Ray-shooting Technique Research Articles

Gravitational microlensing of active galactic nuclei dusty tori

We investigated the gravitational microlensing of active galactic nucleus dusty tori in the case of lensed quasars in the infrared domain. The dusty torus is modeled as a clumpy two-phase medium. To obtain spectral energy distributions and images of tori at different wavelengths, we used the 3D Monte Carlo radiative transfer code SKIRT. A ray-shooting technique has been used to calculate microlensing magnification maps. We simulated microlensing by the stars in the lens galaxy for different configurations of the lensed system and different values of the torus parameters, in order to estimate (a) amplitudes and timescales of high magnification events, and (b) the influence of geometrical and physical properties of dusty tori on light curves in the infrared domain. We found that, despite their large size, dusty tori could be significantly affected by microlensing in some cases, especially in the near-infrared domain (rest-frame). The very long time-scales of such events, in the range from several decades to hundreds of years, are limiting the practical use of this method to study the properties of dusty tori. However, our results indicate that, when studying flux ratios between the images in different wavebands of lensed quasars, one should not disregard the possibility that the near and mid-infrared flux ratios could be under the influence of microlensing.

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.

Detectability of extrasolar moons as gravitational microlenses

We evaluate gravitational lensing as a technique for the detection of extrasolar moons. Since 2004 gravitational microlensing has been successfully applied as a detection method for extrasolar planets. In principle, the method is sensitive to masses as low as an Earth mass or even a fraction of it. Hence it seems natural to investigate the microlensing effects of moons around extrasolar planets. We explore the simplest conceivable triple lens system, containing one star, one planet and one moon. From a microlensing point of view, this system can be modelled as a particular triple with hierarchical mass ratios very different from unity. Since the moon orbits the planet, the planet-moon separation will be small compared to the distance between planet and star. Such a configuration can lead to a complex interference of caustics. We present detectability and detection limits by comparing triple-lens light curves to best-fit binary light curves as caused by a double-lens system consisting of host star and planet -- without moon. We simulate magnification patterns covering a range of mass and separation values using the inverse ray shooting technique. These patterns are processed by analysing a large number of light curves and fitting a binary case to each of them. A chi-squared criterion is used to quantify the detectability of the moon in a number of selected triple-lens scenarios. The results of our simulations indicate that it is feasible to discover extrasolar moons via gravitational microlensing through frequent and highly precise monitoring of anomalous Galactic microlensing events with dwarf source stars.

Microlensing variability in the gravitationally lensed quasar QSO 2237+0305 $\mathsf{\equiv}$ the Einstein Cross

We present the continuation of our long-term spectroscopic monitoring of the gravitationally lensed quasar QSO 2237 + 0305. We investigate the chromatic variations observed in the UV/optical continuum of both quasar images A and B, and compare them with numerical simulations to infer the energy profile of the quasar accretion disk. Our procedure combines the microlensing ray-shooting technique with Bayesian analysis, and derives probability distributions for the source sizes as a function of wavelength. We find that the effective caustic crossing timescale is 4.0 +/- 1.0 months. Using a robust prior on the effective transverse velocity, we find that the source responsible for the UV/optical continuum has an energy profile well reproduced by a power-law R proportional to lambda(zeta) with zeta = 1.2 +/- 0.3, where R is the source size responsible for the emission at wavelength.. This is the first accurate, model-independent determination of the energy profile of a quasar accretion disk on such small scales.

A Fast and Very Accurate Approach to the Computation of Microlensing Magnification Patterns Based on Inverse Polygon Mapping

