Strong Lensing by Binary Galaxies Modelled as Isothermal Spheres
  We study the problem of gravitational lensing by binary galaxies, idealized as two isothermal spheres. In a wide binary, each galaxy possesses individual tangential, nearly astroidal, caustics and roundish radial caustics. As the separation of the binary is made smaller, the caustics undergo a sequence of metamorphoses. The first metamorphosis occurs when the tangential caustics merge to form a single six-cusped caustic, lying interior to the radial caustics. At still smaller separations, the six-cusped caustic undergoes the second metamorphosis and splits into a four-cusped caustic and two three-cusped caustics, which shrink to zero size (an elliptic umbilic catastrophe) before they enlarge again and move away from the origin perpendicular to the binary axis. Finally, a third metamorphosis occurs as the three-cusp caustics join the radial caustics, leaving an inner distorted astroid caustic enclosed by two outer caustics. The maximum number of images possible is 7. Classifying the multiple imaging according to critical isochrones, there are only 8 possibilities: 2 three-image cases, 3 five-image cases, and 3 seven-image cases. When the isothermal spheres are singular, the core images vanish into the central singularity. The number of images may then be 1, 2, 3, 4 or 5, depending on the source location, and the separation and masses of the pair of lensing galaxies. The locations of metamorphoses, and the onset of threefold and fivefold multiple imaging, can be worked out analytically in this case. 
E.M. Shin (Cambridge), N.W. Evans (Cambridge)