Magnification relations in gravitational lensing via multidimensional residue integrals

We investigate the so-called magnification relations of gravitational lensing models. We show that multidimensional residue integrals provide a simple explanation for the existence of these relations, and an effective method of computation. We illustrate the method with several examples, thereby deriving new magnification relations for galaxy lens models and microlensing (point mass lensing).Comment: 16 pages, uses revtex4, submitted to Journal of Mathematical Physic

Probability of Detecting a Planetary Companion during a Microlensing Event

The probability of detecting a planetary companion of a lensing star during a microlensing event toward the Galactic center, averaged over all relevant event and galactic parameters, when the planet-star mass ratio $q=0.001$ has a maximum exceeding 10% at an orbit semimajor axis $a$ near 1.5 AU for a uniform distribution of impact parameters. The maximum probability is raised to more than 20% for a distribution of source-lens impact parameters that is determined by the efficiency of event detection. The averaging procedures are carefully defined, and they determinine the dependence of the detection probabilities on several properties of the Galaxy. The probabilities scale approximately as $\sqrt{q}$. A planet is assumed detectable if the perturbation of the single lens light curve exceeds $2/(S/N)$ for at least 20 consecutive photometric points sometime during the event. Two meter telescopes with 60 second integrations in I-band with high time resolution photometry throughout the duration of an ongoing event are assumed. The probabilities are derived as a function of $a$, where they remain significant for $0.6<a<10$ AU. Dependence of the detection probabilities on the lens mass function, luminosity function of the source stars as modified by extinction, distribution of source-lens impact parameters, and the line of sight to the source are also determined, and the probabilities are averaged over the distribution of the projected planet position, the lens mass function, the distribution of impact parameters, the lens and source distances as weighted by their distributions along the line of sight and over the $I$-band apparent luminosity function of the sources. The extraction of the probabilility as a function of $a$ for a particular $q$ from empirical data is indicated.Comment: 32 pages, 20 figures, In Press, ApJ, Latex format with aas2pp4 forma

Preparation of homogeneous vitreous materials for electronic and optical devices

Vitreous material builds up as series of solidified layers on inside walls of sealed quartz ampoule containing molten constituents of material, and forms well defined shapes to close dimensional tolerances. Ampoules are made of material which does not react with melt and has lower thermal expansion coefficient than solidified layer

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

Extended Source Diffraction Effects Near Gravitational Lens Fold Caustics

Calculations are presented detailing the gravitational lens diffraction due to the steep brightness gradient of the limb of a stellar source. The lensing case studied is the fold caustic crossing. The limb diffraction signal greatly exceeds that due to the disk as a whole and should be detectable for white dwarf sources in our Galaxy and it's satellites with existing telescopes. Detection of this diffraction signal would provide an additional mathematical constraint, reducing the degeneracy among models of the lensing geometry. The diffraction pattern provides pico-arcsecond resolution of the limb profile.Comment: 19 pages including 17 figures, Accepted for publication in ApJ, Minor conceptual change from previous versio

Detection Rates for Close Binaries Via Microlensing

Microlensing is one of the most promising methods of reconstructing the stellar mass function down to masses even below the hydrogen-burning limit. The fundamental limit to this technique is the presence of unresolved binaries, which can in principle significantly alter the inferred mass function. Here we quantify the fraction of binaries that can be detected using microlensing, considering specifically the mass ratio and separation of the binary. We find that almost all binary systems with separations greater than $b \sim 0.4$ of their combined Einstein ring radius are detectable assuming a detection threshold of $3\%$. For two M dwarfs, this corresponds to a limiting separation of \gsim 1 \au. Since very few observed M dwarfs have companions at separations \lsim 1 \au, we conclude that close binaries will probably not corrupt the measurements of the mass function. We find that the detectability depends only weakly on the mass ratio. For those events for which individual masses can be determined, we find that binaries can be detected down to $b \sim 0.2$.Comment: 19 pages including 6 figures. Uses phyyzx format. Send requests for higher quality figures to [email protected]

The Post-Newtonian Limit of f(R)-gravity in the Harmonic Gauge

A general analytic procedure is developed for the post-Newtonian limit of $f(R)$-gravity with metric approach in the Jordan frame by using the harmonic gauge condition. In a pure perturbative framework and by using the Green function method a general scheme of solutions up to $(v/c)^4$ order is shown. Considering the Taylor expansion of a generic function $f$ it is possible to parameterize the solutions by derivatives of $f$. At Newtonian order, $(v/c)^2$, all more important topics about the Gauss and Birkhoff theorem are discussed. The corrections to "standard" gravitational potential ($tt$-component of metric tensor) generated by an extended uniform mass ball-like source are calculated up to $(v/c)^4$ order. The corrections, Yukawa and oscillating-like, are found inside and outside the mass distribution. At last when the limit $f\rightarrow R$ is considered the $f(R)$-gravity converges in General Relativity at level of Lagrangian, field equations and their solutions.Comment: 16 pages, 10 figure

Exotic Statistics for Ordinary Particles in Quantum Gravity

Objects exhibiting statistics other than the familiar Bose and Fermi ones are natural in theories with topologically nontrivial objects including geons, strings, and black holes. It is argued here from several viewpoints that the statistics of ordinary particles with which we are already familiar are likely to be modified due to quantum gravity effects. In particular, such modifications are argued to be present in loop quantum gravity and in any theory which represents spacetime in a fundamentally piecewise-linear fashion. The appearance of unusual statistics may be a generic feature (such as the deformed position-momentum uncertainty relations and the appearance of a fundamental length scale) which are to be expected in any theory of quantum gravity, and which could be testable.Comment: Awarded an honourable mention in the 2008 Gravity Research Foundation Essay Competitio

The Flash Pattern of Photosynthetic Oxygen Evolution after Treatment with Low Concentrations of Hydroxylamine as a Function of the Previous S1/S0-Ratio Further Evidence that NH2OH Reduces the Water Oxidizing Complex in the Dark

Flash induced oxygen evolution patterns of isolated PS II complexes from the cyanobacterium Synechococcus were measured with a Joliot-type electrode. By suitable preflash and dark adaptation procedures, samples were prepared in the state S1 (100%), as well as enriched in S0 (60% S0, 40% S,). After treatment with low concentrations of NH2OH (≤ 100 μм), the two flash patterns were identical. This is further evidence for a reduction of the water oxidizing complex by hydroxylamine in the dark. Two reduced states (S-1 and S-2) below S0 are formed by this reduction

Analytic Time Delays and H_0 Estimates for Gravitational Lenses

We study gravitational lens time delays for a general family of lensing potentials, which includes the popular singular isothermal elliptical potential and singular isothermal elliptical density distribution but allows general angular structure. Using a novel approach, we show that the time delay can be cast in a very simple form, depending only on the observed image positions. Including an external shear changes the time delay proportional to the shear strength, and varying the radial profile of the potential changes the time delay approximately linearly. These analytic results can be used to obtain simple estimates of the time delay and the Hubble constant in observed gravitational lenses. The naive estimates for four of five time delay lenses show surprising agreement with each other and with local measurements of H_0; the complicated Q 0957+561 system is the only outlier. The agreement suggests that it is reasonable to use simple isothermal lens models to infer H_0, although it is still important to check this conclusion by examining detailed models and by measuring more lensing time delays.Comment: 16 pages with 2 embedded figures; submitted to Ap