Geometric deep learning for galaxy-halo connection: a case study for galaxy intrinsic alignments

ABSTRACT Forthcoming cosmological imaging surveys, such as the Rubin Observatory LSST, require large-scale simulations encompassing realistic galaxy populations for a variety of scientific applications. Of particular concern is the phenomenon of intrinsic alignments (IA), whereby galaxies orient themselves towards overdensities, potentially introducing significant systematic biases in weak gravitational lensing analyses if they are not properly modelled. Due to computational constraints, simulating the intricate details of galaxy formation and evolution relevant to IA across vast volumes is impractical. As an alternative, we propose a Deep Generative Model trained on the IllustrisTNG-100 simulation to sample 3D galaxy shapes and orientations along with correlated scalar features, conditioned on the tidal fields and halo mass. The architecture consists of a SO(3) $\times \mathbb {R}^n$ diffusion generative model, implemented with E(3) equivariant Graph Neural Networks that explicitly respect the Euclidean symmetries of our Universe. The generated and the true values for geometric quantities using two-point statistics are statistically consistent; e.g. Wasserstein-1 distances indicate per cent-level (or better) agreement in the 1D distributions of scalar quantities. Notably, our model demonstrates the ability to jointly model Euclidean-valued scalars (galaxy sizes, shapes, and colours) along with non-Euclidean valued SO(3) quantities (galaxy orientations) that are governed by highly complex galactic physics at non-linear scales.