## A robust and efficient method for calculating the magnification of extended sources caused by gravitational lenses
^{1} Institut für Physik, Universität Dortmund,
D-44221 Dortmund, Germany^{2} Space Telescope Science Institute, 3700 San Martin Drive,
Baltimore, MD 21218, USA
To determine the magnification of an extended source caused by gravitational lensing one has to perform a two-dimensional integral over point-source magnifications in general. Since the point-source magnification jumps to an infinite value on caustics, special care is required. For a uniformly bright source, it has been shown earlier that the calculation simplifies if one determines the magnification from the area of the images of the extended source by applying Green's theorem so that one ends up with a one-dimensional integration over the image boundaries. This approach is discussed here in detail, and it is shown that it can be used to yield a robust and efficient method also for limb-darkened sources. It is also shown that the centroid shift can be calculated in a similar way.
* Work carried out at the Space Telescope Science Institute is financed by a research grant from Deutsche Forschungsgemeinschaft ## Contents- 1. Introduction
- 2. Magnification and Green's theorem
- 3. Uniformly bright sources
- 4. Limb-darkened sources
- 5. The centroid shift
- Acknowledgements
- References
© European Southern Observatory (ESO) 1998 Online publication: April 28, 1998 |