The effect of low-mass substructures on the cusp lensing relation

It has been argued that the flux anomalies detected in gravitationally lensed quasi-stellar objects (QSOs) are evidence for substructures in the foreground lensing haloes. In this paper, we investigate this issue in greater detail, focusing on the cusp relation which corresponds to images of a source located to the cusp of the inner caustic curve. We use numerical simulations combined with a Monte Carlo approach to study the effects of the expected power-law distribution of substructures within A cold dark matter (ACDM) haloes on the multiple images. Generally, the high number of anomalous flux ratios in the cusp configurations is unlikely to be explained by 'simple' perturbers (subhaloes) inside the lensing galaxy, modelled by either point masses or extended Navarro, Frenk & White subhaloes. We considered in our analysis a mass range of 10⁵-10⁷ M_⊙ for the subhaloes. We also demonstrate that including the effects of the surrounding mass distribution, such as other galaxies close to the primary lens, does not change the results. We conclude that triple images of lensed QSOs do not show any direct evidence for dark dwarf galaxies such as CDM substructure.