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

Absence of classical and quantum mixing

It is shown, under mild assumptions, that classical degrees of freedom dynamically coupled to quantum ones do not inherit their quantum fluctuations. It is further shown that, if the assumptions are strengthen by imposing the existence of a canonical structure, only purely classical or purely quantum dynamics are allowed.Comment: REVTeX, 4 page

Probing the Atmospheres of Planets Orbiting Microlensed Stars via Polarization Variability

We present a new method to identify and probe planetary companions of stars in the Galactic Bulge and Magellanic Clouds using gravitational microlensing. While spectroscopic studies of these planets is well beyond current observational techniques, monitoring polarization fluctuations during high magnification events induced by binary microlensing events will probe the composition of the planetary atmospheres, an observation which otherwise is currently unattainable even for nearby planetary systems.Comment: 7 pages, 2 figures. To appear in Astrophysical Journal Letter

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 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

Gravitational Microlensing Near Caustics I: Folds

We study the local behavior of gravitational lensing near fold catastrophes. Using a generic form for the lensing map near a fold, we determine the observable properties of the lensed images, focusing on the case when the individual images are unresolved, i.e., microlensing. Allowing for images not associated with the fold, we derive analytic expressions for the photometric and astrometric behavior near a generic fold caustic. We show how this form reduces to the more familiar linear caustic, which lenses a nearby source into two images which have equal magnification, opposite parity, and are equidistant from the critical curve. In this case, the simplicity and high degree of symmetry allows for the derivation of semi-analytic expressions for the photometric and astrometric deviations in the presence of finite sources with arbitrary surface brightness profiles. We use our results to derive some basic properties of astrometric microlensing near folds, in particular we predict for finite sources with uniform and limb darkening profiles, the detailed shape of the astrometric curve as the source crosses a fold. We find that the astrometric effects of limb darkening will be difficult to detect with the currently planned accuracy of the Space Interferometry Mission. We verify our results by numerically calculating the expected astrometric shift for the photometrically well-covered Galactic binary lensing event OGLE-1999-BUL-23, finding excellent agreement with our analytic expressions. Our results can be applied to any lensing system with fold caustics, including Galactic binary lenses and quasar microlensing.Comment: 37 pages, 7 figures. Revised version includes an expanded discussion of applications. Accepted to ApJ, to appear in the August 1, 2002 issue (v574

Carryover Effect of New Soybean Herbicides on Corn

Scepter, Canopy, Gemini, Classic, and Command are new soybean herbicides which were introduced in 1986 and are being used in Kentucky. These herbicides have gained widespread popularity because of their excellent control of cocklebur, pigweeds, morningglories, and velvetleaf. In addition, they can be applied in a variety of ways which makes them attractive to the soybean producer. However, these herbicides do have potential shortcomings in that they can persist in the soil for several months and cause injury to rotational crops such as corn or wheat. Since greater than 60% of the soybeans grown in Kentucky are rotated to corn, it is important to know the persistence potential of these newer soybean herbicides. Chlorimuron is one of the active ingredients in Canopy, Preview, Gemini, Lorox Plus, and Classic. We have conducted research with chlorimuron at rates comparable to those recommended for Canopy and Gemini. Research on the persistence of Scepter, Command, and Canopy was started in 1985. After having been applied to the soil and soybeans grown, corn was planted the following year, and the degree of corn injury monitored. The persistence of Scepter and Command was determined in three tillage systems: conventional moldboard plowing and disking; full-season no-tillage in which a wheat cover crop was killed with Gramoxone Super 10 days prior to planting; double-crop no-tillage in which soybeans were planted after wheat harvest. Canopy persistence was determined in conventionally tilled soils that had a pH of 5.3, 6.3, or 7.3. All herbicides were applied at their labeled rate and at 1.5 and 2 times the labeled rate

Dust Emission Features in NGC 7023 between 0.35 and 2.5 micron: Extended Red Emission (0.7 micron) and Two New Emission Features (1.15 and 1.5 micron)

We present 0.35 to 2.5 micron spectra of the south and northwest filaments in the reflection nebula NGC 7023. These spectra were used to test the theory of Seahra & Duley that carbon nanoparticles are responsible for Extended Red Emission (ERE). Our spectra fail to show their predicted second emission band at 1.0 micron even though both filaments exhibit strong emission in the familiar 0.7 micron ERE band. The northwest filament spectrum does show one, and possibly two, new dust emission features in the near-infrared. We clearly detect a strong emission band at 1.5 micron which we tentatively attribute to beta-FeSi_2 grains. We tentatively detect a weaker emission band at 1.15 micron which coincides with the location expected for transitions from the conduction band to mid-gap defect states of silicon nanoparticles. This is added evidence that silicon nanoparticles are responsible for ERE as they already can explain the observed behavior of the main visible ERE band.Comment: 9 pages, color figures, accepted to the ApJ, color and b/w versions available at http://dirty.as.arizona.edu/~kgordon/papers/ere_1um.htm