Math @ Duke

Publications [#243984] of Arlie O. Petters
Papers Published
 Aazami, AB; Petters, AO, A universal magnification theorem for higherorder caustic singularities,
Journal of Mathematical Physics, vol. 50 no. 3
(Spring, 2009),
pp. 032501, ISSN 00222488 [3447], [doi]
(last updated on 2018/05/25)
Abstract: We prove that, independent of the choice of a lens model, the total signed magnification always sums to zero for a source anywhere in the fourimage region close to swallowtail, elliptic umbilic, and hyperbolic umbilic caustics. This is a more global and higherorder analog of the wellknown fold and cusp magnification relations, in which the total signed magnifications in the twoimage region of the fold and the threeimage region of the cusp are both always zero. As an application, we construct a lensing observable for the hyperbolic umbilic magnification relation and compare it with the corresponding observables for the cusp and fold relations using a singular isothermal ellipsoid lens. We demonstrate the greater generality of the hyperbolic umbilic magnification relation by showing how it applies to the fold image doublets and cusp image triplets and extends to image configurations that are neither. We show that the results are applicable to the study of substructure on galactic scales using observed quadruple images of lensed quasars. The magnification relations are also proven for generic oneparameter families of mappings between planes, extending their potential range of applicability beyond lensing. © 2009 American Institute of Physics.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

