Estimation of halo ellipticity using spin-3 flexion

TL;DR

This paper demonstrates that spin-3 gravitational flexion can effectively estimate dark matter halo ellipticity, providing a new method that also helps identify halo centers, with implications for understanding galaxy formation and dark matter.

Contribution

It introduces a formalism to decompose spin-3 flexion fields and shows how their ratio estimates halo ellipticity, highlighting the impact of centroid offsets.

Findings

Spin-3 flexion ratio estimates halo ellipticity.

Centroid offsets bias ellipticity estimates but help locate halo centers.

Formalism for decomposing arbitrary spin fields into radial and tangential components.

Abstract

Estimating the ellipticity of dark matter haloes at the galaxy or galaxy-cluster scale can provide important constraints on the formation of galaxies or clusters, as well as on the nature of dark matter. We show in this paper that the spin-3 gravitational flexion can add useful information on the ellipticity of lensing haloes. We introduce a general formalism to decompose fields with arbitrary spin into radial and tangential components. The ratio of the tangential and radial flexion components directly estimates the lens ellipticity. We point out that any centroid offset will significantly bias our estimate, which on the other hand can be used to determine the centre of the lens halo.