Separating inner and outer contributions in gravitational lenses with the perturbative method

Context. This paper presents a reconstruction of the gravitational lens SL2S02176-0513 with the singular perturbative method presented in Alard (2007, MNRAS, 382, L58) and Alard (2008, MNRAS, 388, 375). Aims. The ability of the perturbative method to separate the inner and outer contributions of the potential in gravitational lenses is tested using SL2S02176-0513. The gravitational field of the central galaxy is dominated by a nearby group of galaxies located at a distance of a few critical radius in this lens. Methods. The perturbative functionals are re-constructed using local polynomials. The polynomial interpolation is smoothed by Fourier series, and numerically fitted to the Hubble Space Telescope data with a non linear minimization procedure. The potential inside and outside the critical circle is derived from the reconstruction of the perturbative fields. Results. 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. Conclusions. 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 to study the shape of dark matter halos and for the statistical analysis of the effect of dark matter substructures.