1999/06/20 by H. J. Witt, Hans J. Witt, Shude Mao · 39 citations
Engineering · Mathematics · Physics and Astronomy · #Classical mechanics #Distribution (mathematics) #Geometry #Magnification #Mathematical analysis #Mathematics #Moment (physics) #Optics #Phase Equilibria and Thermodynamics #Physics #Shear (geology) #astro-ph
paper · pdf · doi:10.1046/j.1365-8711.2000.03122.x
published in Monthly Notices of the Royal Astronomical Society 311(4), 689-697 (Oxford University Press) · 16 pages, 4 figures, submitted to MNRAS
arxiv created 1999/06/20 · openalex publication_date 2000/02/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present a new method of studying quadruple lenses in elliptical power-law potentials parametrized by ψ(x,y)∝(x2+y2q2)β/2β (). For this potential, the moments of the four image positions weighted by signed magnifications (magnification times parity) have very simple properties. In particular, we find that the zeroth moment—the sum of four signed magnifications satisfies ≃2/(2-β); the relation is exact for β=0 (point-lens) and β=1 (isothermal potential), independent of the axial ratio. Similar relations can be derived when a shear is present along the major or minor axes. These relations, however, do not hold well for the closely related elliptical density distributions. For a singular isothermal elliptical density distribution without shear, the sum of signed magnifications for quadruple lenses is ≈2.8, again nearly independent of the ellipticity. For the same distribution with shear, the total signed magnification is around 2–3 for most cases, but can be significantly different for some combinations of the axial ratio and shear where six or eight images can appear.