TDCOSMO

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

¹ Department of Physics and Astronomy, University of California, Los Angeles, CA 90095, USA
² Department of Astronomy, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
³ Shanghai Key Laboratory for Particle Physics and Cosmology, Shanghai Jiao Tong University, Shanghai 200240, China
⁴ Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministry of Education, Shanghai Jiao Tong University, Shanghai 200240, China
⁵ Department of Astronomy & Astrophysics, University of Chicago, Chicago, IL 60637, USA
⁶ Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637, USA
⁷ Center for Astronomy, Space Science and Astrophysics, Independent University, Bangladesh Dhaka 1229, Bangladesh
⁸ Sub-Department of Astrophysics, Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK
⁹ Dipartimento di Fisica e Astronomia “Augusto Righi”, Alma Mater Studiorum – Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy

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Received: 20 May 2025
Accepted: 5 September 2025

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.