We derive an analytic expression for the mean magnification due to strong gravitational lensing, using a simple lens model: a singular isothermal sphere embedded in an external shear field. We compute separate expressions for two-image and four-image lensing. For four-image lensing, the mean magnification takes a particularly simple form: 〈μ4〉 = 3.6/[γ(1-γ2)], where γ is the external shear. We compare our analytic results with a numerical evaluation of the full magnification distribution. The results can be used to understand the magnification bias that favors the discovery of four-image systems over two-image systems in flux-limited lens surveys.
All Science Journal Classification (ASJC) codes
- Astronomy and Astrophysics
- Space and Planetary Science
- Gravitational lensing
- Methods: analytical