New Dynamical Measurements from a Lensed Quasar Sample: Joint Analysis Constrains the Mass Profile Evolution of Lens Galaxies

Abstract

We present a systematic study of the internal mass structure of early-type galaxies (ETGs) based on 106 galaxy-scale strong gravitational lenses with background quasars, all having spectroscopic redshifts. From this parent sample, we select 24 systems with high-quality ancillary data for joint analysis of strong lensing geometry and stellar kinematics. A key contribution is the derivation of new single-aperture stellar velocity dispersions for 11 lens galaxies via an iterative spectroscopic fitting procedure that mitigates quasar contamination, providing previously unavailable data. We model the total mass-density profile as a power law, $\rho \propto r^{-\gamma}$, and parameterise its logarithmic slope as $\gamma = \gamma_0 + \gamma_z \cdot z_l + \gamma_s \cdot \log \tilde{\Sigma}$, where $z_l$ is the lens redshift and $\tilde{\Sigma}$ the surface mass density. Within a flat $\Lambda$CDM framework and using DESI BAO measurements as a prior, we constrain the parameters via Monte Carlo nested sampling to $\gamma_0 = 1.62^{+0.11}_{-0.12}$, $\gamma_z = -0.35^{+0.08}_{-0.09}$, and $\gamma_s = 0.37^{+0.08}_{-0.07}$ ($68\%$ confidence intervals). Our results robustly demonstrate that $\gamma$ increases with surface mass density ($\gamma_s > 0$) and decreases with redshift ($\gamma_z < 0$). This implies that, at fixed redshift, galaxies with denser stellar cores have steeper mass profiles, while at fixed density, profiles become shallower at higher redshifts. By successfully applying the joint lensing--dynamics method to a substantial, independently acquired sample of lensed quasars, this work provides crucial validation of structural trends previously observed in galaxy--galaxy lensing systems, reinforcing the established evolutionary picture for massive ETGs and establishing lensed quasars as a potent probe of galaxy structure.