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, $ρ\propto r^{-γ}$, and parameterise its logarithmic slope as $γ= γ_0 + γ_z \cdot z_l + γ_s \cdot \log \tildeΣ$, where $z_l$ is the lens redshift and $\tildeΣ$ the surface mass density. Within a flat $Λ$CDM framework and using DESI BAO measurements as a prior, we constrain the parameters via Monte Carlo nested sampling to $γ_0 = 1.62^{+0.11}_{-0.12}$, $γ_z = -0.35^{+0.08}_{-0.09}$, and $γ_s = 0.37^{+0.08}_{-0.07}$ ($68\%$ confidence intervals). Our results robustly demonstrate that $γ$ increases with surface mass density ($γ_s > 0$) and decreases with redshift ($γ_z < 0$). 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.

Figures (5)

• Figure 1: Redshift distributions of the lens and source samples. Left panel: distribution of lens galaxy redshifts ($z_l$). Right panel: distribution of background source (quasar) redshifts ($z_s$). The black bars represent the Parent Sample of 106 systems, and the black shaded region represents the Analysis Sample of 24 systems used for the joint analysis.
• Figure 2: Stellar velocity dispersion measurements for the four lensing galaxies, derived from SDSS-III BOSS spectra. Each system is displayed in two panels. Upper panel: The black line shows the extracted and smoothed one-dimensional spectrum of the galaxy, with the wavelength range adjusted to emphasise absorption features. The red line indicates the best-fitting model obtained from the pPXF software applied to the unsmoothed spectrum. Grey bands mark regions masked during the fitting process owing to contamination by quasar emission lines. Lower panel: The normalised residuals.
• Figure 3: Stellar velocity dispersion measurements for the seven lensing galaxies, derived from DESI DR1 spectra. The layout follows that of Figure \ref{['velocity_dispersion_from_BOSS']}, showing the results of pPXF fitting to the DESI spectral data for velocity dispersion.
• Figure 4: Half-light radius fitting results.
• Figure 5: Posterior probability distributions for the mass density slope parameters $\gamma_0$, $\gamma_z$, and $\gamma_s$. Diagonal panels show the one-dimensional marginalised posterior distributions, with dashed lines indicating the 68% credible intervals and the mean value. Off-diagonal panels show the two-dimensional joint posterior distributions, with contours marking the 68% and 95% credible regions. The constraints, derived from the joint analysis of 24 lensed quasar systems, reveal the dependence of the slope on redshift ($\gamma_z$) and surface mass density ($\gamma_s$).