Unveiling the Angular Momentum of Dark Matter Halos with Motion of Satellite Galaxies

Dark matter halos are spun up by tidal torques originating from large-scale structures, resulting in an average spin parameter—a dimensionless measure of halo angular momentum—of approximately 0.04. Measurement of this angular momentum is crucial for validating the ΛCDM model and understanding the evolution of fundamental characteristics of the galaxy such as morphology and size. However, due to the invisible nature of dark matter, measuring the actual value angular momentum of dark halos is challenging. Here we report the first measurement for the value of angular momentum of dark matter haloes using a novel methodology. By stacking the orbital motions of satellite galaxies according to the projected rotation axes of their central galaxies, we calculate the projected orbital angular momentum of these satellites. This value is then converted into the intrinsic angular momentum of the dark matter halos using a conversion factor obtained from sophisticated hydrodynamical simulations. Applying this method to a selection of galaxy groups and clusters from the Sloan Digital Sky Survey (SDSS), we observe dark matter halo spins ranging between 0.0025 and 0.066 for halos with masses from [10 ^12.5 ,10 ¹⁴ ] M _⊙ . These results are in excellent agreement with the predictions from the widely accepted ΛCDM model, thus substantiating a fundamental aspect of the theory of structure formation.