0000000000011811
AUTHOR
T. Mediavilla
RESOLVING THE INNERMOST REGION OF THE ACCRETION DISK OF THE LENSED QUASAR Q2237+0305 THROUGH GRAVITATIONAL MICROLENSING
We study three high magnification microlensing events, generally recognized as probable caustic crossings, in the optical light curves of the multiply imaged quasar Q 2237+0305. We model the light curve of each event as the convolution of a standard thin disk luminosity profile with a straight fold caustic. We also allow for a linear gradient that can account for an additional varying background effect of microlensing. This model not only matches noticeably well the global shape of each of the three independent microlensing events but also gives remarkably similar estimates for the disk size parameter. The measured average half-light radius, $R_{1/2}=(3.0\pm 1.5)\sqrt{M/0.3M\odot}$ light-da…
Some topological properties of the Inverse Lens Mapping
Away from critical curves, lens mapping can be seen as a linear invertible transformation of the plane even for regions (cells) of relatively large size. However, close to critical curves the departures from linearity can be very strong. We discuss the topological problems induced by the mapping of regions of the image plane that include critical curves (critical cells).
Statistics of Microlensing Caustic Crossings in Q~2237+0305: Peculiar Velocity of the Lens Galaxy and Accretion Disk Size
We use the statistics of caustic crossings induced by microlensing in the lens system Q~2237+0305 to study the lens galaxy peculiar velocity. We calculate the caustic crossing rates for a comprehensive family of stellar mass functions and find a dependence of the average number of caustic crossings with the effective transverse velocity and the average mass, $\langle n \rangle \propto {v_{eff} / \sqrt{\langle m \rangle}}$, equivalent to the theoretical prediction for the case of microlenses with identical masses. We explore the possibilities of the method to measure $v_{eff}$ using the $\sim$12 years of OGLE monitoring of the four images of Q 2237+0305. To determine a lower limit for $v_{ef…
NEW DEVELOPMENTS ON INVERSE POLYGON MAPPING TO CALCULATE GRAVITATIONAL LENSING MAGNIFICATION MAPS: OPTIMIZED COMPUTATIONS
We derive an exact solution (in the form of a series expansion) to compute gravitational lensing magnification maps. It is based on the backward gravitational lens mapping of a partition of the image plane in polygonal cells (inverse polygon mapping, IPM), not including critical points (except perhaps at the cell boundaries). The zeroth-order term of the series expansion leads to the method described by Mediavilla et al. The first-order term is used to study the error induced by the truncation of the series at zeroth order, explaining the high accuracy of the IPM even at this low order of approximation. Interpreting the Inverse Ray Shooting (IRS) method in terms of IPM, we explain the previ…
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 pi…
Studying the microlenses mass function from statistical analysis of the caustic concentration
The statistical distribution of caustic crossings by the images of a lensed quasar depends on the properties of the distribution of microlenses in the lens galaxy. We use a procedure based in Inverse Polygon Mapping to easily identify the critical and caustic curves generated by a distribution of stars in the lens galaxy. We analyze the statistical distributions of the number of caustic crossings by a pixel size source for several projected mass densities and different mass distributions. We compare the results of simulations with theoretical binomial distributions. Finally we apply this method to the study of the stellar mass distribution in the lens galaxy of QSO 2237+0305.