The two-screen gravitational lens

Gravitational lensing by systems of two galaxy-like potentials located at different redshifts and separations are studied. We show that there is roughly a 1–10 per cent chance of a gravitational lens system being affected by two lenses at the same redshift, and that there is roughly a 1–10 per cent chance of a gravitational lens system being affected by two lenses at different redshifts. We show that two lenses interact significantly for transverse separations | 4r+, ₀| where |r+, ₀| is the radius of the outer critical line of the singular potential. Nearly aligned lenses at different redshifts show interactions over almost all of redshift space. The interactions can lead to either increases or decreases in the total cross-section relative to the cross-section of two isolated lenses depending on the system's geometry, and the amplification of the brightest images. The behaviour of the image structures is dominated by the effects of caustics, and in particular the fold caustics, as in the single screen case. Typical image separations are | 2r+, ₀| as in the isolated lenses; larger separations are found only as the distance between the most widely separated images in the lens, in which case the separations approach | 4r+, ₀|⁠. This means that ‘chaining’ marginal lenses together cannot explain the so called dark matter lenses 2345 + 007, 1635 + 267 and 0023 + 171 for which there are only two widely separated images. Highly amplified images are almost always part of a high image multiplicity system (five or seven images rather than three images). This implies that amplification bias is associated with high image multiplicities.