SHAPE: cosmology with cluster halo intrinsic alignments from subhalo distributions

Galaxy clusters trace the most massive dark matter haloes, whose shapes and orientations reflect the imprint of the cosmic large-scale tidal field. This paper introduces the Subhalo-based Halo Alignment and Projected Ellipticity (SHAPE) technique, which reconstructs cluster halo shapes from the projected distribution of subhaloes, providing a novel approach to investigate intrinsic alignment (IA) correlations between cluster halo shapes and the surrounding density field. We measure halo shapes and orientations using different line-of-sight projection depths and find that, with modest projection depths, the shapes and orientations recovered by SHAPE show good agreement with those measured directly from the simulation particles. Using these SHAPE-derived shapes, we compute IA correlation functions from N-body simulations in both real and redshift space. The IA correlation multipoles exhibit features consistent with baryon acoustic oscillations around 100 Mpc/h and show redshift-space distortion (RSD) effects that agree well with predictions from a non-linear alignment model incorporating RSD. We further demonstrate that the structure growth rate parameter can be robustly estimated without bias from these IA correlations, providing a new avenue for cosmological parameter estimation. Expanding the IA correlations in an associated Legendre basis yields results consistent with those from the standard Legendre expansion, but with improved statistical significance. These results suggest that SHAPE may enhance cosmological parameter constraints in future galaxy surveys.