Two-dimensional galaxy cluster shapes using lensing data: a simulated analysis

Context. Cluster morphology reflects assembly history and dynamical state. High-resolution weak lensing can reveal departures from spherical symmetry, but its ability to recover two-dimensional shapes remains less explored. Aims. We assess how reliably weak lensing recovers projected cluster morphology and its dependence on orientation and dynamical state. We also compare large-scale weak-lensing morphology with that traced by strong lensing near the cluster centre. Methods. We study three clusters at z=0.22 from The Three Hundred Project, representing relaxed, mildly disturbed and unrelaxed systems. For each, we consider three random projections and three along the principal axes of the mass tensor. For each projection, we generate 128 weak-lensing catalogues with a source density of 30 arcmin-2 and intrinsic ellipticity dispersion σ ε=0.3. We constrain mass and concentration from one-dimensional NFW and BMO fits, then recover ellipticity, position angle and centre using a two-dimensional elliptical NFW model. We also measure morphology from true convergence maps, Kaiser & Squires reconstructions and strong-lensing tangential critical lines. Results. Recovered parameters depend on orientation and dynamical state. The relaxed cluster has similar inner and large-scale shapes, whereas disturbed systems appear more elliptical centrally. Two-dimensional weak-lensing modelling recovers the projected mass orientation despite source sampling and shape noise. Kaiser & Squires reconstructions recover the position angle well but favour rounder mass distributions. Centroid offsets are larger in unrelaxed systems. Conclusions. Combining weak- and strong-lensing morphology probes cluster structure across physical scales and offers a promising way to investigate morphology and dynamical state.