Formalism for testing theories of gravity using lensing by compact objects. III: Braneworld gravity

Braneworld gravity is a model that endows physical space with an extra dimension. In the type II Randall-Sundrum braneworld gravity model, the extra dimension modifies the spacetime geometry around black holes, and changes predictions for the formation and survival of primordial black holes. We develop a comprehensive analytical formalism for far-field black hole lensing in this model, using invariant quantities to compute all geometric optics lensing observables. We then make the first analysis of wave optics in braneworld lensing, working in the semi-classical limit. We show that wave optics offers the only realistic way to observe braneworld effects in black hole lensing. We point out that if primordial braneworld black holes exist, have mass M, and contribute a fraction f of the dark matter, then roughly 3e5 x f (M/1e-18 Msun)^(-1) of them lie within our Solar System. These objects, which we call "attolenses," would produce interference fringes in the energy spectra of gamma-ray bursts at energies ~100 (M/1e-18 Msun)^(-1) MeV (which will soon be accessible with the GLAST satellite). Primordial braneworld black holes spread throughout the universe could produce similar interference effects; the probability for "attolensing" may be non-negligible. If interference fringes were observed, the fringe spacing would yield a simple upper limit on M. Detection of a primordial black hole with M <~ 1e-19 Msun would challenge general relativity and favor the braneworld model. Further work on lensing tests of braneworld gravity must proceed into the physical optics regime, which awaits a description of the full spacetime geometry around braneworld black holes.Comment: 13 pages, 3 figures; accepted in PRD; expanded discussion of prospects for observing attolensing with GLAS

The Theory of Caustics and Wavefront Singularities with Physical Applications

This is intended as an introduction to and review of the work of V, Arnold and his collaborators on the theory of Lagrangian and Legendrian submanifolds and their associated maps. The theory is illustrated by applications to Hamilton-Jacobi theory and the eikonal equation, with an emphasis on null surfaces and wavefronts and their associated caustics and singularities.Comment: Figs. not include

Mathematics of Gravitational Lensing: Multiple Imaging and Magnification

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes. We discuss recent advances in the mathematics of stochastic lensing, discussing a general formula for the global expected number of minimum lensed images as well as asymptotic formulas for the probability densities of the microlensing random time delay functions, random lensing maps, and random shear, and an asymptotic expression for the global expected number of micro-minima. Multiple imaging in optical geometry and a spacetime setting are treated. We review global magnification relation results for model-dependent scenarios and cover recent developments on universal local magnification relations for higher order caustics.Comment: 25 pages, 4 figures. Invited review submitted for special issue of General Relativity and Gravitatio

Image distortion in non perturbative gravitational lensing

We introduce the idea of {\it shape parameters} to describe the shape of the pencil of rays connecting an observer with a source lying on his past lightcone. On the basis of these shape parameters, we discuss a setting of image distortion in a generic (exact) spacetime, in the form of three {\it distortion parameters}. The fundamental tool in our discussion is the use of geodesic deviation fields along a null geodesic to study how source shapes are propagated and distorted on the path to an observer. We illustrate this non-perturbative treatment of image distortion in the case of lensing by a Schwarzschild black hole. We conclude by showing that there is a non-perturbative generalization of the use of Fermat's principle in lensing in the thin-lens approximation.Comment: 22 pages, 6 figures, to appear in Phys. Rev. D (January 2001

Gravitational lensing by stars with angular momentum

Gravitational lensing by spinning stars, approximated as homogeneous spheres, is discussed in the weak field limit. Dragging of inertial frames, induced by angular momentum of the deflector, breaks spherical symmetry. I examine how the gravito-magnetic field affects image positions, caustics and critical curves. Distortion in microlensing-induced light curves is also considered.Comment: 9 pages, 9 figures; to appear in MNRA

