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Second-order singular pertubative theory for gravitational lenses

Abstract : The extension of the singular perturbative approach to the second order is presented in this paper. The general expansion to the second order is derived. The second-order expansion is considered as a small correction to the first-order expansion. Using this approach, it is demonstrated that in practice the second-order expansion is reducible to a first order expansion via a re-definition of the first-order pertubative fields. Even if in usual applications the second-order correction is small the reducibility of the second-order expansion to the first-order expansion indicates a potential degeneracy issue. In general, this degeneracy is hard to break. A useful and simple second-order approximation is the thin source approximation, which offers a direct estimation of the correction. The practical application of the corrections derived in this paper is illustrated by using an elliptical NFW lens model. The second-order pertubative expansion provides a noticeable improvement, even for the simplest case of thin source approximation. To conclude, it is clear that for accurate modelization of gravitational lenses using the perturbative method the second-order perturbative expansion should be considered. In particular, an evaluation of the degeneracy due to the second-order term should be performed, for which the thin source approximation is particularly useful.
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https://hal-insu.archives-ouvertes.fr/insu-03747709
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Submitted on : Monday, August 8, 2022 - 4:09:46 PM
Last modification on : Thursday, November 24, 2022 - 5:02:58 PM
Long-term archiving on: : Wednesday, November 9, 2022 - 6:51:55 PM

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C. Alard. Second-order singular pertubative theory for gravitational lenses. Monthly Notices of the Royal Astronomical Society, 2018, 475, pp.244-247. ⟨10.1093/mnras/stx3172⟩. ⟨insu-03747709⟩

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