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Analytic expressions for mean magnification by a quadrupole gravitational lens

Tehani K. Finch·Lisa P. Carlivati·Joshua N. Winn·Paul L. Schechter
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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 2-image and 4-image lensing. For 4-image lensing, the mean magnification takes a particularly simple form: _4 = 3.6/(gamma*(1-gamma^2)), where gamma is the external shear. We compare our analytic results to 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.

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Tehani K. Finch, Lisa P. Carlivati, Joshua N. Winn, Paul L. Schechter. 2002-05-28. Analytic expressions for mean magnification by a quadrupole gravitational lens. https://doi.org/10.1086/342163

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