TDCOSMO XXI. Accurate stellar velocity dispersions of the SL2S lens sample and the fundamental plane of the lensing mass

TL;DR

The paper delivers subpercent-accurate stellar velocity dispersions for the SL2S lens sample by implementing an enhanced kinematic pipeline that leverages cleaned stellar libraries, instrument-specific S/N calibration, and rigorous treatment of systematics and covariances. It merges new SL2S measurements with prior work to reassess scaling relations, notably the lensing-mass fundamental plane, under both isothermal and flexible power-law mass profiles. The results show that SL2S, SLACS, and TDCOSMO galaxies occupy a common lensing-mass plane with little intrinsic scatter, supporting a cohesive picture of massive galaxy structure and evolution along the plane and enabling SL2S as a viable external dataset for time-delay cosmography. The analysis also highlights how evolving galaxy structure can occur within the fundamental plane, offering insights into growth mechanisms like envelope accretion and dry mergers.

Abstract

We reanalyzed spectra that were taken as part of the SL2S lens galaxy survey with the goal to obtain the stellar velocity dispersion with a precision and accuracy sufficient for time-delay cosmography. In order to achieve this goal, we imposed stringent cuts on the signal-to-noise ratio (S/N), and employed recently developed methods to mitigate and quantify residual systematic errors that are transferred from template libraries and fitting process. We also quantified the covariance across the sample. For galaxy spectra with S/N $>20/$Å, our new measurements have an average random uncertainty of 3-4\%, an average systematic uncertainty of 2\%, and a covariance across the sample of 1\%. We find a negligible covariance between spectra taken with different instruments. The systematic uncertainty and covariance need to be included when the sample is used as an external dataset in time-delay cosmography. We revisited empirical scaling relations of lens galaxies based on the improved kinematics. We show that the SL2S sample, the TDCOSMO time-delay lens sample, and the lower-redshift SLACS sample follow the same correlation of the effective radius, stellar velocity dispersion, and lensing mass, known as the lensing-mass fundamental plane, as the previously derived correlation that assumed isothermal mass profiles for the deflectors. We also derived for the first time the lensing-mass fundamental plane assuming free power-law mass density profiles, and we show that the three samples also follow the same correlation. This is consistent with a scenario in which massive galaxies evolve by growing their radii and mass, but stay within the plane.

Figures (13)

• Figure 1: Spectra of the 16 of the 31 lens galaxies that were observed with LRIS on the Keck Telescope. In each panel, the black line shows the observed spectrum, and the red line shows the best-fit model from pPXF. The gray regions mark the wavelength range that we excluded from the fitting and typically these regions correspond to atmospheric absorption lines. Each panel also indicates the name of the system, the lens galaxy redshift, and prominent absorption features in the spectra.
• Figure 2: Spectra of the remaining 15 of the 31 galaxies observed with LRIS. The line styles of the figure are same as Fig. \ref{['fig:LRIS_galaxy_1']}.
• Figure 3: Spectra of 13 lens galaxies observed with the Xshooter spectrograph on the VLT. In each panel, the gray line shows the observed spectrum, and the red line presents the best-fit model from pPXF. We also plot the smoothed version (the yellow line) of the observed spectrum. The gray bands mark the wavelength range we excluded from the fit and typically they correspond to the atmospheric absorption lines. Each panel also indicates the name of the system, the lens galaxy redshift, and prominent absorption features in the spectra.
• Figure 4: Spectra of three lens galaxies from the SL2S sample observed with DEIMOS on the Keck Telescope. In each panel, the black line shows the observed spectrum, and the red line shows the best-fit model from pPXF. The gray regions mark the wavelength range we excluded from the fit.
• Figure 5: Example of typical variation in $\sigma_{\text{inst}}$ as a function of wavelength for three instruments: LRIS-red, Xshooter, and DEIMOS. Each plot for each instrument has two panels. The top panel shows $\sigma_{\text{inst}}$ in km s$^{-1}$ units, and the bottom panel shows it in Å unit over the observed wavelength. In all panels, the black line shows the average $\sigma_{\text{inst}}$ over the wavelength range.