Three-point intrinsic alignments of galaxies and haloes in the FLAMINGO simulations

Abstract: Third-order statistics provide information beyond two-point measures, but extracting this information requires accurate and consistent modelling. We measure and detect the three-point correlation function and third-order aperture-mass statistics of intrinsic alignments (IA) for galaxies and for haloes with $M_{\rm halo} > 10^{13}\,{\rm M}_\odot$ in the $(2.8\,\mathrm{Gpc})^3$ simulation volume of the FLAMINGO hydrodynamical simulation suite. We model the third-order aperture-mass statistics and show that on large scales both the galaxy and halo samples are well described by the tree-level effective field theory (EFT) of IA across the three dark matter density-shape combinations and a wide range of triangle configurations, with the alignment amplitude consistent with that inferred from two-point statistics. We compare the full EFT to several other models: a version neglecting the velocity-shear term, the non-linear alignment model (NLA), and to a reduced EFT assuming co-evolution relations that follow from the assumption that alignment is linear in Lagrangian space. The first two models yield biased constraints on the alignment amplitude, but the reduced EFT performs remarkably well, achieving a low reduced chi-squared and minimal bias. We examine the redshift and mass dependence of the higher-order bias parameters, finding that the linear Lagrangian bias assumption is approximately satisfied across the explored halo mass and redshift ranges for both galaxies and haloes, suggesting that the galaxies broadly follow the alignment properties of their host haloes. These co-evolution relations can be valuable for photometric shear surveys, where limited constraining power on IA parameters favours models with fewer free parameters.