TDCOSMO. XII. Improved Hubble constant measurement from lensing time delays using spatially resolved stellar kinematics of the lens galaxy

TL;DR

This paper improves the measurement of the Hubble constant using gravitational lensing time delays by incorporating spatially resolved stellar kinematics to break the mass-sheet degeneracy, leading to a more robust and precise estimate.

Contribution

First to use spatially resolved kinematics to break the mass-sheet degeneracy in time-delay cosmography, enabling a flexible mass model and a more accurate H0 measurement.

Findings

H0 = 77.1_{-7.1}^{+7.3} km s^{-1} Mpc^{-1} from a single lens

Measurement accounts for all uncertainties including line-of-sight effects

Results consistent with previous estimates using simpler models

Abstract

Strong-lensing time delays enable measurement of the Hubble constant ($H_{0}$) independently of other traditional methods. The main limitation to the precision of time-delay cosmography is mass-sheet degeneracy (MSD). Some of the previous TDCOSMO analyses broke the MSD by making standard assumptions about the mass density profile of the lens galaxy, reaching 2% precision from seven lenses. However, this approach could potentially bias the $H_0$ measurement or underestimate the errors. For this work, we broke the MSD for the first time using spatially resolved kinematics of the lens galaxy in RXJ1131$-$1231 obtained from the Keck Cosmic Web Imager spectroscopy, in combination with previously published time delay and lens models derived from Hubble Space Telescope imaging. This approach allowed us to robustly estimate $H_0$, effectively implementing a maximally flexible mass model. Following a blind analysis, we estimated the angular diameter distance to the lens galaxy $D_{\rm d} = 865_{-81}^{+85}$ Mpc and the time-delay distance $D_{\Delta t} = 2180_{-271}^{+472}$ Mpc, giving $H_0 = 77.1_{-7.1}^{+7.3}$ km s$^{-1}$ Mpc$^{-1}$ - for a flat $\Lambda$ cold dark matter cosmology. The error budget accounts for all uncertainties, including the MSD inherent to the lens mass profile and the line-of-sight effects, and those related to the mass-anisotropy degeneracy and projection effects. Our new measurement is in excellent agreement with those obtained in the past using standard simply parametrized mass profiles for this single system ($H_0 = 78.3^{+3.4}_{-3.3}$ km s$^{-1}$ Mpc$^{-1}$) and for seven lenses ($H_0 = 74.2_{-1.6}^{+1.6}$ km s$^{-1}$ Mpc$^{-1}$), or for seven lenses using single-aperture kinematics and the same maximally flexible models used by us ($H_0 = 73.3^{+5.8}_{-5.8}$ km s$^{-1}$ Mpc$^{-1}$). This agreement corroborates the methodology of time-delay cosmography.