Adaptive Reconstruction of Cluster Halos (ARCH): Integrating Shear and Flexion for Substructure Detection

We present ARCH (Adaptive Reconstruction of Cluster Halos), a new gravitational lensing pipeline for cluster mass reconstruction that applies a joint shear-flexion analysis to JWST imaging. Previous approaches have explored joint shear+flexion reconstructions through forward modeling and Bayesian inference frameworks; in contrast, ARCH adopts a staged optimization strategy that incrementally filters and selects candidate halos rather than requiring a global likelihood model or strong priors. This design makes reconstruction computationally tractable and flexible, enabling systematic tests of multiple signal combinations within a unified framework. ARCH employs staged candidate generation, local optimization, filtering, forward selection, and global strength refinement, with a combined fit metric weighted by per-signal uncertainties. Applies to Abell 2744 and El Gordo, the pipeline recovers convergence maps and subcluster masses consistent with published weak+strong lensing results. In Abell 2744 the central core mass within 300$h^{-1}$ kpc is $2.1\times {10}^{14}{M}_{\odot }{h}^{-1}$, while in El Gordo the northwestern and southeastern clumps are recovered at $2.6\times {10}^{14}{M}_{\odot }{h}^{-1}$ and $2.3\times {10}^{14}{M}_{\odot }{h}^{-1}$. Jackknife resampling indicates typical 1$\sigma$ uncertainties of ${10}^{12}-{10}^{13}{M}_{\odot }{h}^{-1}$, with the all signal and shear+$\mathcal{F}$ reconstructions providing the most stable results. These results demonstrate that flexion, when anchored by shear, enhances sensitivity to cluster substructure while maintaining stable cluster-scale mass recovery.