NEW DEVELOPMENTS ON INVERSE POLYGON MAPPING TO CALCULATE GRAVITATIONAL LENSING MAGNIFICATION MAPS: OPTIMIZED COMPUTATIONS
- Instituto de Astrofisica de Canarias, Via Lactea S/N, 38200 La Laguna, Tenerife (Spain)
- Departamento de Estadistica e Investigacion Operativa, Universidad de Cadiz, Avda Ramon Puyol s/n, 11202, Algeciras, Cadiz (Spain)
- Departamento de Astronomia y Astrofisica, Universidad de Valencia, 46100 Burjassot, Valencia (Spain)
- Escuela Superior de Informatica, Universidad de Castilla-La Mancha, Paseo de La Universidad 4, 13071 Ciudad Real (Spain)
- Dpto. de Fisica Teorica y del Cosmos, Campus de Fuentenueva, Universidad de Granada, 18071 Granada (Spain)
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 previously reported N {sup -3/4} dependence of the IRS error with the number of collected rays per pixel. Cells intersected by critical curves (critical cells) transform to non-simply connected regions with topological pathologies like auto-overlapping or non-preservation of the boundary under the transformation. To define a non-critical partition, we use a linear approximation of the critical curve to divide each critical cell into two non-critical subcells. The optimal choice of the cell size depends basically on the curvature of the critical curves. For typical applications in which the pixel of the magnification map is a small fraction of the Einstein radius, a one-to-one relationship between the cell and pixel sizes in the absence of lensing guarantees both the consistence of the method and a very high accuracy. This prescription is simple but very conservative. We show that substantially larger cells can be used to obtain magnification maps with huge savings in computation time.
- OSTI ID:
- 21612756
- Journal Information:
- Astrophysical Journal, Vol. 741, Issue 1; Other Information: DOI: 10.1088/0004-637X/741/1/42; Country of input: International Atomic Energy Agency (IAEA); ISSN 0004-637X
- Country of Publication:
- United States
- Language:
- English
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