A new method of calculating microlensing magnification patterns is proposed that is based on the properties of the backward gravitational lens mapping of a lattice of polygonal cells defined at the image plane. To a first-order approximation, the local linearity of the transformation allows us to compute the contribution of each image-plane cell to the magnification by apportioning the area of the inverse image of the cell (transformed cell) among the source-plane pixels covered by it. Numerical studies in the κ = 0.1-0.8 range of mass surface densities demonstrate that this method (provided with an exact algorithm for distributing the area of the transformed cells among the source-plane pixels) is more efficient than the inverse ray-shooting technique (IRS). Magnification patterns with relative errors of ~5 × 10-4 are obtained with an image-plane lattice of only 1 ray per unlensed pixel. This accuracy is, in practice, beyond the reach of IRS performance (more than 10,000 rays should be collected per pixel to achieve this result with the IRS) and is obtained in a small fraction (less than 4%) of the computing time that is used by the IRS technique to achieve an error more than an order of magnitude larger. The computing time for the new method is reduced to below 1% of the IRS computing time when the same accuracy is required of both methods. We have also studied the second-order approximation to control departures from linearity that could induce variations in the magnification within the boundaries of a transformed cell. This approximation is used to identify and control the cells enclosing a critical curve.

Radial distribution and strong lensing statistics of satellite galaxies and substructure using high-resolution CDM hydrodynamical simulations

We analyse the number density and radial distribution of substructures and satellite galaxies using cosmological simulations that follow the gas dynamics of a baryonic component, including shock heating, radiative cooling and star formation within the hierarchical concordance Lambda cold dark matter model. We find that the dissipation of the baryons greatly enhances the survival of subhaloes, especially in the galaxy core, resulting in a radial distribution of satellite galaxies that closely follows the overall mass distribution. Hydrodynamical simulations are necessary to resolve the adiabatic contraction and dense cores of galaxies, resulting in a total number of satellites a factor of 2 larger than that found in pure dark matter simulation, in good agreement with the observed spatial distribution of satellite galaxies within galaxies and clusters. Convergence tests show that the cored distribution found by previous authors in pure N-body simulations was due to the physical overmerging of dark matter only structures. We proceed to use a ray-shooting technique in order to study the impact of these additional substructures on the number of violations of the cusp caustic magnification relation. We develop a new approach to try to disentangle the effect of substructures from the intrinsic discreteness of N-body simulations. Even with the increased number of substructures in the centres of galaxies, we are not able to reproduce the observed high numbers of discrepancies observed in the flux ratios of multiply lensed quasars.

Strong gravitational lensing and dynamical dark energy

We study the strong gravitational lensing properties of galaxy clusters obtained from N-body simulations with different kinds of dark energy (DE). We consider both dynamical DE, due to a scalar field self-interacting through Ratra–Peebles (RP) or supergravity (SUGRA) potentials, and DE with constant negative w=p/ρ=−1 (ΛCDM). We have 12 high-resolution lensing systems for each cosmological model with mass greater than 5.0 × 1014 h−1 M⊙. Using a ray shooting technique, we make a detailed analysis of the lensing properties of these clusters, paying particular attention to the number of arcs and their properties (magnification, length and width). We find that the number of giant arcs produced by galaxy clusters changes in a considerable way from ΛCDM models to dynamical dark energy models with an RP or SUGRA potential. These differences originate from the different epochs of cluster formation and from the non-linearity of the strong lensing effect. We suggest that strong lensing is one of the best tools to discriminate among different kinds of dark energy.

A Complete and Efficient Algorithm for Searching 3-D Form-Closure Grasps in the Discrete Domain

A complete and efficient algorithm is proposed for searching form-closure grasps of n hard fingers on the surface of a three-dimensional object represented by discrete points. Both frictional and frictionless cases are considered. This algorithm starts to search a form-closure grasp from a randomly selected grasp using an efficient local search procedure until encountering a local minimum. The local search procedure employs the powerful ray-shooting technique to search in the direction of reducing the distance between the convex hull corresponding to the grasp and the origin of the wrench space. When the distance reaches a local minimum in the local search procedure, the algorithm decomposes the problem into a few subproblems in subsets of the points according to the existence conditions of form-closure grasps. A search tree whose root represents the original problem is employed to perform the searching process. The subproblems are represented as children of the root node and the same procedure is recursively applied to the children. It is proved that the search tree generates O(KlnK/n) nodes in case a from-closure grasp exists, where K is the number of the local minimum points of the distance in the grasp space and n is the number of fingers. Compared to the exhaustive search, this algorithm is more efficient, and, compared to other heuristic algorithms, the proposed algorithm is complete in the discrete domain. The efficiency of this algorithm is demonstrated by numerical examples.