrezeptordefekt in der Pathogenese der ALS nicht in Frage: alle Patienten zeigten eine Normalbefund

On Multiple Einstein Rings

A number of recent surveys for gravitational lenses have found examples of double Einstein rings. Here, we investigate analytically the occurrence of multiple Einstein rings. We prove, under very general assumptions, that at most one Einstein ring can arise from a mass distribution in a single plane lensing a single background source. Two or more Einstein rings can therefore only occur in multi-plane lensing. Surprisingly, we show that it is possible for a single source to produce more than one Einstein ring. If two point masses (or two isothermal spheres) in different planes are aligned with observer and source on the optical axis, we show that there are up to three Einstein rings. We also discuss the image morphologies for these two models if axisymmetry is broken, and give the first instances of magnification invariants in the case of two lens planes.Comment: MNRAS, in press (extra figure included

Localized energy for wave equations with degenerate trapping

Localized energy estimates have become a fundamental tool when studying wave equations in the presence of asymptotically at background geometry. Trapped rays necessitate a loss when compared to the estimate on Minkowski space. A loss of regularity is a common way to incorporate such. When trapping is sufficiently weak, a logarithmic loss of regularity suffices. Here, by studying a warped product manifold introduced by Christianson and Wunsch, we encounter the first explicit example of a situation where an estimate with an algebraic loss of regularity exists and this loss is sharp. Due to the global-in-time nature of the estimate for the wave equation, the situation is more complicated than for the Schr\"{o}dinger equation. An initial estimate with sub-optimal loss is first obtained, where extra care is required due to the low frequency contributions. An improved estimate is then established using energy functionals that are inspired by WKB analysis. Finally, it is shown that the loss cannot be improved by any power by saturating the estimate with a quasimode.Comment: 18 page

Quaestor: Query web caching for database-as-a-service providers

Today, web performance is primarily governed by round-trip latencies between end devices and cloud services. To improve performance, services need to minimize the delay of accessing data. In this paper, we propose a novel approach to low latency that relies on existing content delivery and web caching infrastructure. The main idea is to enable application-independent caching of query results and records with tunable consistency guarantees, in particular bounded staleness. Q uaestor (Query Store) employs two key concepts to incorporate both expiration-based and invalidation-based web caches: (1) an Expiring Bloom Filter data structure to indicate potentially stale data, and (2) statistically derived cache expiration times to maximize cache hit rates. Through a distributed query invalidation pipeline, changes to cached query results are detected in real-time. The proposed caching algorithms offer a new means for data-centric cloud services to trade latency against staleness bounds, e.g. in a database-as-a-service. Q uaestor is the core technology of the backend-as-a-service platform Baqend, a cloud service for low-latency websites. We provide empirical evidence for Q uaestor 's scalability and performance through both simulation and experiments. The results indicate that for read-heavy workloads, up to tenfold speed-ups can be achieved through Q uaestor 's caching. </jats:p

Using Quadruple Lenses to probe the Structure of the Lensing Galaxy

We show here that quadruple lenses can be useful laboratories to probe whether the potential of the lensing galaxy is purely elliptical or whether an additional distortion is present in the deflector plane. For this test we only have to know the relative image positions of the quadruple lens system and the (relative) center of light position of the lensing galaxy. Furthermore we introduce new methods which easily allow us to determine the location (rotation angle relative to the image positions) of the major axis of the lensing galaxy. In due course we can determine the parity of the four images as well. We apply these methods to the 8 currently known quadruple lenses and find that in the case of MG 0414+0534, CLASS 1608+656 and HST 12531-2914 it is impossible to accommodate the relative image positions and the galaxy position with any elliptical potential whereas the other five cases can be described very well with a simple elliptical potential. This method will have important impacts for $\chi^2$-fits and the reconstruction of galaxy models for quadruple lenses.Comment: 10 pages, 2 Postscript figures, uses AASTeX v4.0 macro