The effect of satellite galaxies on gravitational lensing flux ratios

Gravitational lenses with anomalous flux ratios are often cited as possible evidence for dark matter satellites predicted by simulations of hierarchical merging in cold dark matter cosmogonies. We show that the fraction of quads with anomalous flux ratios depends primarily on the total mass and spatial extent of the satellites, and the characteristic length-scale d(1/2) of their distribution. If d(1/2) similar to 100 kpc, then for a moderately elliptical galaxy with a line-of-sight velocity dispersion of similar to 250 km s(-1), a mass of similar to 3 x 10(9) M-circle dot in highly concentrated (Plummer model) satellites is needed for 20 per cent of quadruplets to show anomalous flux ratios, rising to similar to 1.25 x 10(10) M-circle dot for 50 per cent. Several times these masses are required if the satellites have more extended Hernquist profiles. Compared to a typical elliptical, the flux ratios of quads formed by typical edge-on disc galaxies with maximum discs are significantly less susceptible to changes through substructure - three times the mass in satellite galaxies is needed to affect 50 per cent of the systems. In many of the lens systems with anomalous flux ratios, there is evidence for visible satellites (e.g. B2045+265 or MG0414+0534). We show that if the anomaly is produced by substructure with properties similar to the simulations, then optically identified substructure should not be preponderant among lens systems with anomalies. There seem to be two possible resolutions of this difficulty. First, in some cases, visible substructure may be projected within or close to the Einstein radius and wrongly ascribed as the culprit, whereas dark matter substructure is causing the flux anomaly. Secondly, bright satellites, in which baryon cooling and condensation have taken place, may have higher central densities than dark satellites, rendering them more efficient at causing flux anomalies.