The magnification invariant of simple galaxy lens models

Abstract

We demonstrate that for several of the gravitational lens models used to describe galaxies, there exists a quantity we dub the magnification invariant, equaling the sum of the signed magnifications of the images, that is a constant when the image multiplicity is a maximum. This invariant is independent of most of the model parameters, and is independent of the source position as long as the source lies inside the caustic. It is not necessary to solve the lens equations to compute this invariant. For quad lenses, it is usually easy to assign image parities and thus one can compute the sum of the signed fluxes, compare with the magnification invariant of different models, and infer the model magnification factors of the images without fitting. We evaluate the invariant for simple galaxy models, apply it to known cases of quadruple lenses, and discuss implications for the ability of these lens models to reproduce observed image brightnesses.

6 pages, Latex, submitted to ApJ Letters

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• Lensing Properties of Scale-Free Galaxies
• A Universal Magnification Theorem for Higher-Order Caustic Singularities
• Magnification relations in gravitational lensing via multidimensional residue integrals
• Lensed Image Angles: New Statistical Evidence for Substructure
• The Fundamental Surface of Quad Lenses
• Model-free analysis of quadruply imaged gravitationally lensed systems and substructured galaxies
• Euclidean Algorithm for a Gravitational Lens in a Polynomial Equation
• The Quadruple Image Configurations of Asymptotically Circular Gravitational Lenses
• Magnification relations of quad lenses and applications on Einstein crosses
• A Universal Magnification Theorem II. Generic Caustics up to Codimension Five
• Cusp Summations and Cusp Relations of Simple Quad Lenses
• Analytical Solutions of Singular Isothermal Quadrupole Lens
• The Magnification Invariant of Circularly-symmetric Lens Models