The Ray Bundle method for calculating weak magnification by gravitational lenses

We present here an alternative method for calculating magnifications in gravitational lensing calculations -- the Ray Bundle method. We provide a detailed comparison between the distribution of magnifications obtained compared with analytic results and conventional ray-shooting methods. The Ray Bundle method provides high accuracy in the weak lensing limit, and is computationally much faster than (non-hierarchical) ray shooting methods to a comparable accuracy. The Ray Bundle method is a powerful and efficient technique with which to study gravitational lensing within realistic cosmological models, particularly in the weak lensing limit.Comment: 9 pages Latex, 8 figures, submitted to MNRA

A kinematical approach to gravitational lensing using new formulae for refractive index and acceleration

This paper uses the Schwarzschild metric to derive an effective refractive index and acceleration vector that account for relativistic deflection of light rays, in an otherwise classical kinematic framework. The new refractive index and the known path equation are integrated to give accurate results for travel time and deflection angle, respectively. A new formula for coordinate acceleration is derived which describes the path of a massless test particle in the vicinity of a spherically symmetric mass density distribution. A standard ray-shooting technique is used to compare the deflection angle and time delay predicted by this new formula with the previously calculated values, and with standard first order approximations. Finally, the ray shooting method is used in theoretical examples of strong and weak lensing, reproducing known observer-plane caustic patterns for multiple masses.Comment: 11 pages, 7 figures, MNRAS accepte

Teraflop per second gravitational lensing ray-shooting using graphics processing units

Gravitational lensing calculation using a direct inverse ray-shooting approach is a computationally expensive way to determine magnification maps, caustic patterns, and light-curves (e.g. as a function of source profile and size). However, as an easily parallelisable calculation, gravitational ray-shooting can be accelerated using programmable graphics processing units (GPUs). We present our implementation of inverse ray-shooting for the NVIDIA G80 generation of graphics processors using the NVIDIA Compute Unified Device Architecture (CUDA) software development kit. We also extend our code to multiple-GPU systems, including a 4-GPU NVIDIA S1070 Tesla unit. We achieve sustained processing performance of 182 Gflop/s on a single GPU, and 1.28 Tflop/s using the Tesla unit. We demonstrate that billion-lens microlensing simulations can be run on a single computer with a Tesla unit in timescales of order a day without the use of a hierarchical tree code.Comment: 21 pages, 4 figures, submitted to New Astronom

Microlensing with advanced contour integration algorithm: Green's theorem to third order, error control, optimal sampling and limb darkening

Microlensing light curves are typically computed either by ray-shooting maps or by contour integration via Green's theorem. We present an improved version of the second method that includes a parabolic correction in Green's line integral. In addition, we present an accurate analytical estimate of the residual errors, which allows the implementation of an optimal strategy for the contour sampling. Finally, we give a prescription for dealing with limb-darkened sources reaching arbitrary accuracy. These optimizations lead to a substantial speed-up of contour integration codes along with a full mastery of the errors.Comment: 34 pages, 11 figure

Application of the Contouring Method to Extended Microlensed Sources

The method devised by Lewis et al. (1993) for calculating the light curve of a microlensed point source is expanded to two dimensions to enable the calculation of light curves of extended sources. This method is significantly faster than the ray shooting method that has been used in the past. The increased efficiency is used to obtain much higher resolution light curves over increased timescales. We investigate the signatures arising from different source geometries in a realistic microlensing model. We show that a large fraction of high magnification events (HMEs) in image A of Q2237+0305 involve only one caustic, and could therefore yield information on the structure of the quasar continuum through the recognition of a characteristic event shape. In addition, the cataloguing of HMEs into morphological type will, in theory, enable the direction of the transverse motion, as well as the source size to be obtained from long term monitoring.Comment: 10 pages including 4 figures. Accepted for publication in M.N.R.A.