Wind-driven emissions of coarse-mode particles in an urban environment

Quantifying surface–atmosphere exchange rates of particles is important for understanding the role of suspended particulate matter in radiative transfer, clouds, precipitation, and climate change. Emissions of coarse-mode particles with a diameter greater than 0.5 µm provide giant cloud condensation nuclei and ice nuclei. These emissions are critical for understanding the evolution of cloud microphysical properties yet remain poorly understood. Here we introduce a new method that uses lidar retrievals of the elastic backscatter and Doppler velocity to obtain surface number emissions of particles with a diameter greater than 0.53 µm. The technique is applied to study particle number fluxes over a 2-month period from 1 June to 10 August 2022 during the TRACER campaign at an urban site near Houston, TX, USA. We found that all the observed fluxes were positive (upwards), indicating particle emission from the surface. The fluxes followed a diurnal pattern and peaked near noon local time. Flux intensity varied through the 2 months with multi-day periods of strong fluxes and multi-day periods of weak fluxes. Emission particle number fluxes peaked near ∼ 100 cm−2 s−1. The daily averaged emission fluxes correlated with friction velocity and were anticorrelated with surface relative humidity. The emission flux can be parameterized as F= 3000 u*4, where u* is the friction velocity in m s−1 and the emission flux F is in cm−2 s−1. The u* dependence is consistent with emission from wind-driven erosion. Estimated values for the mass flux are in the lower range of literature values from non-urban sites. These results demonstrate that urban environments may play an important role in supplying coarse-mode particles to the boundary layer. We anticipate that quantification of these emissions will help constrain aerosol–cloud interaction models that use prognostic aerosol schemes.</p

Ice Initiation by Aerosol Particles: Measured and Predicted Ice Nuclei Concentrations versus Measured Ice Crystal Concentrations in an Orographic Wave Cloud

The initiation of ice in an isolated orographic wave cloud was compared with expectations based on ice nucleating aerosol concentrations and with predictions from new ice nucleation parameterizations applied in a cloud parcel model. Measurements of ice crystal number concentrations were found to be in good agreement both with measured number concentrations of ice nuclei feeding the clouds and with ice nuclei number concentrations determined from the residual nuclei of cloud particles collected by a counterflow virtual impactor. Using lognormal distributions fitted to measured aerosol size distributions and measured aerosol chemical compositions, ice nuclei and ice crystal concentrations in the wave cloud were reasonably well predicted in a 1D parcel model framework. Two different empirical parameterizations were used in the parcel model: a parameterization based on aerosol chemical type and surface area and a parameterization that links ice nuclei number concentrations to the number concentrations of particles with diameters larger than 0.5 μm. This study shows that aerosol size distribution and composition measurements can be used to constrain ice initiation by primary nucleation in models. The data and model results also suggest the likelihood that the dust particle mode of the aerosol size distribution controls the number concentrations of the heterogeneous ice nuclei, at least for the lower temperatures examined in this case

3-D Seismic Interpretation and Volumetric Estimation of “Osaja Field” Niger Delta, Nigeria

3-D seismic interpretation and petrophysical analysis of the Osaja Field, Niger Delta, was carried out with aim of carrying out a detailed structural interpretation, reservoir characterization and volumetric estimation of the field. Four wells were correlated across the field to delineate the lithology and establish the continuity of reservoir sand as well as the general stratigraphy of the area. The petrophysical analysis carried out, revealed two sand units that are hydrocarbon bearing reservoirs (Sand_A and Sand_B).The spatial variation of the reservoirs were studied on a field wide scale using seismic interpretation. Time and depth structural maps generated were used to establish the structural architecture/geometry of the prospect area of the field. The depth structure map revealed NE-SW trending anticlinal structures with F5 and F6 as faults assisted closures to the reservoir. Furthermore, reservoir parameters such as net pay, water saturation porosity, net-to-gross etc, were derived from the integration of seismic and well log data. The structural interpretation on the 3-D seismic data of the study area revealed a total of seven faults ranging from synthetic to antithetic faults. The petrophysical analysis gave the porosity values of the reservoir Sand_A ranging from 18.1 - 20.3% and reservoir Sand_B ranging from 13.1-14.9% across the reservoir. The permeability values of reservoir Sand_A ranging from 63-540md and reservoir Sand_B ranging from 18-80md hence there is decrease in porosity and permeability of the field with depth.The net-to-gross varies from 22.1% to 22.4% in Rerservoir Sand A to between 5.34- 12% for Rerservoir Sand _A while Sw values for the reservoirs ranges from 38-42% in well 2 to about 68.79-96.06% in well 11. The result of original oil in place for all the wells calculated revealed that well 2 has the highest value with 9.3mmbls. These results indicate that the reservoirs under consideration have a poor to fair hydrocarbon (oil) prospect

Fold Lens Flux Anomalies: A Geometric Approach

We develop a new approach for studying flux anomalies in quadruply-imaged fold lens systems. We show that in the absence of substructure, microlensing, or differential absorption, the expected flux ratios of a fold pair can be tightly constrained using only geometric arguments. We apply this technique to 11 known quadruple lens systems in the radio and infrared, and compare our estimates to the Monte Carlo based results of Keeton, Gaudi, and Petters. We show that a robust estimate for a flux ratio from a smoothly varying potential can be found, and at long wavelengths those lenses deviating from from this ratio almost certainly contain significant substructure.Comment: 16 pages, including 8 figure