The Stellar Velocity Anisotropy of Strong Lensing Massive Elliptical Galaxies and Its Role in the Inference of the Hubble Parameter H ₀ Using Spatially Resolved Kinematics

One of the biggest challenges in cosmology, the Hubble tension, requires independent measurements of H 0 , and strong lensing with time-delay cosmography is a promising avenue. The inclusion of spatially resolved kinematic data helps break the mass–sheet degeneracy, a key limitation in strong lensing. Kinematics, however, suffers from its own degeneracy due to unknown stellar velocity anisotropy, which can bias galaxy mass profile inferences. We investigate the bias in H 0 using a sample of 10 massive elliptical galaxies at z = 0.2 from the Illustris TNG100 simulations. We generate mock line-of-sight velocity-dispersion maps resembling JWST NIRSpec observations and test four anisotropy models: Osipkov–Merritt (OM), Mamon–Łokas (ML), constant β , and a generalized–OM (gOM) profile, under both kinematics-only and joint kinematics plus strong lensing analyses. We find a subpercent average bias in H 0 across 10 galaxies with joint modeling for three models: +0.2% ± 1.6% (ML), −0.9% ± 1.9% (constant) and −0.9% ± 1.6% (gOM), with ∼5% scatter. Joint modeling reduces bias, improves precision, and mitigates outlier results. Overall, the gOM model best recovers galaxy parameters and delivers the most accurate H 0 relative to posterior uncertainties considering both analyses. However, the single-parameter OM model produces large systematic biases: with kinematics-only data, H 0 errors can exceed 20%, and even with joint modeling, it produces an overall bias of +11.5% ± 1.3% (OM). The higher bias in OM is thus unlikely to average out across an ensemble of galaxies. Our findings highlight the impact of anisotropy assumptions on H 0 inference, and more broadly, in galaxy dynamics.