Title: Cluster Galaxies as Probes of Environment and Halo Dynamics

Abstract: Galaxy cluster rotation offers a potential observational probe of dark-matter halo angular momentum and spin–orbit coherence (SOC), the connection between halo spin and the orbital motions of its member galaxies. In this talk, I will briefly review the theoretical and observational context of cluster rotation and SOC, and present recent results from my PhD research on recovering halo spin from galaxy kinematics.

We develop a probabilistic method that uses the projected positions and line-of-sight velocities of cluster galaxies, comparing the resulting velocity maps with DICE dynamical models. We validate the method using independent halos from the Uchuu simulation. The kinematic maps recover information about halo spin and, more robustly, its projected component. Performance is highest when selecting galaxies within Rvir, and improves systematically with the number of observed members and the significance of the rotational signal. Correlations reach (r~0.7) for the richest systems. The projected spin orientation can also be constrained when rotation is significant, whereas inclination remains strongly degenerate with spin amplitude. These results open a path toward observational studies of SOC, galaxy–halo alignments, and spin-dependent halo clustering—or halo spin bias—with broader applications to the galaxy–halo connection and cosmology.