TY - JOUR

T1 - The magnification invariant of simple galaxy lens models

AU - Dalal, N.

N1 - Funding Information:
The author would like to thank John Wavrik for discussions of elimination theory, Jeffrey Rabin and Roger Blandford for many helpful conversations, Kim Griest for encouragement, discussions, and for reading the manuscript, and the anonymous referee for numerous helpful comments and suggestions. This work was supported in part by the US DOE under grant DEFG0390ER 40546.

PY - 1998

Y1 - 1998

N2 - We demonstrate that for several of the gravitational lens models used to describe galaxies, there exists a quantity we dub the magnification invariant, equaling the sum of the signed magnifications of the images, that is a constant when the image multiplicity is a maximum. This invariant is independent of most of the model parameters, and it is independent of the source position as long as the source lies inside the caustic. It is not necessary to solve the lens equations in order to compute this invariant. For quadruple lenses, it is usually easy to assign image parities, and thus one can compute the sum of the signed fluxes, compare it with the magnification invariant of different models, and infer the model magnification factors of the images without fitting. We evaluate the invariant for simple galaxy models, apply it to known cases of quadruple lenses, and discuss implications for the ability of these lens models to reproduce observed image brightnesses.

AB - We demonstrate that for several of the gravitational lens models used to describe galaxies, there exists a quantity we dub the magnification invariant, equaling the sum of the signed magnifications of the images, that is a constant when the image multiplicity is a maximum. This invariant is independent of most of the model parameters, and it is independent of the source position as long as the source lies inside the caustic. It is not necessary to solve the lens equations in order to compute this invariant. For quadruple lenses, it is usually easy to assign image parities, and thus one can compute the sum of the signed fluxes, compare it with the magnification invariant of different models, and infer the model magnification factors of the images without fitting. We evaluate the invariant for simple galaxy models, apply it to known cases of quadruple lenses, and discuss implications for the ability of these lens models to reproduce observed image brightnesses.

KW - Galaxies: structure

KW - Gravitational lensing

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U2 - 10.1086/311761

DO - 10.1086/311761

M3 - Article

AN - SCOPUS:22444455960

SN - 0004-637X

VL - 509

SP - L13-L16

JO - Astrophysical Journal

JF - Astrophysical Journal

IS - 1 PART II

ER -