The H₂ angular momentum – mass relation of local disc galaxies

We present an analysis of the molecular specific angular momentum–mass ( j H 2 − M H 2 ) relation using a sample of 51 nearby disc galaxies from the PHANGS-ALMA survey with deep high-resolution molecular gas rotation curves and surface density profiles. For the very first time, using a statistical sample, we report the discovery of a well-defined j H 2 − M H 2 relation. We quantify the scaling law by fitting a power law with a Bayesian framework, finding j H 2 ∝ M H 2 0.53 . This slope closely resembles the well-known stellar j * – M * (Fall) relation, highlighting the dynamical connection between molecular gas and stars. We show that the j H 2 − M H 2 relation cannot be fully explained by analytic models of disc stability, but instead is well recovered with more complex physics as implemented in the S HARK semi-analytical model. These findings demonstrate the power of our novel j H 2 − M H 2 relation in testing galaxy evolution theories and in setting new constraints for models and simulations that reproduce a realistic interstellar medium. Additionally, our findings provide a critical benchmark for upcoming high-redshift studies of molecular gas kinematics, offering a local baseline to study the evolution of cold gas dynamics across cosmic time.