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

TL;DR

This study assesses how stellar velocity anisotropy assumptions affect the accuracy of Hubble constant measurements from strong lensing galaxies, finding that joint modeling reduces bias and that the choice of anisotropy model significantly impacts results.

Contribution

It introduces a comprehensive analysis of anisotropy models using simulated JWST-like data, highlighting the importance of model choice in precise H0 inference from galaxy kinematics.

Findings

Joint modeling reduces bias and improves precision in H0 estimates.

The generalized-OM model best recovers galaxy parameters and minimizes bias.

Single-parameter OM model can produce large systematic biases exceeding 20%.

Abstract

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 ten 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--Lokas (ML), constant $\beta$, and a generalized--OM (gOM) profile, under both kinematics-only and joint kinematics plus strong lensing analyses. We find a sub-percent average bias in $H_{0}$ across ten galaxies with joint modeling for three models: $+0.2 \pm 1.6\%$ (ML), $-0.9 \pm 1.9\%$ (constant) and $-0.9 \pm 1.6\%$ (gOM), with $\sim 5\%$ 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, produces an overall bias of $+11.5 \pm 1.3\%$ (OM). The higher bias in OM is 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.