## Abstract

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: 〈μ_{4}〉 = 3.6/[γ(1-γ^{2})], 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.

Original language | English (US) |
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Pages (from-to) | 51-56 |

Number of pages | 6 |

Journal | Astrophysical Journal |

Volume | 577 |

Issue number | 1 I |

DOIs | |

State | Published - Sep 20 2002 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics
- Space and Planetary Science

## Keywords

- Gravitational lensing
- Methods: analytical