The magnification invariant of simple galaxy lens models

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.