TDCOSMO

XIII. Cosmological distance measurements in light of the mass-sheet degeneracy: Forecasts from strong lensing and integral field unit stellar kinematics

¹ Max Planck Institute for Astrophysics, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany
e-mail: yildirim@mpa-garching.mpg.de
² Technical University of Munich, TUM School of Natural Sciences, Department of Physics, James-Franck-Str. 1, 85748 Garching, Germany
³ Institute of Astronomy and Astrophysics, Academia Sinica, 11F of ASMAB, No.1, Section 4, Roosevelt Road, Taipei, 10617 Taiwan
⁴ Department of Physics and Astronomy, University of California, Los Angeles, CA, 90095 USA
⁵ Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU, WPI), UTIAS, The University of Tokyo, Chiba, 277-8583 Japan

Received: 28 September 2021
Accepted: 3 May 2023

Abstract

Time-delay distance measurements of strongly lensed quasars have provided a powerful and independent probe of the current expansion rate of the Universe (H₀). However, in light of the discrepancies between early- and late-time cosmological studies, current efforts revolve around the characterisation of systematic uncertainties in the methods. In this work we focus on the mass-sheet degeneracy (MSD), which is commonly considered a significant source of systematics in time-delay strong lensing studies, and aim to assess the constraining power provided by integral field unit (IFU) stellar kinematics. To this end, we approximated the MSD with a cored, two-parameter extension to the adopted lensing mass profiles (with core radius r_c and mass-sheet parameter λ_int), which introduces a full degeneracy between λ_int and H₀ from lensing data alone. In addition, we utilised spatially resolved mock IFU stellar kinematics of time-delay strong lenses, given the prospects of obtaining such high-quality data with the James Webb Space Telescope (JWST) in the near future. We constructed joint strong lensing and generalised two-integral axisymmetric Jeans models, where the time delays, mock imaging, and IFU observations are used as input to constrain the mass profile of lens galaxies at the individual galaxy level and consequently yield joint constraints on the time-delay distance (D_Δt) and the angular diameter distance (D_d) to the lens. We find that mock JWST-like stellar kinematics constrain the amount of internal mass sheet that is physically associated with the lens galaxy and limit its contribution to the uncertainties of D_Δt and D_d, each at the ≤4% level, without assumptions on the background cosmological model. Incorporating additional uncertainties due to external mass sheets associated with mass structures along the lens line of sight, these distance constraints would translate to a ≲4% precision measurement on H₀ in flat Λ cold dark matter cosmology for a single lens. Our study shows that future IFU stellar kinematics of time-delay lenses will be key in lifting the MSD on a per lens basis, assuming reasonable and physically motivated core sizes. However, even in the limit of infinite r_c, where D_Δt is fully degenerate with λ_int and is thus not constrained, stellar kinematics of the deflector, time delays, and imaging data will provide powerful constraints on D_d, which becomes the dominant source of information in the cosmological inference.