Reconstructing the cosmic Horseshoe gravitational lens using the singular perturbative approach

TL;DR

This paper applies a perturbative Fourier series approach to reconstruct the gravitational lens of the cosmic Horseshoe, demonstrating that higher-order terms improve the model's fit and detail recovery without relying on prior assumptions.

Contribution

The study introduces a third-order perturbative expansion method for gravitational lens reconstruction, enhancing detail recovery over previous first- and second-order models.

Findings

Third-order expansion significantly improves fit quality.

Higher orders beyond three do not substantially enhance results.

Perturbative approach recovers lens potential details independently.

Abstract

The cosmic horseshoe gravitational lens is analyzed using the perturbative approach. The two first order perturbative fields are expanded in Fourier series. The source is reconstructed using a fine adaptive grid. The expansion of the fields at order 2 produces a higher value of the chi-square. Expanding at order 3 provides a very significant improvement, while order 4 does not bring a significant improvement over order 3. The presence of the order 3 terms is not a consequence of limiting the perturbative expansion to the first order. The amplitude and signs of the third order terms are recovered by including the contribution of the other group members. This analysis demonstrates that the fine details of the potential of the lens could be recovered independently of any assumptions by using the perturbative approach.