G. Martin, N. A. Hatch, W. Cui, A. Fernandez, Y. M. Bahé, M. S. Fischer, M. Montes, F. R. Pearce, C. G. Sabiu, G. Yepes, J. Yoo

The intracluster light (ICL) has been proposed as a luminous tracer of the dark matter (DM) halo shape in galaxy clusters, with recent observational studies and $Λ$CDM simulations suggesting close alignment between the two components. We test whether this correspondence holds in a self-interacting dark matter (SIDM) cosmology using matched CDM and SIDM ($σ_\mathrm{DM}/m = 0.1$ and $0.5\;\mathrm{cm^{2}\,g^{-1}}$) hydrodynamical cluster simulations from TheThreeHundred project. We measure 3D axis ratios and major-axis orientations as a function of radius for both the DM halo and the stellar (BCG+ICL) distribution, and quantify the spatial correspondence using the Weighted Overlap Coefficient. In the SIDM simulations, DM haloes become significantly rounder in their inner regions with increasing DM cross-section, while the stellar distribution retains the same elongated morphology in both CDM and SIDM. This decoupling is robust across two baryonic physics models and two resolution levels, and is detected at $>5σ$ for $σ_\mathrm{DM}/m = 0.5\;\mathrm{cm^{2}\,g^{-1}}$. It arises because the stellar shape is governed by the accretion geometry of tidally stripped satellites along the large-scale structure, which is identical in CDM and SIDM, whereas, in SIDM, halo shapes respond additionally to local self-interactions. The ICL-DM shape correspondence demonstrated in CDM therefore breaks down in an SIDM universe.