TDCOSMO XXV: A "soup-to-nuts" 6.5% $H_0$ measurement $-$ strong lensing and dynamics with a maximally flexible mass sheet

Abstract

We present a blind time-delay cosmography measurement of the Hubble constant $H_0$ based on the quadruply imaged quasar SDSSJ1433+6007. Our analysis combines deep Hubble Space Telescope imaging, extended time-delay monitoring from the Wendelstein and Maidanak Observatories, and spatially resolved stellar kinematics from the Keck Cosmic Web Imager and Reionization Mapper. We build a robust lens model to reconstruct the mass distribution and high-signal-to-noise kinematic maps to break the mass-sheet degeneracy (MSD), explicitly accounting for the lens galaxy's oblateness, rotation, and anisotropy. Furthermore, we constrain the external convergence ($κ_{\rm ext}$) by characterizing the line-of-sight environment using wide-field photometry from the Dark Energy Spectroscopic Instrument (DESI) Legacy Survey data release 10. We incorporate these constraints into our joint lensing and dynamical model, running multiple iterations to estimate random and systematic uncertainties. Accounting for maximal flexibility of the mass-sheet transformation, and assuming a flat $Λ$CDM cosmology and an $Ω_{\rm m, 0}$ prior from DESI data release 2, we infer $H_0 = 73.2^{+4.8}_{-4.7}$ km s$^{-1}$ Mpc$^{-1}$ (a $6.5\%$ precision), and an internal mass-sheet parameter $λ_{\rm int}=1.12^{+0.05}_{-0.06}$. Notably, $λ_{\rm int}$ is $2σ$ away from unity for this system, highlighting the importance of treating it as a free parameter. Our $H_0$ measurement is consistent with the result from our 2025 milestone paper, and it will be included in our next hierarchical analysis to improve the overall precision. Moving forward, the comprehensive pipeline demonstrated herein establishes a robust framework that can be readily applied to future strongly lensed systems to further refine cosmological constraints.