Perturbative signature of substructures in strong gravitational lenses

Abstract

In the perturbative approach, substructures in the lens can be reduced to their effect on the two perturbative fields f1 and df 0/dθ. A simple generic model of an elliptical lens with a substructure situated near the critical radius is investigated in detail. Analytical expressions are derived for each perturbative field, and basic properties are analysed. The power spectrum of the fields is well approximated by a power law, resulting in significant tails at high frequencies. Another feature of the perturbation by a substructure is that the ratio of the power spectrum at order n of the two fields Rn is almost one. The ratio Rn ≃ 1 is specific to substructures, for instance a higher order distortion (n > 2) but with autosimilar isophotes will result in Rn ∝ 1/n2. Finally, the problem of reconstructing the perturbative field is investigated. Local field models are implemented and fitted to maximize image similarity in the source plane. The non-linear optimization is greatly facilitated, since in the perturbative approach the circular source solution is always known. Examples of image distortions in the subcritical regime due to substructures are presented, and analysed for different source shapes. Provided enough images and signal are available, the substructure field can be identified confidently. These results suggest that the perturbative method is an efficient tool to estimate the contribution of substructures to the mass distribution of lenses. © 2008 The Authors. Journal compilation © 2008 RAS.