Separating inner and outer contributions in gravitational lenses using
  the perturbative method
  This paper presents a reconstruction of the gravitational lens SL2S02176-0513
using the singular perturbative method presented in Alard 2007, MNRAS Letters,
382, 58 and Alard, C., 2008, MNRAS, 388, 375. The ability of the perturbative
method to separate the inner and outer contributions of the potential in
gravitational lenses is tested using SL2S02176-0513. In this lens, the
gravitational field of the central galaxy is dominated by a nearby group of
galaxies located at a distance of a few critical radius. The perturbative
functionals are re-constructed using local polynomials. The polynomial
interpolation is smoothed using Fourier series, and numerically fitted to HST
data using a non-linear minimization procedure. The potential inside and
outside the critical circle is derived from the reconstruction of the
perturbative fields. The inner and outer potential contours are very
different.The inner contours are consistent with the central galaxy, while the
outer contours are fully consistent with the perturbation introduced by the
group of galaxies. The ability of the perturbative method to separate the inner
and outer contribution is confirmed, and indicates that in the perturbative
approach the field of the central deflector can be separated from outer
perturbations. The separation of the inner and outer contribution is especially
important for the study of the shape of dark matter halo's as well as for the
statistical analysis of the effect of dark matter substructures.
