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 quantifies how assumptions about stellar velocity anisotropy influence H0 inferences from time-delay cosmography that combines strong lensing with spatially resolved kinematics. Using ten z = 0.2 ellipticals from IllustrisTNG100, it creates JWST/NIRSpec-like mock data and tests four anisotropy models (OM, ML, constant β, gOM) under both kin-only and kin+lens analyses. The results show that the generalized Osipkov–Merritt (gOM) model most accurately recovers galaxy parameters and yields the smallest H0 bias, while the single-parameter OM model can yield substantial biases, even with joint modelling. Joint modeling generally improves accuracy and precision, with the ML, constant, and gOM models achieving sub-percent biases on average across an ensemble, highlighting the importance of anisotropy flexibility for robust H0 inferences and galaxy-dynamics studies.

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 $β$, 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.

Figures (19)

• Figure 1: Stellar Mass versus Dark Matter Mass for the galaxies in the dataset. The galaxies are marked by different colors and the IDs of these galaxies in TNG100 simulations at $z = 0.2$ are as indicated.
• Figure 2: The stellar velocity anisotropy profiles of the galaxies in the dataset. The velocity anisotropy parameter $\beta(r)$ is plotted as a function of 3D distance r from galaxy center in units of the effective radius $R_{eff}$ of each galaxy. Individual galaxy curves are marked in color and the median anisotropy curve is in bold black.
• Figure 3: Comparison of Dark Matter Density Profiles $\rho(r)$ for the ten TNG galaxies in the Dataset. Both panels show $\rho(r)$ as a function of 3D radius $r$ from the galaxy center. Also shown is the shared legend with the galaxies ID visible. Top panel: Dark matter density curves $\rho(r)$ of the galaxies from the native TNG simulation. Bottom panel: Corresponding log ratio of TNG dark matter profiles of the galaxies with their NFW counterparts derived via Colossus package using their redshift and M200 values.
• Figure 4: Mock example of the anisotropy profiles $\beta(r)$ of the four different models plotted as a function of the 3D radial distance r up to 10 effective radii $R_{eff}$. Here, the anisotropy radius $r_{ani}$ of the OM, ML and gOM models is assumed to equal the effective radius. We assume that $\beta_{\infty}$ equals 0.6 for the gOM model and the constant model has $\beta$ equal to 0.4 everywhere in space.
• Figure 5: Simulated JWST NIRSpec maps for the reference galaxy at a redshift of $z = 0.2$. The dispersions refer to the line-of-sight velocity dispersions. The sub plots included are (a) Original dispersions, (b) Signal-to-noise ratio (SNR), (c) Uncertainty in the Dispersions, and (d) Final dispersions which include PSF effect and noise. All panels share the same spatial scale in arc-seconds and correspond to a $3" \times 3"$ field of view.