Substructure and the Cusp and Fold Relations

Abstract

Gravitational lensing of a background source by a foreground galaxy lens occasionally produces four images of the source. The cusp and the fold relations impose conditions on the ratios of magnifications of these four-image lenses. In this theoretical investigation, we explore the sensitivity of these relations to the presence of substructure in the lens. Starting with a smooth lens potential, we add varying amounts of substructure, while keeping the source position fixed, and find that the fold relation is a more robust indicator of substructure than the cusp relation for the images. This robustness is independent of the detailed spatial distribution of the substructure, as well as of the ellipticity of the lensing potential and the presence of external shear.

7 pages, 5 figures, submitted to MNRAS

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Cited by in corpus (7)

• Measuring Dark Matter Substructure with Galaxy-Galaxy Flexion Statistics
• Gravitational Lenses as High-Resolution Telescopes
• A Systematic Review of Strong Gravitational Lens Modeling Software
• Magnification relations of quad lenses and applications on Einstein crosses
• Galaxies as High-Resolution Telescopes
• Analytical Solutions of Singular Isothermal Quadrupole Lens
• Cusp Summations and Cusp Relations of Simple Quad Lenses