Analytic expressions for mean magnification by a quadrupole gravitational lens

Tehani K. Finch, Lisa P. Carlivati, Joshua N. Winn, Paul L. Schechter

Research output: Contribution to journalReview articlepeer-review

22 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)51-56
Number of pages6
JournalAstrophysical Journal
Issue number1 I
StatePublished - Sep 20 2002
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Gravitational lensing
  • Methods: analytical


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